.04 Spk Availability Of Smart Sprinkler System [623033]

RESEARCH TECHNICAL REPORT
Evaluation of the Availability
of the SMART Sprinkler
System

Evaluation of the Availability of the SMART Sprinkler System

Prepared by
Kaushik Chatterjee

October 2016

FM Global
1151 Boston -Providence Turnpike
Norwood, MA 02062

PROJECT ID 0003053857

Disclaimer
The research presented in this report, including any findings and conclusions, is for informational
purposes only. Any references to specific products, manufacturers, or contractors do not constitute a
recommendation, evaluation or endorsement by Factory M utual Insurance Company (FM Global) of
such products, manufacturers or contractors. FM Global does not address life , safety, or health
issues. The recipient of this report must make the decision whether to take any action. FM Global
undertakes no duty to any party by providing this report or performing the activities on which it is
based . FM Global makes no warranty, express or implied, with respect to any product or process
referenced in this report. FM Global assumes no liability by or through the use of any information in this
report .

FM GLOBAL
PUBLIC RELEASE

i Executive Summary
The Simultaneous Monitoring, Assessment, and Response Technology (SMART) has been designed to
overcome the limitations of traditional wet sprinkler system when used under very high challenge
conditions (e.g., suppression of roll paper fires in high storage configuration warehouses greater than 42
feet storage height). This report presents the results of a study conducted to (1) evaluate the availability
of the SMART sprinkler protect ion system , and compare with that of a traditional wet sprinkler
protection system ; and (2) conduct a comparative cost-benefit analysis for the SMART sprinkler
protection and the traditional wet sprinkler protection systems .
In this study , the same type of water supply ( i.e., public supply and fire pump) has been considered for
both the SMART sprinkler protection and the traditional wet sprinkler protection system s. For the
availability and the cost-benefit analyses, b oth the wired and wireless conf igurations of the SMART
sprinkler system were considered. The cost-benefit analysis has been conduct ed to evaluate the Present
Value of Net Benefit (PVNB), which is the difference between the Present Value (PV) of benefits and the
PV of costs. In this stud y, benefit is defined as risk -reduction ( 𝑅𝑖𝑠𝑘 𝑛𝑜 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 – 𝑅𝑖𝑠𝑘 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 )
achieved from the use of a fire protection system, while costs include I nspection/Testing/Maintenance
(ITM) and initial installation costs for the fire protection system . To evaluate risk for the cost-benefit
analysis of both the SMART sprinkler protection and the traditional wet sprinkler protection systems,
this study considered a representative warehouse (50 ,000 ft2 floor area) with a n approximate total
‘property and outage’ cost of $17.7M and a fire frequency of 0.025/year. In this study, risk is defined as
the product of ‘probability of occurrence of an undesired event’ and ‘severity of consequences
associa ted with the undesired event’.
The main findings/conclusions of this study are as follows:
1. Availability evaluation:
o While the availability of the traditional wet sprinkler system is 0.97 over the lifetime of 30
years, the availabilities of the SMART sprin kler systems are approximately 0.86 ±0.01 and
0.83 ±0.01 , respectively, for the wired and wireless configurations. The higher availability of the
traditional wet sprinkler system is due to its lower complexity and fewer components when
compared to the SMART sprinkler system.
o Due to higher reliability of the wired connections, t he unavailability of the wired SMART
sprinkler system is approximately 20% lower than that of the wireless SMART sprinkler system.
o The difference in the availabilit ies of the traditional wet sprinkler and the SMART sprinkler
systems can be reduced by approximately 50% by increasing the ITM frequency of the SMART
sprinklers from annual to semi -annual.
o The smoke detector, control unit, solenoid valve, and fire pump (inclu ding water supply) are
the critical components with regards to system availability for both the wired and wireless
configurations of the SMART sprinkler system.

FM GLOBAL
PUBLIC RELEASE

ii 2. Cost-benefit analysis:
The cost -benefit analysis has been performed with a limited objective o f providing some
comparative perspective into the costs and benefits associated with the SMART sprinkler
protection and the traditional wet sprinkler protection systems.
o For both the traditional wet sprinkler and the SMART sprinkler systems, t he estimated lifetime
risk-reductions are more than 90% .
o The estimated lifetime ITM cost for the traditional wet sprinkler system is approximately 50%
lower than those of the wired/wireless SMART sprinkler systems.
o For the traditional wet sprinkler system installed in a low storage configuration warehouse (i.e.,
less than 42 feet storage height) , the estimated lifetime PVNB is approximately two to three
times higher than those for the wired/wireless SMART sprinkler systems installed in a high
storage configuration ware house .
o For the SMART sprinkler system , the estimated lifetime PVNBs are comparable with annual and
semi -annual ITMs .
o The estimated lifetime PVNB for the wired SMART sprinkler system is approximately 30%
higher than that for the wireless system.
The SMART sprinkler configuration used in this study is expected to change when implement ed
commercially (e.g., using an alternative to the solenoid valve or using a different activation mechanism
or different sensors). Therefore, the values of the availab ility and the PVNB estimated in this study are
only intended as general guidance and are expected to change according to actual system design and
components .

FM GLOBAL
PUBLIC RELEASE

iii Abstract
This report presents the results of a study conducted to (1) evaluate the availab ility of the
wired/wireless SMART sprinkler protection system s (for warehouses with a storage height greater than
42 feet) , and compare it with that of a traditional wet sprinkler protection system (for warehouses with
a storage height less than 42 feet) ; and (2) conduct a comparative cost-benefit analysis for the SMART
sprinkler protection and the traditional wet sprinkler protection systems. For the availability and the
cost-benefit analyses, both the wired and wireless configurations of the SMART sprinkl er system were
considered. The cost-benefit analysis has been conducted to evaluate Present Value of Net Benefit
(PVNB), which is the difference between the Present Value (PV) of benefits and the PV of costs. In this
study, benefit is defined as risk -reduc tion achieved from the use of a fire protection system, while costs
include Inspection/Testing/Maintenance (ITM) and initial installation costs for the fire protection
system.
While the availability of the traditional wet sprinkler system is 0.97 over the lifetime of 30 years, the
availabilities of the SMART sprinkler systems are approximately 0.86±0.01 and 0.83±0.01 , respectively,
for the wired and wireless configurations. The difference in the availabilit ies of the traditional wet
sprinkler and the S MART sprinkler systems can be reduced by approximately 50% by increasing the ITM
frequency of the SMART sprinklers from annual to semi -annual.
For both the traditional wet sprinkler and the SMART sprinkler systems , the estimated lifetime risk –
reductions a re more than 90% . The estimated lifetime ITM cost for the traditional wet sprinkler system
is approximately 50% lower than those of the wired/wireless SMART sprinkler systems. For the
traditional wet sprinkler system in stalled in a low storage configuratio n warehouse, the estimated
lifetime PVNB is approximately two to three times higher than those for the wired/wireless SMART
sprinkler systems in stalled in a high storage configuration warehouse. The estimated lifetime PVNB for
the wired SMART sprinkler sys tem is approximately 30% higher than for the wireless system.

FM GLOBAL
PUBLIC RELEASE

iv Acknowledgements
The author would like to thank Yibing Xin, Chris topher Wieczorek, and Sergey Dorofeev for providing
valuable inputs regarding the SMART sprinkler system design , installation , and cost; and for reviewing
this report . The author would like to thank Kumar Bhimavarapu and Jens Alkemper for providing
valuable feedback at all stages during this study , and for reviewing this report . The author would like to
thank Franc esco Tamanini an d Louis Gritzo for support ing and encourag ing this study, and for reviewing
this report .

FM GLOBAL
PUBLIC RELEASE

v Table of Contents
Executive Summary ………………………….. ………………………….. ………………………….. ………………………….. …….. i
Abstract ………………………….. ………………………….. ………………………….. ………………………….. …………………… iii
Acknowledgements ………………………….. ………………………….. ………………………….. ………………………….. …… iv
Table of Contents ………………………….. ………………………….. ………………………….. ………………………….. ………. v
List of Figu res ………………………….. ………………………….. ………………………….. ………………………….. …………… vii
List of Tables ………………………….. ………………………….. ………………………….. ………………………….. …………… viii
1. Introduction ………………………….. ………………………….. ………………………….. ………………………….. ………. 1
2. Definition of SMART Sprinkler System ………………………….. ………………………….. ………………………….. .. 2
2.1 Schematic of the System ………………………….. ………………………….. ………………………….. …………. 2
2.2 Operation of the System ………………………….. ………………………….. ………………………….. …………. 3
2.2.1 Wireless System ………………………….. ………………………….. ………………………….. …………. 3
2.2.2 Wired System ………………………….. ………………………….. ………………………….. …………….. 3
2.2.3 Activation of Fire Pump for both Wireless and Wired SMART System …………………….. 3
2.3 Definition of Failure of the System ………………………….. ………………………….. ……………………….. 3
2.4 Study Postulates ………………………….. ………………………….. ………………………….. …………………….. 3
3. Failure Mode and Effect Analysis (FMEA) ………………………….. ………………………….. ……………………….. 6
4. Availability Models for the SMART Sprinklers ………………………….. ………………………….. …………………. 8
4.1 Unavailability Trees ………………………….. ………………………….. ………………………….. ………………… 8
4.2 Parameters for Reliability Distribution and ITM ………………………….. ………………………….. ……. 23
4.2.1 Reliability Distribution ………………………….. ………………………….. ………………………….. . 23
4.2.1.1 Weibull Shape Parameter ………………………….. ………………………….. ………… 23
4.2.1.2 Weibull Characteristic Life ………………………….. ………………………….. ……….. 24
4.2.2 Inspection/Testing/Maintenance (ITM) ………………………….. ………………………….. ……. 26
4.2.2.1 Frequency/Interval ………………………….. ………………………….. …………………. 26
4.2.2.2 Maintenance Duration ………………………….. ………………………….. …………….. 27
4.2.2.3 Maintenance Restoration Factor ………………………….. ………………………….. . 28
4.3 Approximate Costs per Inspection/Testing and Maintenance of SMART Sprinklers to
Estimate Lifetime ITM Costs ………………………….. ………………………….. ………………………….. ….. 28
5. Availability Analysis ………………………….. ………………………….. ………………………….. ……………………….. 31
5.1 Availability of Traditional Wet Sprinkler and Wired/Wireless SMART Sprinkler Systems …….. 31
5.2 Estimated Lifetime ITM Costs for Tradi tional Wet Sprinkler and Wired/Wireless SMART
Sprinkler Systems ………………………….. ………………………….. ………………………….. …………………. 32
5.3 Critical Components of Wired/Wireless SMART Sprinkler Systems ………………………….. ……… 33
5.4 Discussion of Results ………………………….. ………………………….. ………………………….. …………….. 34

FM GLOBAL
PUBLIC RELEASE

vi 6. Risk Estimation ………………………….. ………………………….. ………………………….. ………………………….. …. 35
7. Cost -Benefit Analysis ………………………….. ………………………….. ………………………….. …………………….. 37
8. Conclusions ………………………….. ………………………….. ………………………….. ………………………….. ……… 38
References ………………………….. ………………………….. ………………………….. ………………………….. ……………… 39
Appendix A. Estimated Costs of ITM and Components of Traditional Wet Sprinkler System …………….. 41
Appendix B. Availability Values with Confidence Bounds ………………………….. ………………………….. …….. 44
B.1 Availability Values with Confidence Bounds for Wired/Wireless SMART Sprinkler
Systems ………………………….. ………………………….. ………………………….. ………………………….. ….. 44
B.2 Summary ………………………….. ………………………….. ………………………….. ………………………….. … 45
Appendix C. Estimated Lifetime ITM Costs for Traditional Wet Sprinkler and SMART Sprinkler
Systems ………………………….. ………………………….. ………………………….. ………………………….. 46
C.1 Estimated Lifetime ITM Costs ………………………….. ………………………….. ………………………….. … 46
C.2 Discussion of Re sults ………………………….. ………………………….. ………………………….. …………….. 48
Appendix D. Equations/Data for Risk Estimation and Cost -Benefit Analysis ………………………….. ……….. 50
D.1 Probability of Fire ………………………….. ………………………….. ………………………….. …………………. 50
D.2 Present Value of Money ………………………….. ………………………….. ………………………….. ……….. 50
D.3 Availability Values (updated for renewal upon reinstallation after fire occurrence) …………… 50
D.4 Expected Risk, ITM Costs, and PVNB ( Yearly Values) ………………………….. ………………………….. 51

FM GLOBAL
PUBLIC RELEASE

vii List of Figures
2-1: Schematic of the proof -of-concept design (wireless communication) of the SMART sprinkler
(with system boundaries shown by the dashed line) ………………………….. ………………………….. ……… 2
2-2: Schematic of the proof -of-concept d esign (wired communication) of the SMART sprinkler
(with system boundaries shown by the dashed line) ………………………….. ………………………….. ……… 2
4-1: Unavailability tree f or the wireless SMART sprinklers – Subtree I ………………………….. ………………… 9
4-2: Unavailability tree for the wireless SMART sprinklers – Subtree II ………………………….. ……………… 10
4-3: Unavailability tree for the wireless SMART sprinklers – Subtree III ………………………….. …………….. 11
4-4: Unavailability tree for the wireless SMART sprinklers – Subtree IV ………………………….. …………….. 12
4-5: Unavailability tree for the wireless SMART sprinklers – Subtree V ………………………….. ……………… 13
4-6: Unavail ability tree for the wireless SMART sprinklers – Subtree VI ………………………….. …………….. 14
4-7: Unavailability tree for the wireless SMART sprinklers – Subtr ee VII ………………………….. ……………. 15
4-8: Unavailability tree for the wireless SMART sprinklers – Subtree VIII ………………………….. …………… 16
4-9: Unavailability tree for the wired SMART sprinklers – Subtree I ………………………….. ………………….. 17
4-10: Unavailability tree for the wired SMART sprinklers – Subtree II ………………………….. …………………. 18
4-11: Unavailability tree for the wired SMART sprinklers – Subtree III ………………………….. ………………… 19
4-12: Unavaila bility tree for the wired SMART sprinklers – Subtree IV ………………………….. ………………… 20
4-13: Unavailability tree for the wired SMART sprinklers – Subtree V ………………………….. …………………. 21
4-14: Unavailability tree for the wired SMART sprinklers – Subtree VI ………………………….. ………………… 22
5-1: Availability curves over time for the traditional wet sprinkler and wired/wireless SMART
sprinkler systems ………………………….. ………………………….. ………………………….. ………………………… 31
5-2: PV curves of cumulative ITM costs over time for traditional wet sprinkler protection and
SMART sprinkler protection systems (cost figures refer to 500 head system) ………………………….. . 33
5-3: Critical components of wireless (Left) and wired (Right) SMART sprinkler systems …………………… 33
6-1: PV curves of cumulative risk over time for the traditional wet sprinkler protection and the
SMART sprinkler protection systems ………………………….. ………………………….. ………………………….. 35
6-2: PV curves of cumulative risk -reduction over time for the traditional wet sprinkler protection
and the SMART sprinkler protection systems ………………………….. ………………………….. ………………. 36
B-1: Availability curves (with confidence bounds) over time for wired SMART sprinkler system
(Left: Annual ITM; Right: Semi -annual ITM) ………………………….. ………………………….. …………………. 44
B-2: Availability curves (with confidence bounds) over time for wireless SMART sprinkler system
(Left: Annual ITM; R ight: Semi -annual ITM ) ………………………….. ………………………….. …………………. 44

FM GLOBAL
PUBLIC RELEASE

viii List of Tables
3-1: FMEA of the SMART Sprinklers ………………………….. ………………………….. ………………………….. ……….. 6
3-2: FMEA of the SMART Sprinklers (continued) ………………………….. ………………………….. ………………….. 7
4-1: Typical values of shape parameters for different failure types ………………………….. …………………… 23
4-2: Random values of shape parameters f or components of SMART sprinklers ………………………….. … 24
4-3: Parameter values for MTBF distributions for components of SMART sprinklers ……………………….. 25
4-4: Values of characteristic life for the components of the SMART sprinklers ………………………….. …… 26
4-5: Distribution parameters for maintenance durations for SMART sprinklers ………………………….. ….. 27
4-6: Random values of maintenance durations for components of SMART sprinklers ……………………… 28
4-7: Approximate costs per inspection/testing and maintenance for SMART sprinklers …………………… 29
4-8: Approximate costs for the components of the SMART sprinklers ………………………….. ……………….. 30
5-1: Availability values for the traditional wet sprinkler protection and SMART sprinkler protection
systems ………………………….. ………………………….. ………………………….. ………………………….. ………….. 32
7-1: Estimated lifetime PVNBs for traditional wet sprinkler protection and SMART sprinkler
protection systems ………………………….. ………………………….. ………………………….. ………………………. 37
A-1: ITM frequencies (‘current’) for components of traditional wet sprinkler system ………………………. 41
A-2: Approximate costs per inspection/testing and maintenance for traditional wet sprinkler
system ………………………….. ………………………….. ………………………….. ………………………….. …………… 42
A-3: Approximate costs for the components of the traditional wet sprinkler system ……………………….. 42
B-1: Availability values (confidence bounds) for wired/wireless SMART sprinkler systems ……………….. 45
C-1: Estimated lifetime ITM costs for traditional wet sprinkler system in a warehouse with 500
sprinklers ………………………….. ………………………….. ………………………….. ………………………….. ……….. 46
C-2: Estimated lifetime IT M costs for wireless SMART sprinklers in a warehouse with 500
sprinklers ………………………….. ………………………….. ………………………….. ………………………….. ……….. 47
C-3: Estimated lifetime ITM costs for wired SMART spri nklers in a warehouse with 500 sprinklers …… 48
C-4: Estimated lifetime ITM costs for traditional wet sprinkler and SMART sprinkler systems …………… 49
D-1: Updated availability values for traditional wet sprinkler protection and SMART sprinkler
protection systems ………………………….. ………………………….. ………………………….. ………………………. 51
D-2: Yearly values (approximate) of estimated risk, ITM costs, and PVNB for traditional wet
sprinkler protection and SMART sprinkler protection systems ………………………….. …………………… 52

FM GLOBAL
PUBLIC RELEASE

1 1. Introduction
A major drawback of traditional wet sprinkler fire protection system s is significant response time,
particularly in case of high ceiling clearance. T o overcome th is limitation of the t raditional wet sprinkler
system, an electr onically controlled sprinkler activation system was first conceptualized and developed
by Gefest Enterprise Groupi in collaboration with the Russian Research Institute for Fire Protectionii, with
support from St.-Petersburg State Polytechnic Universityiii [1] [2]. The developed system is intended to
provide fire protection in commercial, industrial, and storage sites with ceiling clearance s up to 65 feet.
FM Global Research has also design ed a system c alled the Simultaneous Monitoring, Assessment, and
Response Technology (SMART) for suppression of fires in challenging storage configurations, such as
high roll paper storage warehouses (i.e., greater than 42 feet storage height) [3] [4].
The objectives of this study are:
1. Evaluate the availability of the SMART sprinkler fire protection system , and compare it with that
of a traditional wet sprinkler fire protection system.
The objective of such a comparison is to evaluate whether SMART sprinkler systems would
provide an availability similar to the availability of a traditional wet sprinkler system that is
considered a benchmark in the fire protection industry .
2. Perform a comparative cost-benefit analysis for the SMART sprinkler protection and the
traditional wet sprinkler protection systems .
The objective of the cost-benefit analysis is limited to provid ing some comparative persp ective
into the costs and benefits associated with the SMART sprinkler protection and the traditional
wet sprinkler protection systems.
The organization of this report is as follows. The definition of the SMART sprinkler system is provided in
Chapter 2, which includes a description of the system and its operation, definition of failure of the
system, and the postulates used in this study to perform the availabi lity and the cost-benefit analyses.
Chapter 3 provides results from a Failure Mode and Effects Analysis (FMEA) of the SMART sprinkler
system. Chapter 4 provides the availability model s for the SMART sprinkler system for both wireless and
wired configurations. Chapter 5 provides results from the availability analysis (i.e., estimated availability
values and the lifetime ITM costs for the SMART sprinkler system and the traditional wet sprinkler
system). Chapter 6 provides results from risk estimations for the traditional wet sprinkler and the
SMART sprinkler protection systems. Chapter 7 provides results from a comparative cost-benefit
analysis for the SMART sprinkler protection and the traditional wet sprinkler protection systems . Finally,
the conclusions are provided in Chapter 8.

i Gefest Enterprise Group, St. -Petersburg, Russia
ii Russian Research Institute for Fire Protection, VNIIPO, Balashikha, Russia
iii St.-Petersburg State Polytechnic University, St. -Petersburg, Russia

FM GLOBAL
PUBLIC RELEASE

2 2. Definition of SMART Sprinkler System
This chapter describes the SMART sprinkler system and its operation requirements, definition of failure
of the system, and postulates used in this study to perform the availability and the cost -benefit analyses.
2.1 Schematic of the System
Figures 2-1 and 2-2 show schematics of the proof -of-concept design of the SMART sprinkler for wireless
and wired configurations, respectively. In case of wired configuration, the sensors communicate directly
with the Programmable Logic Controller (PLC) using wires.

Figure 2-1: Schematic of the proof -of-concept design (wireless communication) of the SMART
sprinkler (with system boundaries shown by the dashed line)

Figure 2-2: Schematic of the proof -of-concept design (wired communication) of the SMART
sprinkler (with system boundaries shown by the dashed line)

FM GLOBAL
PUBLIC RELEASE

3 2.2 Operation of the System
To overcome the limitations of the traditional wet sprinkler system for suppression of roll paper fires in
high storage configuration warehouses , the SMART sprinkler system has been designed to activate and
discharge water (at the desired flow rate) within a small accepta ble window ( a few seconds) after
detection . Accordingly, within that acceptable window, the fire pump should be able to start and
discharge water at the desired flow rate. If the fire pump fails to start/operate within that acceptable
window then the SMART system will be ineffective (i.e., fail to s uppress the fire). The following three
sub-sections provide the operation requirements of the wireless and wired SMART sprinkler systems, as
well as the activation criteria for the fire pump.
2.2.1 Wireless System
In the event of a fire, the smoke detector s and the thermocouple s (TC) detect smoke and heat,
respectively, and send signals to the transceiver module s, which transmit the signals wirelessly to the
master transceiver located at the control unit. The PLC at the control unit analyzes the signals to
determ ine (1) the need for system activation, and (2) the location of the fire and, if needed,
communicates wirelessly (through the master transceiver) with the transceiver module s, which power
the relays to energize and open the solenoid valves for discharge of water through open sprinklers.
2.2.2 Wired System
In the event of a fire, the smoke detector s and the TC s detect smoke and heat, respectively, and send
signals to the PLC (control unit) using wires. The PLC analyzes the signals to determine (1) the need for
system activation, and (2) the location of the fire and, if needed, powers the relay s to energize and open
the solenoid valve s for discharge of water through open sprinklers.
2.2.3 Activation of Fire Pump for both Wireless and Wired SMART System
As per the revise d configuration of the SMART sprinkler system, t he fire pump starts based on a signal
from either one of the sensors (and processing of data by the PLC), unlike the activation of the solenoid
valve of the SMART sprinkler system that require s signals from b oth sensors meeting a defined
threshold.
2.3 Definition of Failure of the System
A failure of the SMART sprinkler system is defined as no/inadequate discharge of water. Inadequate
discharge refers to the case when water is discharged (1) from the incorrect spr inkler with respect to the
fire location, or (2) at an inadequate flow rate (this includes the inability of the fire pump to reach the
desired flow rate within the allowable time frame as applicable to the SMART sprinkler system).
2.4 Study Postulates
1. Availabi lity evaluation:
a. For the purposes of performing the availability/risk analysis, it is assumed that the
proof -of-concept design is functional and effective with regards to the hazard being
protected.

FM GLOBAL
PUBLIC RELEASE

4 b. The components of the SMART sprinkler system have been selected based on the
intended application conditions. For example, the temperature ratings of the
components (e.g., the transceiver) should be adequate to meet the intended
temperature conditions of a roll paper fire.
c. The proof -of-concept design uses a l aptop (with an installed algorithm/software) for
processing of the data from the smoke detectors and the TCs, and for controlling the
activation of the SMART sprinkler system. For the evaluation of the availability of the
SMART sprinkler system, the laptop (along with the algorithm/software) is considered as
a typical PLC (similar to commercial systems).The algorithm/software (installed in the
PLC) is assumed to have been adequately tested to meet the intended design
functionality and effectiveness.
d. The pro of-of-concept design of the wireless SMART system uses a wire to connect the
signal transceiver module with the relay. For the evaluation of the availability of the
wireless SMART system, a signal transceiver and a relay installed on the same Printed
Circu it Board (PCB) are considered.
e. This study considered a conservative case of a single electric motor driven fire pump. In
such cases, the National Fire Protection Association (NFPA) requires the electric power
supply to be reliable [5]. The electric power failure probability used in this study is of the
order of 10-5, which can be considered to be highly reliable. Therefore, a back -up
generator for the fire pump has not been considered in this study.
f. It has been considered that the fire pump would be able to activate and provide the
desired flow rate of water within the acceptable window (a few seconds as applicable to
the SMART system ), provided the sensors (i.e., smoke detector and TC) and the contro l
unit of the SMART system perform as intended. This ability of the fire pump needs to be
investigated through field testing.
g. A typical system lifetime of 30 years was considered for the traditional wet sprinkler and
the SMART sprinkler protection system s.
2. Risk and cost-benefit analysis:
a. The fire frequency (λ), i.e., fire occurrence per warehouse per unit time interval, has
been adopted from [6] for a medium sized warehouse. The upper limit value of
0.02 5/year (instead of the average of 0.0215/year [6]) has been considered in order to
estimate the ‘probability of fire’.
b. For a typical medium sized warehouse (50,000 ft2), the total ‘property and outage’ cost
is considered to be approximately $17.7M @ $354/ft2 [6]. The total cost also includes
any cranes that may be used inside the warehouse . For comparison purposes, the same
total ‘property and outage’ cost value was used for both high storage configuration
(SMART sprinkler protection) and low storage configuration (traditional sprinkler
protection) warehouses.
c. For the SMART sprinkler protection, a typical warehouse requires 500 SMART sprinklers
(in typ ical wet system configuration) on a 10 feet by 10 feet spacing. Furthermore, it
requires:
i. One control unit (i.e., ‘PLC + master transceiver’ for wireless; ‘PLC’ for wired) per
warehouse.

FM GLOBAL
PUBLIC RELEASE

5 ii. One fire pump system per warehouse.
iii. One back -up (UPS) power supply f or SMART sprinklers per warehouse.
d. Similarly, for the traditional wet sprinkler protection, a typical warehouse requires 500
traditional sprinklers on a 10 feet by 10 feet spacing .
e. For the scenario of ‘no protection’ in a warehouse, a severity of loss of 5 0% of the total
‘property and outage’ cost (i.e., approximately $8.85M) was considered. Even without
automatic ceiling sprinkler protection systems, a warehouse can be protected from total
loss by other forms of protection systems (including fire trucks) .
f. The scenario of ‘failed protection system ’ is considered to be equivalent to that of ‘no
protection’. Therefore, for the scenario of ‘failed protection system’ in a warehouse, a
severity of loss of 50% of the total ‘property and outage’ cost (similar to t he scenario of
‘no protection’) was considered along with the installation cost of the protection system
(since the protection system can get damaged during the fire) .
g. To estimate the expected severity of loss with adequate protection (i.e., the protection
system works properly) in a warehouse, a fire damage area of 400 ft2 is adopt ed. The
expected severity of loss can then be estimated to be approximately $141,600 ( 400 ft2
@ approximately $354/ft2 [6]).
h. The estimated cost of installation of a traditional wet sprinkler system is approximately
$280,000 per warehouse @ $5.5/ft2 [6]. The cost also includes the purchasing costs of
the components (including water supply) of the traditional wet sprinkler system. For the
SMART sprinkler protection in a warehouse, the installation cost is assumed to be the
sum of $280,000 and purchasing cos ts of the SMART sprinkler s (traditional sprinklers
will be provided alon g with the SMART sprinklers). No additional labor costs were
considered for installation of the SMART sprinklers.
i. To calculate the Present Value (PV) of cost incurred in future years, a discount rate of
4.8% was used [7].
j. The SMART sprinkler protection system consists of the SMART sprinklers and all the
components of the traditional wet sprinkler system. The unit costs of
Inspection/Testing/Maintenance (ITM) for the SMART sprinkler s has been considered
separately from that for the components of the traditional wet sprinkler system . Each
SMART sprinkler consists of two sensors, a relay, a transceiver (or wired connection for
wired system ), electrical wires, a solenoid valve, and an open sprinkl er. Further more ,
500 SMART sprinklers (in a warehouse) are expected to share a control unit and a back –
up power supply. In comparison, a traditional wet sprinkler system in a warehouse
consists of a fire pump sub -system (one fire pump, electrical motor, an d controller),
check valves, ball valves, piping, and automatic sprinklers. In a warehouse, there is a
significantly higher number of components for a SMART sprinkler protection system
when compared to that for a traditional wet sprinkler protection system .
k. The values considered in this study (for the risk estimation and the cost-benefit analysis)
are expected to vary based on the final (commercial) design of the SMART sprinkler
system as well as the location/facility where the SMART sprinklers are expected to be
installed.

FM GLOBAL
PUBLIC RELEASE

6 3. Failure Mode and Effect Analysis (FMEA)
The FMEA is conducted to identify the credible failure modes of the components, the causes of failures,
and the effects of failures on the SMART sprinklers . This analysis is necessary to build the availability
model for the SMART sprinkler system. Table s 3-1 and 3-2 provi de the results from the FMEA of the
SMART sprinkler s.
Table 3-1: FMEA of the SMART Sprinkler s

Components Functions Failure Modes Potential effects
of failure on the
system Probable causes of
failure
Smoke detector Sense smoke; sound
alarm; and send
signal to transceiver
module No/erroneous
signal to
transceiver
module No/inadequate
discharge through
sprinklers; delayed
activation of fire
pump Wear, corrosion,
detector opening
plugged/blocked,
open circuit in sensing
element
Thermocouple
(TC) module Measure
temperature (heat);
filter noise; send
signal to transceiver
module No/erroneous
signal to
transceiver
module No/erroneous signal
to transceiver
module, hence
no/inadequate
discharge through
sprinklers; delayed
activation of fire
pump Corrosion, loose
connection, open
circuit in sensing
element
Signal transceiver
module Communicate
wirelessly (send and
receive signals) with
the master
transceiver module,
and energize the
relay when required Fail to act (i.e.,
communicate
with master
transceiver,
and/or energize
the relay when
required) Relay doesn’t
function, hence no
discharge through
sprinklers Loss of antenna
communication,
corrosion, overstress,
aging failures such as
electromigration,
diffusion, loss of
power
Wireless
communication Provides connection
between transceiver
modules Communication
failure between
signal and
master
transceivers SMART sprinkler
system failure to
operate (if failure
occurs prior to
activation and not
corrected) External interference,
e.g., radio frequency
Programmable
logic controller
(PLC) Fire event
assessment and
location
determination Fail to
accurately infer
severity and
location of fire
event for
sprinkler
activation No/inadequate
discharge through
sprinkl ers Improper
programming,
corrosion, inadequate
signal input, aging
failures of processors

FM GLOBAL
PUBLIC RELEASE

7 Table 3-2: FMEA of the SMART Sprinklers (continued)

Components Functions Failure Modes Potential effects
of failure on the
system Probable causes of
failure
Master transceiver Wireless
communication
with the
transceiver module Fail to act (i.e.,
communicate
with signal
transceiver
module) PLC fail to operate ;
no/inadequate
discharge through
sprinklers Loss of p ower, loss of
antenna
communication,
corrosion, overstress,
aging failures such as
electromigration,
diffusion
Relay When energized,
provide a path for
energizing the
solenoid valve Fail to provide a
path for
energizing the
solenoid valve Solenoid valve
doesn’t open, hence
no discharge
through sprinklers No power received,
open circuit or broken
wire, wear, corrosion
Solenoid valve Open to allow
water to flow to
sprinkler Fail to open No discharge
through sprinklers Wear, corrosion,
blocked/plugged,
inad equate power to
energize
Latch in open
position once
activated Fail to latch No discharge
through sprinklers
in the event of loss
of power or failure
of control unit Corrosion,
blocked/plugged,
wear
Open sprinkler Discharge water Fail to discharge
(e.g., at
intended
pattern or flow
rate) Fail to extinguish
fire Corrosion,
blocked/plugged
Power supply
(main, back -up) Provide power
supply for
operation of
SMART sprinkler
system as well as
fire pump; back -up
supply provides
power only to
SMART system
upon failure of
main supply Unavailable or
fail to provide
power SMART sprinkler
system as well as
fire pump fail to
operate, no
discharge Power generation
and/or transmission
failure; overstress,
other random failures,
corrosion
Electrical
cable/wire Convey electrical
signals to
components Fail to convey SMART sprinkler
system fail to
activate Broken, worn out

FM GLOBAL
PUBLIC RELEASE

8 4. Availability Model s for the SMART Sprinkler s
Availability is the probability that a system operates properly when needed. Availability of a system
depends on the reliabilities of its components and the ITM parameters. Unavailability of a system can be
caused by the following: (1) the system is in a failed condition or undergoing maintenance; and/or (2)
the system fails to perform as intended w hen needed . For the wired/wireless SMART system s, this
chapter provides the availability models, which include the unavailability trees, and the parameters for
reliability distribution s and ITM (including approximate costs per inspection/testing and mainte nance ).
For the traditional wet sprinkler system, the availability model has been adopted from past studies
related to fire protection systems (e.g., [8] [9]), while the approximate ITM costs are provided in
Appendix A . As discussed in Chapter 2, Section 2.4, the SMART sprinkler protection system consists of
the SMART sprinklers and all the components of the traditional wet sprinkler system.
4.1 Unavailability Trees
The fault tree technique has been used to develop the unavailability trees for the wired/wireless SMART
sprinkler s. The unavailability trees have been developed using the results from the FMEAs (Chapter 3) to
determine the logic leading to the unavailability of the wired/wireless SMART sprinklers.
For better presentation, the unavailability trees have been segregated into multiple figures (subtrees)
with page number references (in each figure) providing connections between the different subtrees.
Figures 4-1 to 4-8 provide the unavailability tree for the wireless SMART sprinkler, while Figures 4-9 to
4-14 provide the unavailability tree for the wired SMART sprinkler.
The solenoid valve failure mode ‘fail to latch’ is only relevant if, after activation, there is an interruption
of signal from the relay to the solenoid valve either due to failure of the power supply or failure of the
relay or wireless communication or oth er components upstream to the relay. Therefore, in the
unavailability trees for the wireless and the wired SMART sprinklers , the intermediate event ‘solenoid
valve fail to maintain open position upon activation’ has been modeled using an ‘AND’ gate with tw o
events, i.e., ‘solenoid valve fail to latch’ and ‘relay fail to provide signal to solenoid valve’.

FM GLOBAL
PUBLIC RELEASE

9

Figure 4-1: Unavailability tree for the wireless SMART sprinklers – Subtree I

SMART sprinklers
unavailable
TOP
Sprinkler failure
G033No/inadequate flow of
water to sprinkler
G050
Solenoid valve fail
to open
G004
Page 10
Delayed activation of
fire pump
G014
Page 15Power supply
unavailable
G028
Page 11
Solenoid valve fail
to latch upon
activation
G073
Page 16

FM GLOBAL
PUBLIC RELEASE

10

Figure 4-2: Unavailability tree for the wireless SMART sprinklers – Subtree II

Solenoid valve fail
to open
G004
Page 9
Solenoid valve fail
to open
G055Relay fail to provide
signal to solenoid
valve
G003
Relay failure
G040
Electrical wire/cable
failure
(relay-solenoid) W2
G059Power supply
unavailable
G028
Page 11
Signal transceiver
fail to provide
signal to relay
G017
Page 12

FM GLOBAL
PUBLIC RELEASE

11

Figure 4-3: Unavailability tree for the wireless SMART sprinklers – Subtree III

Powe r supply
unavail abl e
G028
Page 16
Page 9
Page 10
Powe r (main) supply
unavail abl e
G077Powe r (back-up)
supply unavail abl e
G079

FM GLOBAL
PUBLIC RELEASE

12

Figure 4-4: Unavailability tree for the wireless SMART sprinklers – Subtree IV

Signal transce iver
fa il to provide
signal to re lay
G017
Page 10
Signal transce iver
modul e fa ilure
G019Communicati on fail ure
with control uni t
G020
Page 13Control unit fail to
provide ade qua te
signal
G026
No/ina dequate signals
from se nsors
G034
Page 14Logic control ler
fa ilure
G035

FM GLOBAL
PUBLIC RELEASE

13

Figure 4-5: Unavailability tree for the wireless SMART sprinklers – Subtree V

Communicati on fail ure
with control uni t
G020
Page 16
Page 15
Page 12
Ma ster tra nsceiver
fa ilure
G021Wire less
communi ca tion fa ilure
due to external
interference
G022

FM GLOBAL
PUBLIC RELEASE

14

Figure 4-6: Unavailability tree for the wireless SMART sprinklers – Subtree VI

No/ina dequate signals
from se nsors
G034
Page 15
Page 12
Smoke de tector
fa ilure
G036
Ele ctrical wire /cable
fa ilure
(se nsors-transcei ve r)
W4
G060TC modul e fa ilure
G037

FM GLOBAL
PUBLIC RELEASE

15

Figure 4-7: Unavailability tree for the wireless SMART sprinklers – Subtree VII

Delayed activation of
fire pump
G014
Page 9
Logic controller
failure
G035Control unit fail to
receive signal
G062
Communication failure
with control unit
G020
Page 13
Signal transceiver
module failure
G019No/inadequate signals
from sensors
G034
Page 14

FM GLOBAL
PUBLIC RELEASE

16

Figure 4-8: Unavailability tree for the wireless SMART sprinklers – Subtree VIII

Solenoid valve fail
to latch upon
activation
G073
Page 9
Relay fail to provide
signal to solenoid
valve
G074
Relay failure
G040
Electrical wire/cable
failure
(relay-solenoid) W2
G059
Signal transceiver
module failure
G019Logic controller
failure
G035
Communication failure
with control unit
G020
Page 13
Power supply
unavailable
G028
Page 11Solenoid valve fail
to latch
G031

FM GLOBAL
PUBLIC RELEASE

17

Figure 4-9: Unavailability tree for the wired SMART sprinklers – Subtree I

SMART sprinklers
unavailable
TOP
Sprinkler failure
G033No/inadequate flow of
water to sprinkler
G050
Solenoid valve fail
to open
G004
Page 18
Power supply
unavailable
G028
Page 19Delayed activation of
fire pump
G014
Page 21
Solenoid valve fail
to latch upon
activation
G068
Page 22

FM GLOBAL
PUBLIC RELEASE

18

Figure 4-10: Unavailability tree for the wired SMART sprinklers – Subtree II

Solenoid valve fail
to open
G004
Page 17
Solenoid valve fail
to open
G055Relay fail to provide
signal to solenoid
valve
G003
Relay failure
G040
Power supply
unavailable
G028
Page 19Control unit fail to
provide adequate
signal
G026
Page 20
Electrical wire/cable
failure
(control-relay) L3
G067Electrical wire/cable
failure
(relay-solenoid) W2
G059

FM GLOBAL
PUBLIC RELEASE

19

Figure 4-11: Unavailability tree for the wired SMART sprinklers – Subtree III

Powe r supply
unavail abl e
G028
Page 18
Page 22
Page 17
Powe r (main) supply
unavail abl e
G072Powe r (back-up)
supply unavail abl e
G075

FM GLOBAL
PUBLIC RELEASE

20

Figure 4-12: Unavailability tree for the wired SMART sprinklers – Subtree IV

Control unit fail to
provide adequate
signal
G026
Page 18
No/inadequate signals
from sensors
G034
Page 21
Smoke detector
failure
G036
Electrical wire/cable
failure
(sensors-control) L4
G063TC module failure
G037Logic controller
failure
G035

FM GLOBAL
PUBLIC RELEASE

21

Figure 4-13: Unavailability tree for the wired SMART sprinklers – Subtree V

Dela ye d acti va tion of
fi re pump
G014
Page 17
Logic control ler
fa ilure
G035No/ina dequate signals
from se nsors
G034
Page 20

FM GLOBAL
PUBLIC RELEASE

22

Figure 4-14: Unavailability tree for the wired SMART sprinklers – Subtree VI

Solenoid valve fail
to latch upon
activation
G068
Page 17
Relay fail to provide
signal to solenoid
valve
G069
Relay failure
G040
Logic controller
failure
G035Electrical wire/cable
failure
(control-relay) L3
G067
Power supply
unavailable
G028
Page 19Solenoid valve fail
to latch
G031

FM GLOBAL
PUBLIC RELEASE

23 4.2 Parameters for Reliability Distribution and ITM
For the components of the SMART sprinklers, t his section provides the values of parameters for the
reliability distribution and ITM.
4.2.1 Reliability Distribution
Reliability is the probability that a component performs as intended for a prescribed period of time
when operated within the specified environmental and operating conditions. Inherent reliabili ty
depends on the design and manufacturing processes. However, the actual conditions in the field cannot
be fully controlled, and can deviate from manufacturer’s specifications. Therefore, in general, there are
three broad categories of expected or unexpec ted failures that can affect the reliability of a component
during its lifetime. They are: (1) early life or infant mortality failures that are caused by serious
deficiencies in design and manufacturing processes; (2) random failures that are caused by une xpected
causes such as extreme overstresses or human errors; and (3) aging -related failures that are caused by
aging mechanisms such as wear, fatigue, and/or corrosion.
Weibull distributions are typically used for modeling reliability. Based on the Weibull distribution, t he
reliability, 𝑅(𝑡), at a component lifetime, t, can be estimated using Equation 4-1, where, β is the shape
parameter and η is the characteristic life.
𝑅(𝑡)=exp [−(𝑡
𝜂)𝛽
] 4-1

4.2.1.1 Weibull Shape Parameter
The shape parameter value depends on the type of failure, e.g., if failure is caused due to serious
design/manufacturing process deficienc ies or human errors or overstress es or aging mechanisms. Table
4-1 provides the typical values of shape parameters for different types of failures.
Table 4-1: Typical values of shape parameters for different failure types

# Failure type Value of shape
parameter
1 Serious design/manufacturing process deficiency
related failures < 1
2 Human error or overstress related random failures ≈ 1
3 Aging -related failures > 1

To consider the range of failure types, probability distributions for shape parameters were determined
in this study , and values were randomly sampled from the distributions. Accordingly, a distribution for
the shape parameter with a mean value of 2.25 and a standard dev iation of 0.5 was chosen for all the
components except the wireless communication failure due to external interference and the power
supply failure, for which a distribution with a mean value of 1 and a standard deviation of 0.1 was
chosen. The values for the mean and standard deviation have been chosen to develop a distribution that
can randomly generate all possible values representing all types of failures as discussed above .
Therefore , for each of the components, ten values were randomly sampled from th eir respective

FM GLOBAL
PUBLIC RELEASE

24 distributions. Table 4-2 provides the randomly sampled values for the shape parameters for the
components.
Table 4-2: Random v alues of shape parameters for components of SMART sprinkler s

Components Failure modes Shape parameter values
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10
Smoke detector No/erroneous signal to
transceiver module 2.2 2.2 1.6 1.4 2.3 2.2 2.3 2.2 2.8 1.9
Thermocouple
(TC) module No/erroneous signal to
transceiver module 1.6 2.0 2.9 3.0 2.3 3.6 2.1 3.0 1.3 1.9
Signal
transceiver
module Fail to act (i.e.,
communicate with
master transceiver,
and/or energize the
relay when required) 3.3 2.0 2.2 1.9 2.0 1.7 1.8 1.5 2.9 2.1
Programmable
logic controller Fail to accurately infer
severity and location of
fire event for sprinkler
activation 2.6 2.1 2.7 2.7 2.1 2.2 2.7 2.1 2.6 2.6
Master
transceiver Fail to act (i.e.,
communicate with
signal transceiver
module) 1.6 3.2 2.2 2.2 1.3 3.1 2.6 2.7 3.1 2.8
Wireless
communication Communication failure
due to external
interference 1.1 1.0 1.0 0.8 1.0 0.9 1.1 0.9 0.9 1.0
Electrical
cable/wire Fail to convey electrical
signal 2.8 1.3 1.4 2.4 2.3 3.8 1.8 1.6 2.5 2.4
Power supply
(back -up) Unavailable 1.0 1.2 1.1 1.0 1.0 1.0 0.8 1.0 0.9 0.8
Relay Fail to provide a path
for energizing the
solenoid valve 2.6 2.9 1.3 2.5 2.6 1.9 2.4 2.9 1.5 1.8
Solenoid valve Fail to open 1.6 2.7 2.2 3.2 1.8 2.3 1.6 2.4 1.9 2.2
Fail to latch 2.0 3.0 2.1 2.9 1.8 3.1 2.0 1.3 2.6 1.6
Open sprinkler Fail to discharge (e.g.,
at intended pattern or
flow rate) 2.5 1.9 2.3 2.0 1.6 2.9 2.0 2.6 2.1 3.1

4.2.1.2 Weibull Characteristic Life
The characteristic life is the lifetime at which the component reliability equals 0.368 (or 63.2% of the
components fail). For a given shape parameter for a component, the reliability increases with an
increase in the characteristic life.
In this study, t he values of the characteristic life ( η) were estimated based on the values of the MTBF
and the shape parameters for the components, as shown in Equation 4-2, where, 𝛽 is the Weibull shape
parameter, and 𝛤 is the Gamma function.

FM GLOBAL
PUBLIC RELEASE

25 𝜂=𝑀𝑇𝐵𝐹
Γ(1+1
𝛽) 4-2

The MTBF for a component is the inverse of its failure rate. The probability is approximately 0.5 for a
component to perform reliably (without failure) at the time when it reaches the MTBF value. For the
components of the SMART sprinklers, the MTBF values have been adopted from reliability databases
[10] [11], and past studies related to fire protection systems (e.g., [8] [9]). To characterize uncertainties
with the MTBF values , probability distributions were considered, and values were randomly sampled to
consider a range of failure rates. Table 4-3 provides the parameters of the MTBF distributions for the
components.
Table 4-3: Parameter values for MTBF di stributions for components of SMART sprinklers

Components Failure modes MTBF (years)
Mean 95% upper
bound 95% lower
bound Standard
deviation
Smoke detector No/erroneous signal to transceiver
module 12 15 9 1.5
Thermocouple (TC)
module No/erroneous signal to transceiver
module 57 71 43 7.3
Signal transceiver
module Fail to act (i.e., communicate with
master transceiver, and/or energize the
relay when required) 28 35 21 3.6
Programmable logic
controller Fail to accurately infer severity and
location of fire event for sprinkler
activation 18 23 14 2.3
Master transceiver Fail to act (i.e., communicate with signal
transceiver module) 28 35 21 3.6
Wireless
communication Communication failure due to external
interference 17.2 21 13 2.2
Electrical cable/wire Fail to convey electrical signal 42 52 31 5.3
Power supply (main) Unavailable 10-5 (probability of failure)
Power supply (back -up) Unavailable 7.3 9 5 0.9
Relay Fail to provide a path for energizing the
solenoid valve 65 81 49 8.2
Solenoid valve Fail to open 19 24 14 2.4
Fail to latch 15 19 11 2.0
Open sprinkler Fail to discharge (e.g., at intended
pattern or flow rate) 192 240 144 24.5

For each component, ten values were randomly sampled from their MTBF distribution. The random
values of the MTBF and the shape parameter (see Table 4-2) were used to estimate the values of the
characteristic life using Equation 4-2. Table 4-4 provides values of the characteristic life for the
components.

FM GLOBAL
PUBLIC RELEASE

26 Table 4-4: Values of characteristic life for the components of the SMART sprinkler s

Component Failure modes Characteristic life (years)
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10
Smoke detector No/erroneous signal to
transceiver module 14.0 13.2 12.6 13.2 8.3 13.6 13.4 14.9 11.7 13.3
Thermocouple
(TC) module No/erroneous signal to
transceiver module 62.6 53.7 62.1 71.6 60.1 63.0 65.0 74.5 61.5 54.7
Signal
transceiver
module Fail to act (i.e., communicate
with master transceiver,
and/or energize the relay
when required) 26.9 32.0 38.4 25.2 33.1 28.2 33.3 26.3 30.0 38.5
Programmable
logic controller Fail to accurately infer severity
and location of fire event for
sprinkler activation 17.0 18.7 22.5 14.3 16.4 18.4 22.4 17.6 25.5 20.5
Master
transceiver Fail to act (i.e., communicate
with signal transceiver module) 35.0 32.1 30.3 27.7 32.9 37.4 40.5 26.7 31.1 36.6
Wireless
communication Communication failure due to
external interference 17.3 17.0 19.7 15.6 19.5 16.6 18.8 18.2 14.9 17.6
Electrical
cable/wire Fail to convey electrical signal 50.7 43.5 39.1 51.7 36.3 46.2 44.3 42.5 50.0 49.0
Power supply
(back -up) Unavailable 6.6 8.7 5.4 7.7 7.5 6.5 6.6 5.8 5.5 5.3
Relay Fail to provide a path for
energizing the solenoid valve 77.9 57.1 54.1 81.1 69.3 70.7 62.9 72.3 53.1 80.8
Solenoid valve Fail to open 20.2 17.1 20.1 20.4 22.5 23.6 19.6 15.8 14.7 23.9
Fail to latch 20.5 15.0 14.8 19.9 19.2 19.4 18.3 17.9 16.8 15.2
Open sprinkler Fail to discharge (e.g., at
intended pattern or flow rate) 256.9 232.5 242.0 220.8 175.8 253.0 219.1 209.5 197.5 238.9

4.2.2 Inspection/Testing/Maintenance (ITM)
The ITM parameters include inspection/testing frequency (or interval), maintenance durations, and
restoration factors. The parameters have been determined based on review of relevant industry
standards, as well as past studies rel ated to fire protection systems .
4.2.2.1 Frequency/Interval
To determine the effects of inspection/testing frequencies on the availability of the system, t wo
frequencies of annual and semi -annual were considered in this study for all the components of t he
SMART sprinklers . For the ITM frequencies of the components of the traditional wet sprinkler system,
refer to Appe ndix A : Table A-1.
In this study, correctiveiv maintenance (if necessary) at the time of inspection/testing has been
considered. Some components (e.g., smoke detector and TC module) may be corrected upon failur e
based on sensor data received continuously by the PLC. However, for those components, not all failure
modes can be detected through sensor data monitoring. For example, if the smoke detector fails to send
signal, the PLC would be able to provide a warnin g. However, if the smoke detector detects smoke but

iv A corrective maintenance is usually performed to restore a failed system to an operational status by replacing or
repairing the component that is responsible for the system failure.

FM GLOBAL
PUBLIC RELEASE

27 sends anomalous signals to the PLC, then it cannot be possible for the PLC to detect anomalies and
provide a warning (it would require an additional algorithm and a trained operator to detect such
anomali es). Even a small anomaly in the signal has the potential to cause false activation or missed
activation types of failures. Similarly, for a wireless SMART system, wireless communication failure due
to external interference may be detected upon failure onl y for the case when no signal is received by
the PLC. However, external interference can also cause noisy or anomalous signals, which can not be
detect ed upon failure by the PLC for the same reasons as described above. Therefore, this study
considered a con servative case of corrective maintenance during inspection/testing.
4.2.2.2 Maintenance Duration
Maintenance duration depends on factors such as the extent of failure, the availability of spare parts
(e.g., the lead times) and personnel for conducting maintenance , as well as the ease of conducting the
maintenance. The maintenance durations have been considered based on review of relevant industry
standards, and past studies related to fire protection systems. To characterize the uncertainty,
distributions for main tenance duration were considered for the components. The durations for the
scheduled/planned events such as fixed interval inspection/testing don’t affect the system availability.
Therefore, durations for the scheduled events were not considered in this st udy. Table 4-5 provides the
distribution parameters.
Table 4-5: Distribution parameters for maintenance durations for SMART sprinklers

Components Failure modes Maintenance
duration (days)
Mean Standard
deviation
Smoke detector No/erroneous signal to transceiver module 3 1
Thermocouple (TC) module No/erroneous signal to transceiver module 3 1
Signal transceiver module Fail to act 7 2
Programmable logic controller Fail to accurately infer severity and location of fire event
for sprinkler activation 7 2
Master transceiver Fail to act 7 2
Wireless communication Communication failure due to external interference 3 1
Electrical cable/wire Fail to convey electrical signal 3 1
Power supply (back -up) Unavailable 3 1
Relay Fail to provide a path for energizing the solenoid valve 3 1
Solenoid valve Fail to open 3 1
Fail to latch 3 1
Open sprinkler Fail to discharge 7 2

For wireless communication failure, the maintenance duration reflects the time to detect and remove
the source of external interference, and reactivate the wireless communication. For each of the
components, ten values were randomly sampled from their respective distributions to consider all
possible values, as shown in Table 4-6.

FM GLOBAL
PUBLIC RELEASE

28 Table 4-6: Random values of maintenance durations for components of SMART sprinklers

Component Failure modes Maintenance durations (days)
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10
Smoke detector No/erroneous signal to
transceiver module 2.7 3.5 3.1 1.9 4.4 2.4 1.7 1.0 3.4 1.6
Thermocouple
(TC) module No/erroneous signal to
transceiver module 2.0 2.4 1.6 3.1 4.2 4.2 3.9 2.6 3.7 2.8
Signal transceiver
module Fail to act 8.0 9.1 6.2 9.0 6.3 9.6 3.9 7.6 5.5 4.8
Programmable
logic controller Fail to accurately infer
severity and location of fire
event for sprinkler activation 11.4 4.3 9.0 5.0 7.8 6.4 6.2 5.8 6.7 9.8
Master
transceiver Fail to act 1.2 6.3 3.9 6.5 7.3 6.1 7.6 8.1 3.7 5.3
Wireless
communication Communication failure due to
external interference 1.3 4.0 4.5 2.9 1.4 2.9 3.8 2.6 1.8 3.3
Electrical
cable/wire Fail to convey electrical signal 4.0 1.0 3.4 4.0 3.4 3.6 4.1 2.0 3.7 4.3
Power supply
(back -up) Unavailable 3.7 4.0 3.9 3.5 2.3 2.9 2.7 4.5 4.2 2.7
Relay Fail to provide a path for
energizing the solenoid valve 3.5 2.8 2.3 2.1 0.8 2.6 1.3 4.5 3.1 4.0
Solenoid valve Fail to open 3.0 3.2 1.7 4.4 2.1 0.0 1.9 0.6 3.3 3.3
Fail to latch 1.2 3.1 5.1 1.3 2.6 1.1 4.4 2.6 3.5 3.8
Open sprinkler Fail to discharge 6.7 6.0 7.1 11.0 7.6 8.0 8.0 6.1 8.1 6.0

4.2.2.3 Maintenance Restoration Factor
The restoration factor indicates the percentage (of new condition) to which a component will be
restored after the performance of the maintenance action. For example, the value of the restoration
factor indicates whether a component will be “as good as new ” after the maintenance action (value = 1),
or will not be improved at all (value = 0) but restored to operating condition. The restoration factor
depends on the quality of the maintenance action (repair/replacement) and procedure, which in turn
depends on the failure modes and the causes of the failures. For example, for a solenoid valve failure
mode “fail to open” caused by wear/fatigue, the value of the restoration factor can be considered to be
1 if the maintenance action involves replacement by a new v alve. No restoration has been considered
during corrective ITMs if there is no failure and thus no need for a corrective maintenance.
To characterize the uncertainty, a distribution for the restoration factor s with a mean of 0.5 and
standard deviation of 0.3 was considered. For each component, ten values were randomly sampled from
this distribution to consider all possible values . For the main power supply and the wireless
communication (external interference), 100% restoration was considered for all maint enance actions.
4.3 Approximate C osts per Inspection/Testing and Maintenance of
SMART Sprinklers to Estimate Lifetime ITM Costs
The lifetime costs of ITM can be divided into inspection/testing costs and maintenance costs. The
inspection/testing portion of the lifetime ITM cost is estimated based on labor costs per
inspection/testing of all the SMART sprinklers installed in a warehouse, and the total number of
inspection/testing performed over the lifetime of 30 years; while the maintenance portion of the
lifeti me ITM cost is the sum total of the lifetime maintenance costs for all the components of the SMART

FM GLOBAL
PUBLIC RELEASE

29 sprinklers. A maintenance action is performed if a component is found to be in a degraded or failed
state during a scheduled inspection/testing. Therefore, t he lifetime maintenance costs for a component
of the SMART sprinkler is estimated through the availability analysis based on the costs of maintaining
the component, and the parameters for its reliability distribution and ITM.
The cost per inspection/testin g is based on typical daily labor costs for technicians/engineers who are
involved in determination of the condition of the components using test equipment or visual means as
appropriate. It is assumed that the ITM companies have long term contracts with s ubsidized rates.
There fore, for inspection/testing, a cost of approximately $1000/day (for an eight hour day @
approximately $125/hour) was considered for 100 SMART sprinklers. It has been assumed that the
inspection/testing of all the 500 SMART sprinklers in a warehouse will be conducted during a scheduled
ITM (either annually or semi -annually).
The maintenance cost is divided into fixed and variable costs, and is considered on a per -component
basis. The fixed cost is associated with the re -installation (o f a component after maintenance) related
labor costs (including ensuring that the entire system is operational again). In this study, a fixed cost of
approximately $500 per component has been considered as a reasonable estimate irrespective of the
type of component.
The variable cost is associated with fixing (i.e., repairing or replacing with a new one) a damaged
component to bring it back to its operational status. Therefore, the variable cost depends on the cost of
the component as well as whether repai r or replacement action has been performed, which depends on
the value of the restoration factor (refer to description of restoration factor in Section 4.2.2.3 ). The
variable maintenance cost is considered to be less than or equal to the purchasing cost of a component.
Table 4-7 summarizes the approximate costs per inspection/testing and maintenance (rationale and
postulates as described above).
Table 4-7: Approximate c osts per inspection/testing and maintenance for SMART sprinklers

# Item Approximate
costs Description of costs
1 Inspection/testing cost $5,000 Includes labor costs (including
inspection/testing equipment costs) for
inspection/testing of 500 SMART sprinklers
during a scheduled inspection/testing
2
Maintenance Fixed cost $500 Includes re -installation related labor costs
per component
3 Variable cost Depends on ‘repair or replacement’, cost of component
(Table 4-8)

Table 4-8 provides the approximate c osts considered in this study for the components of the prototype
design of the SMART sprinklers.

FM GLOBAL
PUBLIC RELEASE

30 Table 4-8: Approxima te costs for the components of the SMART sprinklers

# Component Approximate costs
($ per unit)
1 Smoke detector $20
2 Thermocouple (TC) module $150
3 Signal transceiver module $50
4 Programmable logic controller (PLC) $500
5 Master transceiver $500
6 Electrical wire $10 (per connection)
7 Power supply (back -up) $500
8 Relay $50
9 Solenoid valve $500
10 Open sprinkler $100

Based on the approximate cost values provided in Table 4-8, the total costs of 500 SMART sprinklers
(including the control unit and the back -up power supply) are estimat ed to be approximately $460,000
(for wireless configuration) and approximately $430,000 (for wired configuration) . As described in
Chapter 2 Section 2.4, there is one control unit (‘PLC + master transceiver’ for wireless configuration,
and ‘PLC’ for wired configuration) and one back -up power supply per warehouse.

FM GLOBAL
PUBLIC RELEASE

31 5. Availability Analysis
This chapter provides estimated availability values and lifetime ITM costs for the traditional wet
sprinkler protection and the SMART sprinkler protection systems .
5.1 Availability of Traditional Wet Sprinkler and Wired/Wireless
SMART Sprinkler System s
The availability model for the SMART sprinklers (developed in Chapter 4) was used, instead of the one
normally adopted for traditional sprinklers, to calculate the availability of a traditional wet sprinkler
system. Thereafter, availabilit y analysis was performed considering the random values of the reliability
and ITM parameters for the components of the SMART sprinklers (as described in Chapter 4, Section
4.2). For comparison purposes, the following sections provide only the mean values of the availability.
For the lower and upper bounds of the 90% confidenc e intervals, refer to Appendix B : Figures B-1 and
B-2, and Table B-1.
Figure 5-1 compares the availability curves over time for the traditional wet sprinkler and the
wired/wireless SMART sprinkler protection systems .

Figure 5-1: Availability curves over time for the traditional wet sprinkler and wired /wire less
SMART sprinkler systems

Table 5-1 provides the availability values for the traditional wet sprinkler and the SMART sprinkler
system s at 10, 20, and 30 years of life. In Table 5-1, a number within brackets indicates the percentage
difference in the availability when compared to the availability of the traditional wet sprinkler system.

FM GLOBAL
PUBLIC RELEASE

32 Table 5-1: Availability values for the traditional wet sprinkler protection and SMART sprinkler
protection system s

Fire protection
system ITM frequency Availability values
10 years 20 years 30 years
Traditional wet
sprinkler system ‘Current’v ≥ 0.9856 ≥ 0.9779 ≥ 0.9712
Wired SMART
sprinkler system Annual (SMART);
‘current’ (wet) ≥ 0.9301 (5.6%) ≥ 0.8874 (9.3%) ≥ 0.8590 (12.0%)
Semi -annual (SMART);
‘current’ (wet) ≥ 0.9561 (3.0%) ≥ 0.9294 (5.0%) ≥ 0.9108 (6.0%)
Wireless SMART
sprinkler system Annual (SMART);
‘current’ (wet) ≥ 0.9013 (8.6%) ≥ 0.8569 (12.4%) ≥ 0.8261 (15.0%)
Semi -annual (SMART);
‘current’ (wet) ≥ 0.9403 (4.6%) ≥ 0.9119 (6.7%) ≥ 0.8913 (8.0%)

Based on the uncertainty analysis (see Appendix B ), the uncertainty in the availability of the SMART
sprinkler system at the lifetime of 30 years was found to be approximately ±0.01 .
5.2 Estimated Lifetime ITM Costs for Traditional Wet Sprinkle r and
Wired/Wireless SMART Sprinkler Systems
Appendix C provides the estimated lifetime ITM costs for the traditional wet sprinkler and the
wired/wireless SMART sp rinkler systems . The inspection/testing portion of the lifetime ITM cost s has
been estimated based on approximate labor costs per inspection/testing (as provided in Table 4-7 for
the SMART sprinklers; and Table A-2 for the traditional wet sprinkler system) and the total numbe r of
inspection/testing performed over the lifetime of 30 years . The maintenance portion of the lifetime ITM
costs is the sum total of the estimated lifetime maintenance costs for all the components. The lifetime
maintenance costs for a component has been estimated through the availability analysis based on the
fixed and variable costs of maintaining the component (refer to Tables 4-7 and 4-8 for the SMART
sprinklers; and Tables A-2 and A-3 for the traditional wet sprinkler system), and the parameters for their
reliability distribut ion and ITM.
The estimated lifetime ITM costs (Appendix C , Table C-4) were broken down into yearly values (for a
lifetime of 30 years) , and their PVs were estimated as shown in Table D-2 (Appendix D ). Figure 5-2 shows
the PV curves of cumulative ITM costs over time for the traditional wet sprinkler p rotection and the
SMART sprinkler protection systems.

v The ‘current’ ITM frequency represents the frequencies used for the traditi onal wet sprinkler system in past
studies (e.g., [8] [9]). Refer to Appendix A : Table A-1 for the ‘current’ ITM frequencies for the components of the
traditional wet sprinkler system.

FM GLOBAL
PUBLIC RELEASE

33

Figure 5-2: PV curves of cumulative ITM cost s over time for traditional wet sprinkler protection
and SMART sprinkler protection systems (cost figures refer to 500 head system)

5.3 Critical Components of Wired/Wireless SMART Sprinkler System s
Figure 5-3 provides the critical components of the wired/ wireless SMART sprinkler system s with respect
to their percent contribution to the unavailability of the system.

Figure 5-3: Critical components of wireless (Left) and wired (Right) SMART sprinkler system s
For both the wireless and the wired SMART sprinkler protection systems, the smoke detector is the most
critical componen t because its MTBF value is the lowest (the back -up power supply has an even lower
MTBF, but failure of the back -up power is conditional upon the failure of the main power supply). For

FM GLOBAL
PUBLIC RELEASE

34 the wireless SMART sprinkler protection system, the control unit (maste r transceiver and PLC) is the
second ranked component followed by wireless communication (external interference), the solenoid
valve (fail to open), and the fire pump (including water supply). For the wired SMART sprinkler
protection system, the control un it (PLC) is the second ranked component followed by the solenoid
valve (fail to open), the fire pump (including water supply), and electrical wires .
5.4 Discussion of Results
Due to less complexity and fewer components, the availability of the traditional we t sprinkler protection
system is approximately 11% to 14% higher than those of the wired/wireless SMART sprinkler protection
systems. In a similar fashion , the estimated lifetime ITM cost s for the traditional wet sprinkler system is
approximately 50% lower than those of the wired/wireless SMART sprinkler systems. The difference in
the availabilities of the traditional wet sprinkler and the SMART sprinkler systems can be reduced by
approxima tely 50% by increasing the ITM frequency of the SMART sprinklers from annual to semi –
annual with relatively small increase (approximately 10%) in the estimated lifetime ITM costs. This is
because the estimated lifetime ITM cost s for 500 SMART sprinklers (i n a warehouse) are dominated by
the lifetime maintenance cost s rather than the inspection/testing labor cost s (refer to Appendix C for
more details). Thus, an incre ase in the ITM frequency doesn’t have much effect on the estimated
lifetime ITM cost s.
Due to the higher reliability of the wired connections, t he unavailability of the wired SMART sprinkler
system is approximately 20% lower than that of the wireless SMAR T sprinkler system. It should be noted
that the availabilities of the SMART sprinkler system s are based on the reliability/ITM/criticality of all the
components (including the water supply components such as fire pump). For example, both the wired
and wire less SMART sprinkler systems contain the smoke detector and the solenoid valve, whose
reliabilities are relatively poor and have much higher contributions (by a relative combined value of
more than 40%) to the system unavailability. Therefore, when compared to the wireless SMART system,
a 20% lower unavailability for the wired system is consistent with judgement or expectations .

FM GLOBAL
PUBLIC RELEASE

35 6. Risk Estimation
In this study, risk is defined as the product of ‘probability of occurrence of an undesired even t’ and
‘severity of consequences associated with the undesired event’. For a warehouse with a protection
system installed, the availability values estimated in Chapter 5 were used to estimate the risk, as shown
in Equation 6-1. For details regarding the estimation of ‘probability of fire’, refer to Appendix D .
𝑅𝑖𝑠𝑘 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 ($,𝑡)
=[𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑓𝑖𝑟𝑒(𝑡)×𝑈𝑛𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑦𝑠(𝑡)
×𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 𝑜𝑓 𝑙𝑜𝑠𝑠 𝑓𝑎𝑖𝑙𝑒𝑑 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑦𝑠($)]
+[𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑓𝑖𝑟𝑒(𝑡)×𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑦𝑠(𝑡)
×𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 𝑜𝑓 𝑙𝑜𝑠𝑠 𝑎𝑑𝑒𝑞𝑢𝑎𝑡𝑒 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 ($)]
6-1

For a warehouse without any protection system, the risk can be calculated using Equation 6-2.
𝑅𝑖𝑠𝑘 𝑛𝑜 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 ($,𝑡)=𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑓𝑖𝑟𝑒(𝑡)×𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 𝑜𝑓 𝑙𝑜𝑠𝑠 𝑛𝑜 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 ($) 6-2

For warehouse s with and without protection system s, the loss severit ies (including for failed and
adequate protection) are discussed in Chapter 2, Section 2.4. Based on Equations 6-1 and 6-2, the yearly
values of the expected risk wer e calculated for warehouses ‘with protection system’ as well as ‘with no
protection’. The PVs of the yearly values of expected risk were then estimated based on Equation D-2
(Appendix D ). For more details regarding the yearly estimates of risk and the PV, refer to Appendix D ,
Section D.4. Figure 6-1 shows the PV curves of cumulative risk over time.

Figure 6-1: PV c urves of cumulative risk over time for the traditional wet sprinkler protection and
the SMART sprinkler protection systems

FM GLOBAL
PUBLIC RELEASE

36 For a high storage configuration warehouse with a SMART sprinkler protection system installed, the
estimated lifetime risk is highest (approximately $400,000) for the wireless system with annual ITM
(lowest availability), whereas the estimated lifetime risk is lowest (approximately $200,000) for the
wired system with semi -annual ITM. For a low storage configurati on warehouse with a traditional wet
sprinkler protection system installed, the estimated lifetime risk is approximately $100,000.
Figure 6-2 shows the PV curves of cu mulative risk -reduction ( 𝑅𝑖𝑠𝑘 𝑛𝑜 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 – 𝑅𝑖𝑠𝑘 𝑤𝑖𝑡ℎ 𝑝𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 )
over time for the traditional wet sprinkler protection and the SMART sprinkler protection systems.

Figure 6-2: PV curves of cumulative risk -reduction over time for the traditional wet sprinkler
protection and the SMART sprinkler protection systems

For the traditional wet sprinkler and the wired/wireless SMART sprinkler systems, t he estimated lifetime
risk-reduction s are more than 90% . In Figure 6-2, the reduction in risk at time zero is the same for all
systems. This is because the availability is assumed to be 100% for all the protection systems at time
zero.

FM GLOBAL
PUBLIC RELEASE

37 7. Cost -Benefit Analysis
In this study, the cost-benefit analysis has been perform ed using the cost-benefit model provided in the
report [7] published by the National Institute of Standards and Technology ( NIST ). As per the NIST
report, the generalized Present Value of Net Benefits (PVNB) can be estimated using Equation 7-1,
where 𝐵𝑡 is the dollar value of benefits in period 𝑡, 𝐶𝑡 is the dollar value of costs in period 𝑡, 𝑇 is the
number of discounting time periods in the study period (lifetime of 30 years), and 𝑑 is the discounting
rate per time period (refer to Chapter 2, Section 2.4 for the discounting rate used in this study) .
𝑃𝑉𝑁𝐵 =∑𝐵𝑡−𝐶𝑡
(1+𝑑)𝑡𝑇
𝑡=0 7-1

A positive PVNB implies that the PV of benefits outweigh s the PV of costs. In this study, ‘benefit ’ is
defined as the risk -reduction achieved from the use of a fire protection system, whereas ‘costs’ include
ITM and initial installation costs for the fire protection system (refer to Appendix D , Table D-2 for the
values of expected risk, initial installation and ITM costs, and the PVNB) .
For the traditional wet sprinkler protection and the S MART sprinkler protection systems, Table 7-1
provides the estimated lifetime PVNB s.
Table 7-1: Estimated l ifetime PVNB s for traditional wet sprinkler protection and SMART
sprinkler protection systems

Fire protection
system ITM frequency Estimated l ifetime
PVNB (approx.)
Traditional wet
sprinkler ‘Current ’ ≈ $2,177,699
Wired SMART
sprinkler Annual for SMART;
‘current ’ for wet ≈ $825,791
Semi -annual for SMART;
‘current ’ for wet ≈ $752,678
Wireless SMART
sprinkler Annual for SMART;
‘current ’ for wet ≈ $605,229
Semi -annual for SMART;
‘current ’ for wet ≈ $582,793

For the traditional wet sprinkler system installed in a low storage configuration warehouse, the
estimated lifetime PVNB is approximately two to three times higher than those for the wired/wireless
SMART sprinkler systems installed in a high storage config uration warehouse. For the SMART sprinkler
system, the estimated lifetime PVNBs are comparable with annual and semi -annual ITMs. The estimated
lifetime PVNB for the wired SMART sprinkler system is approximately 30% higher than the wireless
system.

FM GLOBAL
PUBLIC RELEASE

38 8. Conclus ions
This study evaluated the availability of the wired/wireless SMART sprinkler protection system s for high
storage configuration warehouses , and compared it with that of the traditional wet sprinkler protection
system for low storage configuration warehouses . Further, this study conducted a comparative cost-
benefit analysis for the SMART sprinkler protection and the traditional wet sprinkler protection systems .
While the availability of the traditional wet sprinkler s ystem is 0.97 at the lifetime of 30 years, the
availabilities of the SMART sprinkler systems are approximately 0.86 ±0.01 and 0.83 ±0.01 , respectively,
for the wired and wireless configurations. The higher availability of the traditional wet sprinkler system
is due to lower complexity and fewer components when compared to the SMART sprinkler system. Due
to higher reliability of the wired connections, the unavailability of the wired SMART sprinkler system is
approximately 20% lower than that of the wireless SM ART sprinkler system. The difference in the
availabilities of the traditional wet sprinkler and the SMART sprinkler systems can be reduced by
approximately 50% by increasing the ITM frequency of the SMART sprinklers from annual to semi –
annual.
For both the traditional wet sprinkler and the SMART sprinkler systems, the estimated lifetime risk –
reductions are more than 90%. The estimated lifetime ITM cost for the traditional wet sprinkler system
is approximately 50% lower than those of the wired/wi reless SMART sprinkler systems. For the
traditional wet sprinkler system installed in a low storage configuration warehouse, the estimated
lifetime PVNB is approximately two to three times higher than those for the wired/wireless SMART
sprinkler systems in stalled in a high storage configuration warehouse. For the SMART sprinkler system,
the estimated lifetime PVNBs with annual and semi -annual ITMs are comparable. The estimated lifetime
PVNB for the wired SMART sprinkler system is approximately 30% higher th an that of the wireless
system.
The SMART sprinkler configuration used in this study is based on a proof -of-concept design, which is
expected to change when used commercially (e.g., using an alternative to the solenoid valve or using a
different activation mechanism or different sensors). Therefore, the values of the availability and the
PVNB estimated in this study are only intended as general guidance and are expected to change
according to actual system design and components.
In this study, the cost -benefit analysis has been performed with a limited objective of providing some
comparative perspective into the costs and benefits associated with the SMART sprinkler and the
traditional wet sprinkler protection systems. The results may be sensitive to the co st values considered
in this study for components and ITM. Further, the results are expected to change based on the final
(commercial) design of the SMART sprinkler system, and the location/facility where the SMART
sprinklers are expected to be installed. Since the objective of the cost -benefit analysis was limited, a
sensitivity (or uncertainty) analysis was not performed in this study for the cost -benefit estimates .

FM GLOBAL
PUBLIC RELEASE

39 References
1. S. Kopylov, L. Tanklevskiy, M. Vasiliev, V. Zima, and A. Sn egirev, "Advantages of Electronically
Controlled Sprinklers (ECS) for Fire Protection of Tunnels," in Proceedings of the Fifth
International Symposium on Tunnel Safety and Security , New York, USA, 2012, pp. 87 -92.
2. L.T. Tanklevskiy, M.A. Vasiliev, L.M. Meshman, A.Yu. Snegirev, and A.S. Tsoi, "A Novel
Methodology of Electrically Controlled Sprinkler Activation," in Proceedings of the Thirteenth
International Interflam Conference , London, England, 2013, pp. 1263 -1268.
3. Y. Xin, K. Burchesky, J. de Vries, H. Magistrale, X. Zhou, and S. D'Aniello, "SMART Sprinkler
Protection for Highly Challenging Fires – Phase 1: System Design and Function Evaluation," FM
Global, Norwood, Research Technical Report #0003048211, 2016.
4. Y. Xin, K. Burchesky, J. de Vries, H. Magistrale, X. Zhou, and S. D'Aniello, "SMART Sprinkler
Protection for Highly Challenging Fires – Phase 2: Full -Scale Fire Tests in Rack Storage," FM Global,
Norwood, Research Technical Report #0003051689, 2016.
5. National Fire Protection Association, "Standard for the Installation of Stationary Pumps for Fire
Protection," NFPA, Standard #20, 2016.
6. BRE Global, "An Environmental Impact and Cost Benefit Analysis for Fire Sprinklers in Warehouse
Buildings," BRE, R eport #271836 December, 2013.
7. D.T. Butry, M.H. Brown, and S.K. Fuller, "Benefit -Cost Analysis of Residential Fire Sprinkler
Systems," National Institute of Standards and Technology, Gaithersburg, Maryland, Technical
Report NISTIR #7451, September 2007.
8. K. Chatterjee, K. Bhimavarapu, R. Kasiski, and W. Doerr, "Ensuring the Availability of Complex
Systems," in Proceedings of the Twelfth Probabilistic Safety Assessment and Management (PSAM)
Conference , Honolulu, Hawaii, 2014.
9. K. Chatterjee and K. Bhimavarapu, "Availability -Based Inspection, Testing, and Maintenance (ITM)
Requirements for Fire Protection Systems," in Proceedings of the International Topical Meeting
on Probabilistic Safety Assessment and Analysis (PSA) , Sun Valle y, Idaho, 2015.
10. Reliability Information Analysis Center, "Nonelectronic Parts Reliability Data (NPRD)," RIAC,
Database 301st ed., 2011.
11. SINTEF, "Offshore Reliability Data (OREDA)," Det Norske Veritas (DNV), Database 4th ed., 2009.

FM GLOBAL
PUBLIC RELEASE

40 12. A. Hasofe r, V. Beck, and I. Bennetts, "Risk Analysis in Building Fire Safety Analysis," Oxford, U.K.,
2007.
13. L. Leung. (2016, January) The Institute of Fire Engineers (Hong Kong branch). [Online].
http://www.hkife.org/IFEHK/upload_i/20090315_Result_pro/Fire%20O ccurrences%20in%20Buil
dings.pdf

FM GLOBAL
PUBLIC RELEASE

41 Appendix A. Estimated Cost s of ITM and Components of
Traditional Wet Sprinkler System
Do not delete this hidden text. This is what allows successive numbering to work correctly 000
As considered in this study (refer to Chapter 4 Section 4.3), the inspection/testing of all the 500 SMART
sprinklers is expected to be conducted during a scheduled ITM (either annually or semi -annually). In
comparison, the components of the traditiona l wet sprinkle r system have different inspection/testing
frequencies, as shown in Table A-1.
Table A-1: ITM frequencies (‘current’) for components of traditional wet sprinkler system

# Component ITM frequency
1 Controller
Weekly/annually 2 Electric motor
3 Fire pump
4 Piping Upon failure
5 Check valves Annually
6 Alarm check valve Quarterly
7 Ball/gate/globe valves Weekly/annually
8 Sprinklers 10 years
9 Public w ater supply Upon failure

Table A-2 provides the approximate costs per inspection/testing and maintenance for the traditional
wet sprinkler system that have been used to estimate its lifetime ITM costs. The same postulates used
for determining the ITM costs for the SMART sprinklers (refer to Table 4-7) have also been used for the
traditional wet sprinkler system. When compare d to 500 SMART sprinklers, the inspection/testing of the
traditional wet sprinkler system would involve only a few components (e.g., the fire pump and the ball
valves during a weekly ITM; or the fire pump , the ball valves, and the check valves during an an nual ITM)
during a scheduled inspection/testing . Therefore, it has been considered that a scheduled
inspection/testing of traditional wet sprinkler system can be completed in a day. Accordingly, a labor
cost of approximately $1000/day (for an eight hour day @ approximately $125/hour) has been
considered for a scheduled inspection/testing of the traditional wet sprinkler system.
The ‘fixed’ maintenance cost has been considered to be same as that for the SMART sprinklers (i.e.,
labor cost of approximately $500) , while the ‘variable’ maintenance cost depends on the cost of the
component and whether ‘repair or replacement’ action has been performed .

FM GLOBAL
PUBLIC RELEASE

42 Table A-2: Approximate c osts per ins pection/testing and maintenance for traditional wet
sprinkler system

# Item Costs
(approx.) Description of costs
1 Inspection/testing $1,000 Includes labor costs (including
inspection/testing equipment costs)
per inspection/testing
2 Maintenance Fixed cost $500 Includes re -installation related labor
costs per component
Variable cost Depends on ‘repair or replacement’, cost of
component (Table A-3)

Table A-3 provides approximate purchasing cost s considered in this study for the components of the
traditional wet sprinkler system. The cost of public water supply is not provided in Table A-3 because its
maintenance is considered to be the responsibility of the town/city/state .
Table A-3: Approximate costs for the components of the traditional wet sprinkler system

# Component Approximate c osts
($ per unit)
1 Controller $5,000
2 Electric motor $5,000
3 Fire pump $5,000
4 Piping $2,000
5 Check valve $50
6 Alarm check valve $100
7 Ball/gate/globe valves $50
8 Sprinklers $100

In Table A-3, the approximate cost values for the components (except th at for the sprinklers which was
considered to be the same as that of the sprinklers in Table 4-8) have been consider ed based on review
of manufacturer websites and other online resources as well as with consideration of the installation
costs for the traditional wet sprinkler system used in this study (refer to Chapter 2, Section 2.4). The
costs of all the components of the traditional wet sprinkler system (including public water supply) are
included in the installation costs. In this study, it has been considered that for large buildings such as
warehouses, the labor costs for installation outweigh the purc hasing costs for the components. Based
on Table A-3, considering a warehouse with 500 traditional sprinklers, the total costs of components
could be more than $75,000, which is approximately one-third of the total installation cost considered in
this study.

FM GLOBAL
PUBLIC RELEASE

43 The approximate cost values provided in Table A-3 could change based on the sprinkler layouts, water
discharge flowrate requirements, and other protection configurations based on the actual design of the
warehouse . Since both the traditional wet sprinkler system as well as the wired/wireless SMART
sprinkler system use the same components for water supply, the cost values provided in Table A-3 can
provide a comparative perspective into the costs and benefits associated with these systems.

FM GLOBAL
PUBLIC RELEASE

44 Appendix B. Availability Values with Confidence Bounds
Do not delete this hidden text. This is what allows successive numbering to work correctly 000
Corresponding to each of the ten random combinations ( Chapter 4, Section 4.2) of reliability and ITM
parameters for the components of the SMART sprinklers , the av ailability curves over time were
generated. Thereafter, the ‘standard error of the mean’ method (used for small sample sizes) was used
to determine the mean and 9 0% confidence bounds. The confidence bounds represent the expected
variation in the mean avail ability.
B.1 Availability Values with Confidence Bounds for Wired /Wireless
SMART Sprinkler Systems
Figures B-1 and B-2 provide the availability curves over time for wired and wireless SMART sprinkler
systems, respectively.

Figure B-1: Availability curves (with confidence bounds) over time for wired SMART sprinkler
system (Left: Annual ITM ; Right: Semi -annual ITM )

Figure B-2: Availability curves ( with confidence bounds) over time for wireless SMART sprinkler
system (Left: Annual ITM ; Right: Semi -annual ITM )

FM GLOBAL
PUBLIC RELEASE

45 B.2 Summary
Table B-1 provides the confidence bounds of the availability values as estima ted in this study for the
wired/ wireless SMART sprinkler system s.
Table B-1: Availability values ( confidence bounds) for wired/wireless SMART sprinkler system s

Protection
system ITM frequency Availability values (9 0% lower bound – mean – 90% upper bound)
10 years 20 years 30 years
Wired SMART
sprinkler system Annual (SMART);
‘current ’ (wet) 0.9223 – 0.9301 – 0.9380 0.8780 – 0.8874 – 0.8968 0.8494 – 0.8590 – 0.8687
Semi -annual (SMART);
‘current ’ (wet) 0.9521 – 0.9561 – 0.9602 0.9242 – 0.9294 – 0.9346 0.905 2 – 0.9108 – 0.9164
Wireless SMART
sprinkler system Annual (SMART);
‘current ’ (wet) 0.8943 – 0.9013 – 0.9083 0.8486 – 0.8569 – 0.8652 0.8177 – 0.8261 – 0.8345
Semi -annual (SMART);
‘current ’ (wet) 0.9365 – 0.9403 – 0.9442 0.9070 – 0.9119 – 0.9167 0.886 4 – 0.8913 – 0.8961

FM GLOBAL
PUBLIC RELEASE

46 Appendix C. Estimated Lifetime ITM Cost s for Traditional
Wet Sprinkler and SMART Sprinkler System s
Do not delete this hidden text. This is what allows successive numbering to work correctly 000
For the traditional wet sprinkler protection and the SMART sprinkler protection systems, t his appendix
provides the estimated lifetime ITM cost s, which have been used to estimate the yearly ITM costs
(including PV values) in Appendix D : Table D-2 and plot the PV curves of the ITM costs in Chapter 5,
Section 5.2.
C.1 Estimated Lifetime ITM Cost s
Table C-1 provides the estimated lifetime ITM cost s for the traditional wet sprinkler system with the ITM
frequencies as provided in Appendix A , Table A-1. During a scheduled ITM (e.g., weekly, quarterly, or
annually), inspection/testing is expec ted to be conducted for all the components with the same ITM
frequency (e.g., a weekly inspection/testing of the fire pump and the ball valves; or an annual
inspection/testing of the check valves, the ball valves, and the fire pump). The inspection/testing costs
are based on the ITM frequencies, e.g., weekly (total number of inspection/testing in a lifetime of 30
years is 53*30) or quarterly (total number of inspection/testing in a lifetime of 30 years is 4*30). Since
the piping is expected to be maintained immediately ‘upon failure’, no additional cost for the
inspection/testing of the piping was considered.
Table C-1: Estimated lifetime ITM costs for traditional wet sprinkler system in a warehouse
with 500 sprinklers

# ITM Component Estimated l ifetime cost s
(approx.) per warehouse
1
Maintenance All except sprinklers $6,000
2 Sprinklers (500) $1,500
3 Inspection/testing Fire pump (including controller
and motor), ball valves – weekly 53*30*1000 = $1,590,000
Alarm check valve – quarterly 4*30*1000 = $120,000
Fire pump (including controller
and motor), ball valves, check
valves – annually 1*30*1000 = $30,000
Sprinklers – every 10 years 3*1000 = $3,000
4 Total lifetime ITM cost s (approx.) per warehouse ≈ $1.75M

Table C-2 provides the estimated lifetime ITM cost s for the wireless SMART sprinklers for both annual
and semi -annual ITM frequencies. As discussed in Chapter 4, Section 4.3, the inspection/testing of all the
500 SMART sprinklers (both wired and wireless) is expected to be conducted during a scheduled ITM ,

FM GLOBAL
PUBLIC RELEASE

47 i.e., either annually (total number of inspection/testing in a lifetime of 30 years is 30) or semi -annually
(total number of inspection/testing in a lifetime of 30 years is 60 ).
Table C-2: Estimated lifetime ITM cost s for wireless SMART sprinklers in a warehouse with 500
sprinklers

# ITM Component Estimated l ifetime
costs (approx.) Quantity
per
warehouse Estimated l ifetime cost s
(approx.) per warehouse
Annual
ITM Semi –
annual
ITM Annual ITM Semi –
annual ITM
1
Maintenance PLC $1,400 $1,600 1 $1,400 $1,600
2 Master
transceiver $400 $500 1 $400 $500
3 Wireless
communication $700 $800 1 $700 $800
4 Back -up power
supply $4,000 $4,500 1 $4,000 $4,500
5 Remaining
components (per
SMART sprinkler) $2,800 $3,100 500 $2,800*500
= $1.40M $3,100*500
= $1.55M
6 Inspection/testing All components of SMART sprinklers installed in a
warehouse $5,000*30
= $150,000 $5,000*60
= $300,000
7 Total lifetime ITM cost s (approx.) per warehouse ≈ $1.56M ≈ $1.86M

Table C-3 provides the estimated lifetime ITM cost s for the wired SMART sprinklers for both annual and
semi -annual ITM frequencies.

FM GLOBAL
PUBLIC RELEASE

48 Table C-3: Estimated l ifetime ITM cost s for wired SMART sprinkler s in a warehouse with 500
sprinklers

# ITM Component Estimated l ifetime
costs (approx.) Quantity
per
warehouse Estimated l ifetime cost s
(approx.) per warehouse
Annual
ITM Semi –
annual
ITM Annual ITM Semi –
annual ITM
1
Maintenance PLC $1,400 $1,600 1 $1,400 $1,600
2 Back -up power
supply $4,000 $4,500 1 $4,000 $4,500
3 Remaining
components (per
SMART sprinkler) $2,500 $2,800 500 $2,500*500
= $1.25M $2,800*500
= $1.40M
4 Inspection/testing All components of SMART sprinklers installed in a
warehouse $5,000*30
= $150,000 $5,000*60
= $300,000
5 Total lifetime ITM cost s (approx.) per warehouse ≈ $1.41M ≈ $1.71M

C.2 Discussion of Results
The estimated lifetime ITM cost s for 500 wired/wireless SMART sprinkler s (as provided in Tables C-2 and
C-3) is domin ated by the lifetime maintenance costs for the components, rather than the
inspection/testing labor costs; while the estimated lifetime ITM cost s for the traditional wet sprinkler
system (as provided in Table C-1) is dominated by the inspection/testing labor costs. This is because the
inspection/testing of all the 500 SMART sprinkler s is expected to be conducted during a scheduled ITM
(either annually or semi -annually) ; on the other hand, the inspection/testing frequencies are different
for different components of the traditional wet sprinkler system thereby incurring substantial
inspection/testing labor costs. Furthermore, each SMART sprinkler comprises of more than five
components, thus incurring substantial lifetime maintenance costs overall for 500 SMART sprinkler s
installed in a warehouse.
The lifetime ITM cost s for the SMART sprinkler protection system includes the lifetime ITM costs for t he
SMART sprinklers and for the traditional wet sprinkler system. Table C-4 provides the estimated lifetime
ITM costs for the traditional wet sprinkler and the SMART s prinkler protection systems.

FM GLOBAL
PUBLIC RELEASE

49 Table C-4: Estimated l ifetime ITM costs for traditional wet sprinkler and SMART sprinkler
systems

Protection
system ITM frequency Estimated l ifetime
ITM cost s (approx.)
Traditional wet
sprinkler system ‘Current’ ≈ 1.75M
Wired SMART
sprinkler system Annual (SMART); ‘current’ (wet) ≈ 3.16M
Semi -annual (SMART); ‘current’ (wet) ≈ 3.46M
Wireless SMART
sprinkler system Annual (SMART); ‘current’ (wet) ≈ 3.31M
Semi -annual (SMART); ‘current’ (wet) ≈ 3.61M

For the traditional wet sprinkler system , the estimated lifetime ITM cost s are approximately 50% lower
than those of the wired/wireless SMART sprinkler system s.

FM GLOBAL
PUBLIC RELEASE

50 Appendix D. Equations/Data for Risk Estimation and Cost –
Benefit Analysis
Do not delete this hidden text. This is what allows successive numbering to work correctly 000
This appendix provides the equations and data that have been used to plot the estimated lifetime ITM
costs in Chapter 5 and the risk curves in Chapter 6, and evaluate the PVNB s in Chapter 7.
D.1 Probability of Fire
The ‘probability of fire’ can be modeled based on a Poisson distribution [12] [13]. The probability of
occurrence of ‘ 𝜒’ fires in a time interval, 𝑇, can be calculated using Equation D-1, where 𝜆 represents the
fire frequency .
𝑃𝑓𝑖𝑟𝑒 =exp(−𝜆𝑇)×(𝜆𝑇)𝜒
𝑓𝑎𝑐𝑡𝑜𝑟𝑖𝑎𝑙 (𝜒) D-1

D.2 Present Value of Money
The present value (PV) of a sum of money at a future time, 𝐶𝑡, is calculated using Equation D-2, where 𝑑
is the discount ing rate.
𝑃𝑉 = 𝐶𝑡
(1+𝑑)𝑡 D-2

D.3 Availability Values (updated for renewal upon reinstallation after
fire occurrence)
After fire occurrence, the protection system needs to be reinstalled in the warehouse. Therefore, the
availability of the protection system is renewed to a value of 1 (age = 0 years). To account for this
renewal, Monte Carlo simulation (100,000 ) was performed using the software package Oracle® Crystal
Ball to estimate the averaged availability values (based on original values provided in Chapter 5, Sectio n
5.1) considering the expected number of fires over the lifetime of the protection system (fire frequency
of 0.025/year) . Table D-1 provides the updated availability values for the traditional wet sprinkler and
the SMART sprinkler protection systems .

FM GLOBAL
PUBLIC RELEASE

51 Table D-1: Updated a vailability values for traditional wet sprinkler protection and SMART
sprinkler protection systems

Fire protection
system ITM frequency Availability values
10 years 20 years 30 years
Traditional wet
sprinkler system ‘Current ’ ≥ 0.9868 ≥ 0.9816 ≥ 0.9781
Wired SMART
sprinkler system Annual (SMART);
‘current ’ (wet) ≥ 0.9379 ≥ 0.9088 ≥ 0.8940
Semi -annual (SMART);
‘current ’ (wet) ≥ 0.9608 ≥ 0.9426 ≥ 0.9329
Wireless SMART
sprinkler system Annual (SMART);
‘current ’ (wet) ≥ 0.9091 ≥ 0.8789 ≥ 0.8627
Semi -annual (SMART);
‘current ’ (wet) ≥ 0.9453 ≥ 0.9260 ≥ 0.9150

D.4 Expected Risk , ITM Cost s, and PVNB (Yearly Values)
Table D-2 provides the initial installation costs (approximate) for the fire protection systems, and
estimated yearly values of the probability of fire, the risk, the ITM cost s, and the PVNB s. To support page
size requirements, only the values for every five years (starting from zero year and ending at 30 years)
have been provided in Table D-2 (Note: the ye arly values in the table are at the time indicated such as at
5 years, and are not the cumulative values except for the PVNB, which is defined as such in Chapter 7) .
As discussed in Chapter 2, Section 2.4, the installation costs for the SMART sprinkler system in a
warehouse include the purchasing costs for 500 SMART sprinkle rs and the installation cost s for the
traditional wet sprinkler system ( approximately $280,000). No additional labor cost is considered for
installation of the SMART sprinklers. Refer to Chapter 4, Section 4.3 for the purchasing costs of 500
SMART sprinklers (approximately $430,000 for wired configuration , and approximately $460,000 for
wireless configuration ).
The probability of fire has been est imated using Equation D-1 for a period of one year. The risk values
have been estimated using Equations 6-1 (with protection) and 6-2 (no protection). The approximate
yearly ITM costs were estimated by breaking down the estimated lifetime ITM costs (as provided in
Appendix C , Table C-4) into yearly valu es (for a lifetime of 30 years). For the risk and the ITM cost s, the
PV values were estimated using Equation D-2 (with a discount rate of 4.8%, refer to Chapter 2, Section
2.4). The PVNB values were estimated using Equation 7-1.

FM GLOBAL
PUBLIC RELEASE

52 Table D-2: Yearly values (approximate) of estimated risk, ITM cost s, and PVNB for traditional
wet sprinkler protection and SMART sprinkler protection systems

Year → 0 5 years 10 years 15 years 20 years 25 years 30 years
Occurrence probability of a fire in time interval of a year 0 0.025 0.025 0.025 0.025 0.025 0.025
Roll paper warehouse: Property + outage costs (excluding protection
system) $17,700,000
Installation costs of wired SMART sprinkler protection system $710,000
Installation costs of wireless SMART sprinkler protection system $740,000
Installation costs of traditional wet sprinkler protection system $280,000
Warehouse with n o
protection Expected risk (yearly values) 0 $221,250 $221,250 $221,250 $221,250 $221,250 $221,250
PV of expected risk (yearly values) 0 $175,016 $138,443 $109,513 $86,628 $68,525 $54,206
Warehouse with wired
SMART sprinkler
system – annual ITM Expected risk (yearly values) 0 $12,558 $18,162 $22,118 $25,014 $27,015 $28,499
PV of expected risk (yearly values) 0 $9,934 $11,365 $10,948 $9,794 $8,367 $6,982
ITM costs of protection system (yearly values) 0 $105,333 $105,333 $105,333 $105,333 $105,333 $105,333
PV of ITM costs (yearly values) 0 $83,322 $65,910 $52,137 $41,242 $32,624 $25,806
PVNB -$710,000 -$248,001 $96,245 $355,990 $554,290 $707,134 $825,791
Warehouse with w ired
SMART sprinkler
system – semiannual
ITM Expected risk (yearly values) 0 $9,356 $12,770 $15,242 $17,055 $18,398 $19,339
PV of expected risk (yearly values) 0 $33,772 $73,210 $112,042 $147,273 $177,757 $203,314
ITM costs of protection system (yearly values) 0 $115,333 $115,333 $115,333 $115,333 $115,333 $115,333
PV of ITM costs (yearly values) 0 $91,232 $72,167 $57,087 $45,157 $35,721 $28,256
PVNB -$710,000 -$282,661 $42,655 $292,354 $485,361 $635,420 $752,678
Warehouse with
wireless SMART
sprinkler system –
annual ITM Expected risk (yearly values) 0 $19,720 $25,011 $29,145 $32,145 $34,365 $35,972
PV of expected risk (yearly values) 0 $15,599 $15,650 $14,426 $12,586 $10,644 $8,813
ITM costs of protection system (yearly values) 0 $110,333 $110,333 $110,333 $110,333 $110,333 $110,333
PV of ITM costs (yearly values) 0 $87,277 $69,039 $54,612 $43,200 $34,172 $27,031
PVNB -$740,000 -$331,394 -$28,140 $199,060 $371,332 $503,288 $605,229
Warehouse with
wireless SMART
sprinkler system –
semiannual ITM Expected risk (yearly values) 0 $13,248 $16,461 $19,059 $21,020 $22,508 $23,618
PV of expected risk (yearly values) 0 $10,480 $10,300 $9,434 $8,230 $6,971 $5,786
ITM costs of protection system (yearly values) 0 $120,333 $120,333 $120,333 $120,333 $120,333 $120,333
PV of ITM costs (yearly values) 0 $95,187 $75,296 $59,561 $47,115 $37,269 $29,481
PVNB -$740,000 -$351,669 -$56,357 $169,481 $343,314 $477,971 $582,793
Warehouse with
traditional wet
sprinkler system Expected risk (yearly values) 0 $5,765 $6,506 $7,113 $7,675 $8,079 $8,461
PV of expected risk (yearly values) 0 $4,560 $4,071 $3,521 $3,005 $2,502 $2,073
ITM costs of protection system (yearly values) 0 $58,333 $58,333 $58,333 $58,333 $58,333 $58,333
PV of ITM costs (yearly values) 0 $46,143 $36,501 $28,873 $22,840 $18,067 $14,291
PVNB -$280,000 $405,191 $944,872 $1,369,994 $1,705,028 $1,969,232 $2,177,699