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BSE Public CPD Lecture – Alternative Water Suppression Systems for Tall Atria Organized by the Department of Building Services Engineering, a public CPD lecture delivered by Professor W.K. Chow and Dr. N.K. Fong on Alternative Water Suppression Systems for Tall Atria was held on 20 March 2010 (Saturday). Over 50 participants have attended the lecture. Powerpoint files of the CPD lecture Powerpoint files of the CPD lecture Water suppression systems are commonly used in active fire protection strategy for shopping malls with or without an atrium. Because of the high headroom in an atrium, it is difficult to activate a sprinkler under a low level fire. The atrium floor is often used for temporary exhibitions, sales or performance shows. There will be high transient occupant loadings. Large amounts of combustibles used to be placed in there. Flooding the atrium floor with excess water discharged from a sprinkler would affect evacuation and cause serious property damage. Alternative water systems are proposed and used in shopping malls with atrium. In the lecture, Professor Chow delivered an informative presentation on two of alternative water systems, water gun and longthrow sprinkler. He also explained these two with his example research projects and experiments in collaboration with institutions in Mainland China. Reliability of sprinkler system was then presented by Dr. Fong. Presentation Participants

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BSE Public CPD Lecture – Alternative Water Suppression Systems for Tall Atria Organized by the Department of Building Services Engineering, a public CPD lecture delivered by

Professor W.K. Chow and Dr. N.K. Fong on Alternative Water Suppression Systems for Tall Atria

was held on 20 March 2010 (Saturday). Over 50 participants have attended the lecture.

Powerpoint files of the CPD lecture

Powerpoint files of the CPD lecture

Water suppression systems are commonly used in active fire protection strategy for shopping malls

with or without an atrium. Because of the high headroom in an atrium, it is difficult to activate a

sprinkler under a low level fire. The atrium floor is often used for temporary exhibitions, sales or

performance shows. There will be high transient occupant loadings. Large amounts of

combustibles used to be placed in there. Flooding the atrium floor with excess water discharged

from a sprinkler would affect evacuation and cause serious property damage. Alternative water

systems are proposed and used in shopping malls with atrium.

In the lecture, Professor Chow delivered an informative presentation on two of alternative water

systems, water gun and longthrow sprinkler. He also explained these two with his example

research projects and experiments in collaboration with institutions in Mainland China. Reliability of

sprinkler system was then presented by Dr. Fong.

Presentation Participants

CPD Lecture:“Alternative Water Suppression Systems for Tall Atria”

Professor W.K. ChowChair Professor of Architectural Science and Fire EngineeringDirector, Research Centre for Fire EngineeringHead of Department, Department of Building Services EngineeringLeader, Area of Strength: Fire Safety Engineering The Hong Kong Polytechnic University, Hong Kong, ChinaFounding President, Society of Fire Protection Engineers - Hong Kong ChapterPresident, Asia-Oceania Association for Fire Science and Technology

20 March 2010CPDWSS2010.ppt

2

Part 1: Introduction Water Gun An Example Project with Water Gun Research Partners on Water GunCoffee Break

Part 2: Sidewall Long-Throw Sprinklers at Height Nominal Discharge Density The Water Coverage Test at Harbin Conclusions

Topics Covered

3

Tsim Sha Tsui East (TSTE)

1. Introduction Atriums are commonly built in big buildings in the Far

East since the development of Tsimshatsui East in HongKong in the early 1980s.

4

HONG KONG

KOWLOON

NEW TERRITORIES

Hong Kong Int’l Airport

Lantau Island

Since then, tall atriums up to 100 m are found inshopping malls, banks, public transport terminals andmulti-purpose complexes in other big cities.

5

There are many reasons why such atriums weredesigned.

For example, giving a better view, providing space fornatural ventilation, utilization of daylighting and usingas a public access and gathering area.

Mega Box

6

But the most important reason is to keep the ‘plot arearatio’ low.

The value of this ratio is important in urban planningin densely populated cities while determining theusable area by the Authority.

In some atriums, the space used to be crowded withpeople.

Therefore, fire safety is a concern and smokeextraction system is identified to be an essential fireservice installation in atriums with a big space volume,say over 28,000 m3 in Hong Kong.

7

Many combustibles are placed in the floor level, or inspaces adjacent to the atrium void with ‘open’ designs.

Combustibles Combustibles

(b) Foam furniture

Combustibles: Big hall of the airport terminal

(a) Restaurant

8

Combustibles: Catering service in the atrium of a mall

9

Design fire is the most important factor in sizing both thedynamic and static smoke exhaust systems.

The heat release rate of the fire can grow up to high valuesat a very fast rate when the atrium floor is full ofcombustibles.

Recent Swedish full-scale burning tests on burning potatocrisps showed that the heat release rate is up to 6 MW.

2.5 minutes Fully-developed

10

2 minutes Heat release rate

Swedish Work onPotato crisps and cheese

nibbles burn fiercely

11

Firefighting against post-flashover big firesis a threat.

- Texaco Road fire, May 2007.

- Castle Peak Road fire, March 2010.

Post-flashover Big Fire

Particularly, no sprinkler or the system isnot working.

12

Industrial building on Texaco Road, Tsuen Wan May 2007

Oriental Daily (May 23, 2007)

13

Lai Cheong Factory Building on Castle Peak RoadMarch 2010

The Standard (March 9, 2010)

14

Understanding on the environment in post-flashover big fire is limited.

Need more researches on post-flashover fire.

Full-scale burning tests required.(Burning money, resources required !)

Suppression is necessary to control the heatrelease rate to a low value, say below 5 MW.

15

Necessary to install fire suppression system.

Hea

t rel

ease

rate

Extinguishment

Control

Uncontrolled fire

Suppression

Time

Operating the active protection system

Another possibility

16

A common design in the past 20 years is to install automaticsprinkler systems at the high headroom ceiling.

There are concerns on the possible big fire size in activatingthe sprinkler head.

(Difficult to activate the sprinkler head except high

Heat Release Rate, But useless! )

Atrium Sprinkler

Still burning even if there is a sprinkler operating.

Control or Suppression, not extinguishment.

17

Appropriate fire suppression systems must beinstalled to control the fire.

2 systems will be introduced in this talk.

- Water gun

- Sidewall sprinkler at height

18

2. Water Gun

19

There are three parts in a water gun:

- A system based on optical section detectiontechnology.

- The dual wavelength detector.

- The water gun.

Information reported from:C.L. Chow, W.K. Chow & H.Y. Yuan, “A preliminary discussion on selecting active fire protection systems for atria in green or sustainable buildings”, Architectural Science Review, Vol. 47, No. 3, p. 229-236 (2004).

20

The optical detection technology is based on the fact that theoptical intensity of incident light will be attenuated whenthere are aerosols, vapour, dust and other fine particles.

There are emitters and receivers operating continuously togive an optical sectional plane for smoke detection.

The light section emitters (infrared illuminators) would emitinfrared beams to the receivers.

If the receivers cannot receive infrared beams due toattenuation of aerosols, vapour, dust or fine particles,reduction in optical intensity will be fedback to a computer.

2.1 Optical Detection

21

The dual wavelength detector would be operatedautomatically to search for the wave emitted from theburning object.

A primary information processor was developed toanalyze the recorded signals.

Whether the attenuation is due to smoke or fineparticles generated from other activities would bedecided by the developed software.

This processor would also determine the kind of fire.

2.2 Dual Wavelength Detector

22

The water flow rate and operating pressure headrequired for the water gun are then calculatedautomatically.

The pump set would then be started up by the controlpanel to discharge water for fire fighting.

2.3 Water Gun

The design of the pump and water distribution system should be based on full-scale burning tests.

23

3. An Example Project with Water GunGlazing

2/F

3/F

R/F

1/F

G/F

29 m diameter

31 m diameter

33 m diameter

27 m diameter

35 m diameter

(a) Isometric view

5 m

5 m

5 m

5 m

5 m

Atrium void

Adjacent shops

Water gun

Dual wavelength detectors

Optical plane

4 m

12 m

Glazing

5 m

(b) Elevation

30 m

24

Proper distribution of the emitters and receivers isimportant to ensure that the entire protected area will becovered.

In the example shopping mall, an optical plane is formed bytwo light section emitters and eight light section receiversinstalled at 4 m above the floor level of G/F.

Receiver R

Emitter E

RR

R

R

RR

RR

R

E

E

Positions of the optical section emitters and receivers at G/F

3.1 Optical Detection

25

There are three dual wavelength detectors at a height 12 mabove the floor level.

Dual wavelength detector

Positions of the dual wavelength detectors

3.2 Dual Wavelength Detector

26

The water gun is installed at 2/F at a height 15 m above thefloor level.

The water gun

Water gun

(a) Location (b) Pictorial view

3.3 Water Gun

27

For protecting the atrium, the design maximum flowrate of the system is 20 L/s.

Different water operating flow rates would beestimated by the control panel itself.

There are two pumps, one for duty and the other asstandby, in the pump set.

The maximum supply head of the pumps would be98.7 m head.

As the covering radius of the water gun is 50 m, onlyone gun is required.

28

The dual wavelength detector is for flame recognition.

Colour and infrared video images taken will be analyzed bythe image processing technique.

Flame characteristics of the fire such as:

- flame temperature varying from 900 to 1400oC; giving offelectromagnetic wavelength from visible light to infra red;fluctuating area increasing with frequency of 3 to 30 Hz;

- flaming area increasing if there is a real fire;

- and colour used to be yellow, red or white, not green norblue, are used to develop the decision logic of the software forflame recognition.

29

In this system, image segmentation, colourdifference, differences between images, irregularedges, flickering.

Flame movement will be investigated to decidewhether it is a real fire.

If there is a real fire, the size, type and location ofthe fire will be determined so that the water guncan target at it.

30

There are two parts in the water gun:

- The first part is the gun unit itself including thewater gun, a motor, an electromagnetic valve, amanual controller and a Charge Coupled Device(CCD) video camera.

- The second part is a host computer, data samplinginterface and communication interface. The watergun serves as both a fire searching and firesuppressing device, in conjunction with the firedetection system.

31

Once a fire is detected, a signal will be sent to thecentral control unit for sounding the alarm andactuating it to be ready for action.

The CCD video camera is placed above the water guntube with its axis adjusted parallel to the axis of thegun tube.

The maximum detection distance for the CCD videocamera is 100 m.

The maximum distance covered by the water gun is 50m.

32Hong Kong 香港

Chongqing 重慶

Harbin 哈爾濱

Beijing 北京

Shenyang 瀋陽

Langfang 廊坊

Xi’an 西安Hefei 合肥

Hangzhou 杭州

Kaohsiung 高雄

Taipei 台北

4. Research Partners on Water Gun

33

University of Science and Technology of China

USTC

Research staff State Key Laboratory of Fire Science

34

Example on determining water pressure and flow rate

A product development site at Hefei, Anhui, China

Water gun on fire

35

36

37

38

39

The hall Professor Wu Longbiao吳龍標

40

Another possible candidate is sidewall long-throwsprinklers.

5. Sidewall Long-Throw Sprinklers at Height

Reference: W.K. Chow, Y. Gao, G.W. Zou & H. Dong, “Performance evaluation of sidewall long-throw sprinklers at height”, 9th AIAA/ASME Joint Thermophysics and Heat Transfer Conference, 5-8 June 2006, San Francisco, California, USA, Paper AIAA-2006-3288 presented (2006).

41

Smoke

Water spray

Long-throw sidewall sprinkler

Fire

Water collection

Water spraySprinkler nozzle

Water discharged in a test

IR Detector

8 m

42

As the sprinkler head for this design is notimmersed in a smoke reservoir as in normalsprinkler systems, it will be activated by the firedetection system.

Once a fire is detected, it will act at the fire directly,instead of cooling the smoke layer.

In this way, the fire can be controlled at a certainsize.

It was demonstrated to work up to 3 m high.

Water discharged would not act at the hot glassenvelope.

43

A Project:

Provide sufficient water coverage at 3 m height to a range,up to 8 m

Water discharged

8 mRange

Height 3 m

44

Sidewall long-throw sprinklers had been installed atheight up to 14.5 m.

Tests to demonstrate the water coverage at floor.

Whether the discharged sprinkler water spray cancontrol a testing wood crib fire will also bedemonstrated.

Water would be discharged to long distances up to 8 mfrom the wall.

Another project

45

The sidewall long-throw sprinkler is regarded by thelocal Authority as a new design to atrium space,especially when it is installed at height of 14.5 m.

Water distribution at the floor level has to comply withthe Loss Prevention Council (LPC) rules in the UnitedKingdom, UK.

However, field data on heights up to 14.5 m is notavailable in the literature.

Tests for evaluating the performance of sidewall long-throw sprinkler installed at height will be reported.

46

Sprinklers are commonly installed in buildings forcontrolling fire.

Upon actuation, water would be discharged from thesprinkler head.

The amount of water received at the floor level isimportant and should satisfy the specified requirements.

An important design parameter, the design density of thewater spray is specified clearly in the design guides suchas the Loss Prevention Council (LPC) rules.

The value should be adequate in the Assumed MaximumArea of Operations (AMAO), say 5 mm/min, for asprinkler system of Ordinary Hazard (OH) class inshopping malls.

6. Nominal Discharge Density

47

The water discharge density specified by the nominaldischarge density NDD (in mm/min) is applied to agroup of sprinklers, rather than a single sprinkler onthe mass flux density.

In field measurement, NDD is a measure of thedistribution of water flux varying along the radialdistance and circumference of two long-throwsprinklers mounted in radial formation.

This is the operating characteristic of two long-throwsprinklers covering the same area where the containerarea is fixed.

48

NDD (in mm/min) is given by the water flow rate intothe protected area Qf (in L/min) derived by the area ofcoverage under consideration Ac (in m2):

NDD can be deduced from the water application raterequired for a particular fire load.

Heat removal rate = Flow rate × Latent heat ofvaporization.

c

f

AQ

NDD =

49

The minimum water flow rate for each sprinkler is 131L/min.

The minimum water pressure is 2 bar.

Not more than 10% of the protected area has a waterdischarge density less than 1.125 mm/min.

The minimum average water discharge density is 5mm/min.

The testing criteria for a system classified as Ordinary Hazard Group III (OH III) under LPC Rules in UK are summarized as:

50

Field measurements were carried out in a small townLanxi in Harbin, Heilongjiang, China.

A test rig was constructed with a pair of sidewall long-throw sprinklers installed at height of 14.5 m to carry outfield tests.

The protected area of 20 m2 of length 8 m and width 2.5 m atground level as specified in LPC rules was set up in atemporary hall with adequate ceiling height.

7. The Water Coverage Test at Harbin

51

Hong Kong 香港

Chongqing 重慶

Harbin 哈爾濱

Beijing 北京

Shenyang 瀋陽

Langfang 廊坊

Xi’an 西安Hefei 合肥

Hangzhou 杭州

Our Partners

Kaohsiung 高雄

Taipei 台北

黑龍江省

Harbin 哈爾濱市

Lanxi 蘭西

Heilongjiang Province

呼蘭河之西 Harbin

53

Experimental rig

12 m

16 m

1.5 m

12 m

Sprinkler pipe

Protected area 20 m2

(8 m x 2.5 m)Water inlet

To branch pair at 14.5 m

(a) The rig

(c) Long-throw sprinkler nozzle

(d) The branch pair

NozzleFlow meter

Branch pipe

(b) A photograph of the site

54

Sprinkler pumps with a frequency inverter were set up sothat the operating pressure and flow rate at the nozzle couldbe adjusted.

Such water supply and pump would give a discharge rateof 5 mm/min at each sprinkler head and providesufficient water for a 10-minute discharge test.

The supply tank size was 2.5 m by 2 m by 1.5 m (height).

Sprinkler pumps and control would give water pressurevaried from 2 to 5 bar.

The supply flow rate was adjusted to give a minimum valueof 131 L/min for each sprinkler head.

The collection containers were arranged in the protectedarea 20 m2 (8 m by 2.5 m).

55

96 (16 x 6) Water container (0.5 m x 0.5 m)

Centerline of sprinkler spray

Centerline of sprinkler spray

8 m

2.5 m

2.5 m

2.5 m

Sprinkler nozzle

Sprinkler nozzle

The water discharge density received in the protectedarea was measured by 96 water collection containers ofsize 0.5 m (L) x 0.5 m (W) x 0.5 m (H).

56

Three tests were performed.

– Test 1: Pressure 0.31 MPa; flow rate 16.6 m3/h(or 277 L/min).

– Test 2: Pressure 0.31 MPa; flow rate 16.7 m3/h(or 278 L/min).

– Test 3: Pressure 0.31 MPa; flow rate 16.7 m3/h(or 278 L/min).

The results were then assessed for compliance with thedesign guides, in satisfying the code requirement on waterdischarge density.

57

The water supply was kept discharging for 10 minutes.

The volume of water distributed over themeasurement area was measured to determine thecollected water level in each bucket.

After discharging water in each test, the volume ofwater received at each cubic container was measuredby determining the collected water level.

Based on the test data, the water discharge density ofthe measuring area was calculated with typical resultfor Test 1 shown in the following table.

58

Measured NDD for Test 1

1.79 2.54 3.38 4.20 4.16 3.72 2.78 3.96 4.18 5.46 5.22 4.70 3.53 4.77 5.51 5.88 5.66 4.85 4.21 5.36 6.20 6.40 6.08 4.93 4.49 5.48 6.68 7.20 6.18 4.86 4.37 6.16 7.22 7.20 6.92 5.18 4.45 6.22 7.24 7.80 6.98 5.98 4.23 5.80 7.05 7.88 7.90 6.64 3.91 5.46 6.86 7.87 7.90 6.96 3.66 5.15 6.40 7.46 7.82 6.79 3.44 4.55 5.82 6.93 7.26 6.86 3.22 4.04 5.11 6.10 6.72 6.45 2.99 3.64 4.41 5.15 5.84 5.90 2.90 3.38 3.97 4.46 4.67 5.11 2.89 3.36 3.83 4.06 4.46 4.34

Total

55.54 73.09 87.51 98.21 97.96 87.12 Average NDD 499.42 mm/min ÷ 96 = 5.20 mm/min > 5 mm/min

Area ratio less than 1.125 mm/min: 0 ÷ 155 = 0% < 10%

Sprinkler Sprinkler

59

A summary of the test results is:

– The proposed protected area 20 m2 (8 m by 2.5 m)received an average NDD above 5 mm/min.

– None of the proposed protected area received waterless than 1.125 mm/min.

It is observed that in each protected area, the followingLPC criteria are satisfied for sprinklers installed at such aheight of 14.5 m under a flow rate of 270 L/min.

60

A wood crib of 20 kg ignited by a 0.6 m diameterpool fire with 1 litre gasoline was tested.

Sprinkler water pressure was 0.31 MPa and flowrate 16.5 m3hr-1.

Water discharged at 4 min 33 s.

The fire was extinguished at 7 min 40 s.

Wood Crib Fire

61

Wood crib fire

(a) The crib (b) Action of sprinkler

62

Atrium floor has to be properly protected.

An accidental fire, if occurred, can becontrolled at a certain value.

2 new water fire suppression systems arediscussed.

8. Conclusions

63

Sidewall long-throw sprinkler had beeninstalled at height up to 14.5 m.

Water discharged for appropriate designwill still give adequate NDD to satisfy theLPC criteria.

Can control fire up to a certain size.

Assessment of sprinkler reliability:

Works reported in the literature.

64

Sprinkler will perform 4 functions, at least

- Detection

- Alarm

- Activation

- Suppression

Failures of components must be studied thoroughlyby including all the above 4 functions.

There are some preliminary studies.

Reliability of Sprinkler System

65

Works reported by Koffel (2005)

The Alliance for Fire and Smoke Containment and Control

http://afscc.org/ReliabilityofSprinklerSystems.html

66

67

68

Water gun is an ‘equipment’, might not beaccepted as a ‘Fire Service Installation’.Need strong justification by scientificresearch.

Reliability to watch.

But how?

Anything reported?

69

C.L. Chow, W.K. Chow & H.Y. Yuan, “A preliminarydiscussion on selecting active fire protection systems for atriain green or sustainable buildings”, Architectural ScienceReview, Vol. 47, No. 3, p. 229-236 (2004).

W.K. Chow, Y. Gao, G.W. Zou & H. Dong, “Performanceevaluation of sidewall long-throw sprinklers at height”, 9thAIAA/ASME Joint Thermophysics and Heat TransferConference, 5-8 June 2006, San Francisco, California, USA,Paper AIAA-2006-3288 presented (2006).

Two Key References Attached:

1

Reliability of Sprinkler System

Dr. N.K. FongDepartment of Building Services EngineeringThe Hong Kong Polytechnic UniversityHong Kong, China

2

Sprinkler SystemDifferent components Hazard classification Sprinkler heads

Type, spacing and location Piping arrangement Water source Power Special requirement

Highrise building special ceiling configuration beam etc.

3

Sprinklers Failure

www.nfpa.org/assets/files/PDF/OSsprinklers.pdf US experience with sprinklers and other automatic fire extinguishing equipment by John R. Hall Jr.

4

Sprinkler headsTwo modes of failure are possible with sprinklers:complete failure – failure of the sprinkler to release water, andpartial failure – water is released but is not distributed in the intended pattern. In this paper, the former is the main concern and the reasons leading to complete failure may include:

5

cracks in the bulb allowing the liquid to escape. The remaining liquid cannot expand sufficiently to fracture the bulb;a strut of glass from the bulb holding the valve assembly in position after the bulb has burst;failure of the valve assembly to release due to corrosion or the gasket being too tight in the orifice;minor water leakage (or slow weep) from the valve assembly cooling the bulb, when affected by heat, causing either complete failure of the bulb to burst, or failure to burst at the correct temperature;Corrosion of heat collector of soldered type sprinklers affects the sensitivity of the heat sensing element.

Omega sprinkler heads a line manufactured by the Central Sprinkler Company have failed to activate in several fires. Swelling of the rubber “O-Ring” in the sprinkler head has been identified as the problem’s cause.

6

ValvesThere are several types of valves installed in a sprinkler system including gate valve, check valve, subsidiary valve and alarm valve set. The major failure of gate valves and subsidiary valves is the valves being shut. The possible reasons include valve defective or leaking, system under repair or being altered. Water supplyThe lack of water supply will mostly due to closed valves. Other unavoidable and unusual reasons may include interruption of water supply as a result of an explosion or through earthquake damage.

7

PipeworkThe most common failure of pipework is blockage due to entry of debris.

Microbiologically Influenced Corrosion (MIC).

http://www.fpemag.com/archives/article.asp?issue_id=27&i=176

8

OthersOther possible causes of system shutdown or failure include defective equipment, antiquated systems, substandard sprinkler design and inadequate maintenance.Human errors like not restoring the system to full operation following a fire or testing are also common reasons.

9

Care, Maintenance and Inspection of sprinkler systems

Basic Principles of maintenance and inspection( NFPA, Fire Protection Handbook 17th Edition)

1) sprinkler protection is complete in the area of protection2) no obstruction - avoid situation inhibit the distribution of water discharge from the sprinklers3) constant water supply4) no opportunity for the sprinklers to freeze5) all devices forming a part of sprinkler system, alarm, supervisory systems, or water supply are in dependable operating condition

10

Reliability

The ability of an item to operate can be designated Deterministically probabilistically (through a probability) used to quantitatively measure the reliability of an

item treats reliability as the conditional probability of the

successful achievement of an item’s intended function (with given designated conditions)

11

Tools for Sprinkler Reliability Studies

1. Reliability block diagram methods for series, parallel, standby, share load and

complex systems2. Logic Tree methods fault tree method success tree method event tree method master plant logic diagram

12

Example of Fault Trees

No water for sprinkler system

Pumps not working

OR gate

No water from main 2

No water from main 1

AND gate

13

Example of Event Trees

Fail

Site power Voltagemonitor

Dieselgenerator

operate

Fail

operate SprinklerSystem operate

System failureFail

System failure

14

Reliability Study of Sprinkler System

One of the reliability parameters needed to be considered for sprinkler system is Availability The probability that a system is available for use at a

given timeA fraction of time that a system is in an operational

state

15

Example: Idealized periodic testing and repair for unrevealed failures

Avai

labi

lity

A(t)

0

1

T0 2T0 3T0 4T0

t

16

Unrevealed Failures of Sprinkler System

For a system is not in continuous operation, failures may occur but remain uncovered.For backup or other emergency equipment (e.g. pumps)The primary loss of availability may be due to failures in the standby mode Not detected until an attempt is made to use the system

Use periodic testing can due with these classes of failuresBesides, the standby components can be analyzed by Markov methodUsed to study many component failure interaction

17

Example: Use Markov method to study Reliability with standby systems

1

3

4

2

λa

λb

( ) ( )tPtPdtd

a 11 λ−=For state 1From 12

For state 2From 24

( ) ( ) ( )tPtPtPdtd

ba 212 λλ −=

( ) ( )tPtPdtd

b 24 λ=

( ) ( ) tettR λλ −+= 1( ) ( ) ( ) ( ) ( )tPtPtRtPtRlComponentOperationai

i 21 +=⇒= ∑∈ If λa = λb=λ

Solve for P1, P2

System failure

Primary unit failure

backup unit failure

18

References

Maintainability, Availability & Operational Readiness Engineering by Dimitri Kececigolu, Prentice Hall

Reliability by Mohammad Modarres and Francisco Joglar-Billoch, The SFPE Handbook of Fire Protection Engineering, Section 5 / Chapter 3, NFPA 3rd ed., p.5-24

Introduction to reliability Engineering by E.E. Lewis, John Wiley &Sons, 1987

Uncertainty by K.A. Notarianni, The SFPE Handbook of Fire Protection Engineering, Section 5 / Chapter 4, NFPA 3rd ed., p.5-40