SYSTEM SAFETY ASSESSMENT RELIABILITY OF SYSTEMS AND EQUIPMENT

SYSTEM SAFETY ASSESSMENT RELIABILITY OF SYSTEMS AND EQUIPMENT

TYPES OF FAILURE : - Systematic - Non-Systematic Infant Mortality Random Wear-out WEIBULL DISTRIBUTION DORMANT (LATENT) FAILURES BOOLEAN ALGEBRA EXAMPLES

TYPES OF FAILURE SYSTEMATIC AND

Reliability of Systems & Equipment SYSTEMATIC FAILURES

Definitions DEF-STAN 00-56: Failure. The inability of a system or component to fulfil its operational requirements. Failures may be systematic or due to physical change. Systematic Event. An event that can be due to faults in the specification, design, construction, operation or maintenance of the system or its components.

Definitions Suggested Definition of Systematic Failure An undesired state of a system, that is not associated with physical degradation of a component, that results from a given set of conditions being satisfied.

Reliability of Systems & Equipment NON-SYSTEMATIC FAILURES

Non-Systematic Failures NON-SYSTEMATIC FAILURES MAY BE DIVIDED INTO THREE MAIN TYPES: INFANT MORTALITY RANDOM WEAR-OUT

Non-Systematic Failures INFANT MORTALITY FAILURES - Are usually attributable to inadequacies in manufacture, maintenance, or design. The inadequacies result in a reduction in the ability of a component, equipment, or system to survive the environment to which it is subjected. Infant mortality failures exhibit relatively high failure rates during early life.

Non-Systematic Failures RANDOM FAILURES - Are usually attributable to external occurrences. As such they are not related to the age of a component. Random Failure exhibit failure rates that are independent of component age and hence are constant with time.

Non-Systematic Failures WEAR-OUT FAILURES - Are usually attributable to a progressive deterioration of a component Wear-out failures exhibit progressively higher failure rates with component age.

Example Bath-tub Curve Failure Rate per unit time 5.E-03 4.E-03 3.E-03 2.E-03 1.E-03 0.E+00 Failure Rate variation with Time INFANT MORTALITY RANDOM FAILURES 0 1000 2000 3000 4000 5000 6000 Age - Unit Time Multiple Failure Modes WEAR OUT

An Example of a Component In-service Failure With Age Aircraft Rudder Jacks

An Example of a Component In-service Failure With Age

Failure rate variation with time THE WEIBULL DISTRIBUTION

Weibull Distribution THREE VARIABLE DISTRIBUTION P = e - η S ( β t - γ ) γ = MINIMUM LIFE η β = CHARACTERISTIC LIFE = SHAPE PARAMETER

Weibull Distribution P = e - η S WHEN γ = 0, AND β = 1 ( P = e - S ( t - γ) β η t ) η IS CONSTANT WITH TIME AND EQUAL TO THE MTBF

Weibull Distribution β = 1 RANDOM FAILURES FAILURE RATE 0.00005 0.00004 0.00003 0.00002 0.00001 0 0 20000 40000 60000 80000 100000 120000 140000 HOURS

Weibull Distribution β = 0.5 INFANT MORTALITY FAILURE RATE 0.00005 0.00004 0.00003 0.00002 0.00001 0 0 20000 40000 60000 80000 100000 120000 140000 HOURS

Weibull Distribution β = 3 WEAR OUT 0.00005 FAILURE RATE 0.00004 0.00003 0.00002 0.00001 0 0 20000 40000 60000 80000 100000 120000 140000 HOURS

Weibull Distribution 0.00007 COMBINED FAILURE MODES FAILURE RATE 0.00006 0.00005 0.00004 0.00003 0.00002 0.00001 INFANT MORTALITY RANDOM WEAR OUT ALL FAILURES BANHEIRA or BATH TUB 0 0 50000 100000 150000 200000 HOURS

UK Human Mortality Rate

UK Males Mortality Rate

Reliability of Systems & Equipment SIMPLE THEORY FOR MULTIPLE FAILURES

Simple Theory For Multiple Failures CONSIDER TWO SIMILAR CHANNELS EACH HAVING A PROBABILITY OF FAILURE OF X DURING A GIVEN TIME PERIOD T THE PROBABILITY OF BOTH FAILING DURING PERIOD T = X 2 IF THERE ARE N CHANNELS THE PROBABILITY OF FAILURE OF ALL CHANNELS DURING PERIOD T = X N

Simple Theory For Multiple Failures IF AN AIRCRAFT ELECTRICAL POWER GENERATION SYSTEM HAS n CHANNELS EACH WITH A FAILURE PROBABILITY OF X = 10-3 PER HOUR THEN ASSUMING ALL CHANNELS ARE TOTALLY INDEPENDENT THE PROBABILITY OF SINGLE CHANNEL AND TOTAL SYSTEM FAILURE IS GIVEN BY:- Number of Channels n Failure of Single Channels per Hour nx Failure of Total System per Hour (X) n 1 1x10-3 1x10-3 2 2x10-3 1x10-6 3 3x10-3 1x10-9 4 4x10-3 1x10-12

Reliability of Systems & Equipment PROBABILITY OF FAILURE DURING A GIVEN TIME PERIOD

Probability of Failure Random Failures P f = 1 - e -λt = 1 - [1 - λt + λ 2 t 2 - λ 3 t 3 +...] 2! 3! = λt - λ 2 t 2 + λ 3 t 3 -...] 2! 3! If λt is small P f λt

Probability of Failure Random Failures THE PROBABILITY OF FAILURE DURING TIME t, FOR A COMPONENT WITH FAILURE RATE λ IS GIVEN BY : λt Assumptions: Failure probabilities are small Failure rates are constant with time

Reliability of Systems & Equipment DORMANT (LATENT) FAILURES

Dormant Failures 1-e -λt

Dormant Failures 1 e λ t λ t Error at 1,000 hours approximately 5%

Dormant Failures CHECK SYSTEM AT THIS TIME P f PEAK PROBABILITY MEAN PROBABILITY T 2T 3T time

Dormant Failures Probability of two items having failed by time T one of which is dormant the other active :- λ λ T 1 2 2 = MEAN PROBABILITY PER HOUR ACTIVE FAILURE DORMANT FAILURE 34

Probability of Two Items Having Failed By Time T One of Which is Dormant the Other Active :- MEAN PROBABILITY PER HOUR = λ 1 λ 2 2 T MEAN RISK SET ORDER

Dormant Failures Probability of two items having failed by time T the first of which is dormant (but not both) approximates to :- λ λ T λ T λ 1 2 + 1 2 2 2 = λ 1 λ 2 T 36

Dormant Failures MEAN PROBABILITY PER HOUR = Probability of two items having failed by time T the first of which is dormant (but not both) approximates to :- λ 1 λ 2 = T MEAN RISK EITHER ORDER

Reliability of Systems & Equipment FURTHER EXAMPLES

Question 6.1.1 Draw a dependence diagram for a TRIPLE engine failure on a THREE-engined aircraft. 39

Question 6.1.1 E1 E2 E3 40

Question 6.1.2 Draw a dependence diagram for a DOUBLE engine failure on a THREE- engined aircraft. 41

Question 6.1.2 [1] [2] E1 E2 E1 E2 E3 E2 E1 E3 E2 [3] E1 E2 E1 E3 E1 E2 E3 E3 E3 42

Question 6.1.3 Given that the average engine failure rate is 1x10-4 per hour, calculate the probability of a double engine failure due to independent causes during a 1 hour flight. 43

Question 6.1.3 Calculate the probability of a double engine failure due to independent causes during a 1 hour flight. E1 E2 E1 E2 E3 E3 = (E1xE2) + (E2xE3) + (E1xE3) Probability for each engine =λt = (1x10-4 ) x 1 = (1x10-4 ) 2 + (1x10-4 ) 2 + (1x10-4 ) 2 = 3x10-8 / flt 44

Question 6.1.4 Given that the duration of the aircraft take-off phase is 1 minute, calculate the probability of a double engine failure during take-off. What assumption have you made regarding the probability of engine failure at take-off thrust? 45

Question 6.1.4 t Is the answer : (a) 5x10-10?; or (b) 8.3x10-12? (E1xE2) + (E2xE3) + (E1xE3) λ = (1/60 x 1x10-4 ) 2 + (1/60 x 1x10-4 ) 2 + (1/60 x 1x10-4 ) 2 = 8.3x10-12 Assumption: The probability we have used for engine failure is appropriate for the take off phase 46

Question 6.2 WINDSCREEN WASH SYSTEM B C1 C2 S1 S2 T T M1 V1 Left Screen Wash V2 Right Screen Wash M2 47

Question 6.2 B C1 C2 S1 S2 T M1 V1 Left Screen Wash V2 M2 Right Screen Wash Prob. (Loss of both Left and Right Screen Wash) = (C1 + S1 + M1 + V1)x(C2 + S2 + M2 + V2) + B + T 48

Question 6.2 Prob. (Loss of both Left and Right Screen Wash) B C1 C2 S1 S2 T M1 V1 = (C1 + S1 + M1 + V1)x(C2 + S2 + M2 + V2) + B + T Left Screen Wash V2 M2 Right Screen Wash Dependence Diagram: C1 S1 M1 V1 B T C2 S2 M2 V2 49

Question 6.3 Fire Detector A Fuse A Fire Detector B Fire Warning Lamp DC Busbar Fuse B Relevant failure rates: Failure Rate/Flt hr Loss of power from DC busbar 4 x 10-6 Fire detector failed open circuit 5 x 10-5 Fire detector failed short circuit 2 x 10-5 Fuse open circuit 1 x 10-6 Lamp filament failure 5 x 10-6 50

Question 6.3.1 Relevant failure rates: Failure Rate/flt hr Fire Detector A Fuse A Fire Detector B Fuse B DC Busbar Loss of power from DC busbar 4 x 10-6 Fire detector failed o/c 5 x 10-5 Fire detector failed s/c 2 x 10-5 Fuse open circuit 1 x 10-6 Fire Warning Lamp filament failure 5 x 10-6 Lamp Loss of fire detection capability (per flight) Loss of power from DC busbar Fuse A o/c Fuse B o/c Fire Detector A o/c Fire Detector B o/c Lamp Filament failure Prob. (Loss of fire detection capability)/flt = 4x10-6 + (1x10-6 + 5x10-5 )(1x10-6 + 5x10-5 ) + 5x10-6 = 9x10-6 51

Question 6.3 Fire Detector A Fuse A Fire Detector B Fire Warning Lamp Fuse B Relevant failure rates: Failure Rate/flt hr DC Busbar Loss of power from DC busbar 4 x 10-6 Fire detector failed o/c 5 x 10-5 Fire detector failed s/c 2 x 10-5 Fuse open circuit 1 x 10-6 Lamp filament failure 5 x 10-6 52

Question 6.3.2 Relevant failure rates: Failure Rate/flt hr Fire Detector A Loss of power from DC busbar 4 x 10-6 Fuse A Fuse B Fire Detector B Fire Warning Lamp Fire detector failed o/c 5 x 10-5 Fire detector failed s/c 2 x 10-5 Fuse open circuit 1 x 10-6 DC Busbar Lamp filament failure 5 x 10-6 Fire Detector A s/c Fire Detector B s/c Prob. (False fire warning due to system malfunction)/flt = 2x10-5 + 2x10-5 = 4x10-5 53

Question 6.3.1 and 6.3.2 Fire Detector A Fuse A Fire Detector B Fire Warning Lamp ONE SYSTEM BUT TWO DEPENDENCE DIAGRAMS DC Busbar Fuse B Loss of fire detection capability Fuse A o/c Detector A o/c Loss DC busbar Lamp Filament failure Fuse B o/c Detector B o/c False fire warning Fire Detector A s/c Fire Detector B s/c The SYSTEM DIAGRAM describes the OPERATIONAL logic. The DEPENDENCE DIAGRAM describes the FAULT logic. 54

Question 6.3.3 Loss of Fire Detection Capability prior to Maintenance Check at Time T Dependence Diagram Fuse A o/c Fire Detector A o/c Loss of power from DC busbar Lamp Filament failure Fuse B o/c Fire Detector B o/c 55

Question 6.3.3 Loss of Fire Detection Capability prior to Maintenance Check at Time T Fuse A o/c Fire Detector A o/c Loss of power from DC busbar Lamp Filament failure Fuse B o/c Fire Detector B o/c Probability of loss of fire detection capability/flight. = 4x10-6 + (1x10-6 + 5x10-5 )(1x10-6 + 5x10-5 )T + 5x10-6 = 4x10-6 + (51x10-6 )(51x10-6 )T + 5x10-6 = 9x10-6 + 2.6x10-9 T and if T = 1000 = 9x10-6 + 2.6x10-6 Probability = 11.6 x10-6 = 1.16 x10-5 per flight 56

Useful References and Data Sources 1.UK Ministry of Defence, Safety Management Requirements for Defence Systems, Issue 1, DEF-STAN-00-56, United Kingdom Author. 2.M.J. Moroney, Facts from Figures, UK Penguin Books. 3.A.D.S. Carter, Mechanical Reliability, 2nd Edition, 1986, UK Macmillan Education Ltd. 4.United States of America Department of Defense, Military Handbook Reliability of Electronic Equipment, MIL-HDBK-217F, 2 December 1991, United States of America Author. 5.The UK Central Statistical Office, Annual Abstract of Statistics, 1991, United Kingdom Author. 6.The UK Central Statistical Office, Social Trends 21, 1991, United Kingdom Author. 57