1. 1 Reliability Prediction A Quest for Reliable Parameters By Yair Shai

2. 2 Goals Compare the MTBCF & MTTCF parameters in view of complex systems engineering. Failure repair policy as the backbone for realistic MTBCF calculation. Motivation for modification of the technical specification requirements.

3. 3 Promo : Description of Parameters timet1t2t3t4t5.......  Failure Event of an Item Repairable Items: M ean T ime B etween F ailures = Non Repairable Items: M ean T ime T o F ailure = r =Number of Failures Semantics ?

4. 4 MTBF = MTTF ?? An assumption: Failed item returns to “As Good As New” status after repair or renewal. note: Time To Repair is not considered. UP DOWN TIME

5. 5 Critical Failures Moving towards System Design A System Failure resulting in (temporary or permanent) Mission Termination. COMPUTER SUBSYSTEM A simple configuration of parallel hot Redundancy. A Failure: any computer failure A Critical Failure: two computers failed X X

6. 6 Critical Failures A clue for Design Architecture MTBCF Mean Time Between Critical Failures MTTCF Mean Time To Critical Failure SAME? Remember the assumptions Determining the failure repair policy: COLD REPAIR No time for repair actions during the mission

7. 7 Functional System Design Operational Demand: At least two receiver units and one antenna should work to operate the system. CPU POWER SUPPLY POWER SUPPLY 4 CHANNEL RECEVER CONTROLER UNIT A UNIT B UNIT C UNIT D POWER SUPPLY ANTENA 2 / 4 sw Switch control

8. 8 From System Design to Reliability Model Serial model : Rs = R1x R2 Parallel model : Rs = 1- (1-R1)x(1-R2) K out of N model : Rs = Binomial Solution CPUPS1 CPUPS1 CONTPS2 A B C D 2 / 4 x x x ANT sw Is this a Critical Failure ? INDEPENDENT BLOCKS

9. 9 From RBD Logic Diagram to Reliability Function R sys (t)= f( serial / parallel / K out of N) Classic parameter evaluation : WARNING !!! After each repair of a critical failure - The whole system returns to status “As Good As New”. Is this realistic ? Simple mathematical manipulation : MTTCFMTBCF [ S.Zacks, Springer-Verlag 1991, Introduction To Reliability Analysis, Par 3.5]

10. 10 Realistic interpretation : MTBCF = MTTCF Only failed Items which cause the failure are repaired to idle. All other components keep on aging. MTBCF vs. MTTCF A New Interpretation Common practice interpretation : MTBCF = MTTCF = MTTCFF Each repair “Resets” the time count to idle status (or) Each failure is the first failure. First

11. 11 Presentation I TTCF 2 3 1 2 3 1 3 1 2 1 2 3 1 2 ABC HAD WE KNOWN THE FUTURE… Simple 3 aging components serial system model A B C

12. 12 Presentation II Simple 3 aging components serial system model ABC TBCF 1 1 1 3 2 2 32 3 4 HAD WE KNOWN THE FUTURE… 4 A B C

13. 13 Presentation III Simple 3 aging components serial system model ABC A B C TBCF 1 1 1 3 2 2 32 3 4 A B C TTCF 2 3 1 2 3 1 3 1 2 HAD WE KNOWN THE FUTURE… 1 4 2 3 1 2 MTBCF < MTTCF

14. 14 Simulation Method MONTE – CARLO MATHCAD N=100,000 SETS MIN (X 1,1 X 2,1 X 3,1 ) MIN (X 1,2 X 2,2 X 3,2 ) ……………………. MIN (X 1,N X 2,N X 3,N ) _________________ N=100,000 SETS MIN (X 1,1 X 2,1 X 3,1 ) MIN (X 1,2 Δ 1,2 Δ 2,2 ) ……………………. MIN (X 1,N Δ 1,N Δ 2,N ) _________________

15. 15 How “BIG” is the Difference ? 1. Depends on the System Architecture. 2. Depends on the Time-To-Failure distribution of each component. 3. The difference in a specific complex electronic system was found to be ~40% Note: True in redundant systems even when all components have constant failure rates.

16. 16 Why Does It Matter ? Suppose a specification demand for a system’s reliability : MTBCF = 600 hour Suppose the manufacturer prediction of the parameter: MTBCF = 780 hour ATTENTION !!! How was it CALCULATED ???? Is this MTBCF or MTTCF ???? X -40% “Real” MTBCF = 480 < 600 (spec)

17. 17 Example 1 Aging serial system – each component is weibull distributed

18. 18 התפלגות ווייבול זהה לכל הפריטים

19. 19 התפלגות ווייבול זהה לכל הפריטים

20. 20 התפלגות ווייבול זהה לכל הפריטים

21. 21 התפלגות ווייבול זהה לכל הפריטים

22. 22 Example 2 Two redundant subsystems in series – each component is exponentially distributed

23. 23 Constant failure rate

24. 24 serial parallel Constant failure rate

25. 25 A Comment about Asymptotic Availability (*) (*) [ S.Zacks, Springer-Verlag 1991, Introduction To Reliability Analysis, Par 4.3]

26. 26 Repair policies 1.“Hot repair” is allowed for redundant components. 2.All components are renewed on every failure event. 3.All failed components are renewed on every failure event. 4.Failed components are renewed only in blocks which caused the system failure. 5.Failed subsystems are only partially renewed.

27. 27 Conclusions System configuration and distribution of components determine the gap. Repair policy should be specified in advance to determine calculation method. Flexible software solutions are needed to simulate real MTBCF for a given RBD. Predict MTBCF not MTTCF