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Reliability Prediction

Reliability Prediction. By Yair Shai. A Quest for Reliable Parameters. Goals. Compare the MTBCF & MTTCF parameters in view of complex systems engineering. Failure repair policy as the backbone for realistic MTBCF calculation.

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Reliability Prediction

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

  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. Promo : Description of Parameters t1 t2 t3 t4 t5 ....... time r =Number ofFailures  Failure Event of an Item Repairable Items: Mean Time Between Failures = Semantics ? Non Repairable Items: Mean Time To Failure =

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

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

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

  8. From System Design to Reliability Model A ANT CPU PS1 INDEPENDENT BLOCKS B ANT CONT PS2 sw x C ANT CPU PS1 x x D ANT Is this a Critical Failure ? 2 / 4 Serial model : Rs = R1x R2 Parallel model : Rs = 1- (1-R1)x(1-R2) K out of N model : Rs = Binomial Solution

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

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

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

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

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

  14. Simulation Method MONTE – CARLO MATHCAD MIN (X1,1 X2,1 X3,1) MIN (X1,1 X2,1 X3,1) MIN (X1,2 X2,2 X3,2) MIN (X1,2 Δ1,2Δ2,2) N=100,000 SETS N=100,000 SETS ……………………. ……………………. MIN (X1,N X2,N X3,N) MIN (X1,N Δ1,NΔ2,N) _________________ _________________

  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. 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 -40% X ATTENTION !!! How was it CALCULATED ???? Is this MTBCF or MTTCF ???? “Real” MTBCF = 480 < 600 (spec)

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

  18. התפלגות ווייבול זהה לכל הפריטים

  19. התפלגות ווייבול זהה לכל הפריטים

  20. התפלגות ווייבול זהה לכל הפריטים

  21. התפלגות ווייבול זהה לכל הפריטים

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

  23. Constant failure rate

  24. serial Constant failure rate parallel

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

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

  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

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