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Real Time Systems

Real Time Systems. Reliability Exercise Solution. Exercise - System Components. Consider an EW system made up of the following components: 2 touch displays, only one of which need function for the system to function each touch display contains identical software

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Real Time Systems

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  1. Real Time Systems Reliability Exercise Solution

  2. Exercise - System Components • Consider an EW system made up of the following components: • 2 touch displays, only one of which need function for the system to function • each touch display contains identical software • one system processor and the system integration software • an ECM with embedded jammer software • Assume that all hardware utilization is 100% • in other words all hardware functions for the entire mission duration RMC - Maj RW Smith Reliability Exercise Solution - 2

  3. Exercise - Component Data RMC - Maj RW Smith Reliability Exercise Solution - 3

  4. Exercise - Questions • a) Determine the overall system reliability for a 4 hour mission? • b) What is the probability of having at least one functional display for a 2 hour mission? • c) What is the weakest link in the system? What could be done to improve the overall system reliability (assuming that you can not significantly change the component reliabilities without serious redesign). Draw the new reliability block diagram and find Rsys RMC - Maj RW Smith Reliability Exercise Solution - 4

  5. Exercise - Questions (continued) • Assume that we now have 4 equivalent ECM subsystems (combined hardware and software) and that for the system to be functional any 3 of the 4 must be functional. • d) Draw the new reliability block diagram and calculate the system reliability. RMC - Maj RW Smith Reliability Exercise Solution - 5

  6. Exercise part a - Solution (1) • recall that for execution time base failure rates you must convert to calendar time using t = c  therefore TDs,t = c TDs, = (0.65)(.002) = 0.0013 and RTDs (t= 4 hrs) = e-(.0013)(4) = 0.995 similarly SPs,t = 0.0095, RSPs (t= 4 hrs) = 0.963 ECMs,t = 0.0042, RSPs (t= 4 hrs) = 0.983 RMC - Maj RW Smith Reliability Exercise Solution - 6

  7. Exercise part a - Solution (2) • now draw the reliability block diagram: therefore RSys = (1-(1-.95)2)(.995)(.98)(.963)(.925)(.983) TDh TDs SPh SPs ECMh ECMs TDh Note: The touch display software is not redundant. RMC - Maj RW Smith Reliability Exercise Solution - 7

  8. Exercise part b - Solution • recall that = - ln( R(t=T)) / T therefore TDh = -ln (R(t=4)) / 4 = 0.00125 and RTDh (t= 2 hrs) = e-(.00125)(2) = 0.9975 RTDs (t= 2 hrs) = e-(.0013)(2) = 0.9974 giving RSys (t= 2 hrs) = (1 - (1-.9975)2) (.9974) = 99.74% RMC - Maj RW Smith Reliability Exercise Solution - 8

  9. Exercise part c - Solution • the weakest link is the ECM hardware • adding a redundant ECM hardware component is the easiest solution for increasing system reliability (probably not the cheapest though) first ECMh = -ln (.925) / 4 = 0.0195 and with a redundant ECM h/w component RSys(4 hrs) = (1-(1-.95)2)(.995)(.98)(.963)(1-(1-.925)2))(.983) = 91.6% (vice the original 85.2%) RMC - Maj RW Smith Reliability Exercise Solution - 9

  10. Exercise part d - Solution • recalling the “k out of n” formula gives RECMh (t= 4 hrs) = [ ] RECMh3 (1-RECMh) + RECMh4 = 4(.925)3 (.075) + (.925)4 = 0.9695 plugging back into system reliability equation gives RSys = 89.3% 4 3 RMC - Maj RW Smith Reliability Exercise Solution - 10

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