Our assumption that the coverage probability is a given number is often unjus-tified in

Chapter 8, Problem 12

(choose chapter or problem)

Our assumption that the coverage probability is a given number is often unjus-tified in the modeling of fault-tolerant computers. In this problem we consider acoverage model of intermittent faults. (This is a simplified version of the modelproposed by Stiffler [STIF 1980].) The model consists of five states as shown inFigure 8.P.4. In the active state A, the intermittent fault is capable of producingerrors at the rate and leading to the error state E. In the benign state B, theaffected circuitry temporarily functions correctly. In state D the fault has beendetected, and in the failure state F an undetected error has propagated so thatwe declare the system to have failed. Set up the differential equations for thefive state probabilities. If we assume that all transition rates are greater than 0,then states A, B, and E are transient while states D and F are absorbing states.Given that the process starts in state A, it will eventually end up in either stateD or state F. In the former case the fault is covered; in the latter it is not.We can, therefore, obtain an expression for coverage probability, c = limt D(t).Using the final value theorem of Laplace transforms (see Appendix D), show thatc = lims0sD(s) = + q + Having obtained the value of c, we can then use an overall reliability modelsuch as those in Examples 8.35 and 8.37. Such a decomposition is intuitivelyappealing, since the transition rates in the coverage model will be orders ofmagnitude larger than those in the overall reliability model. For a detailed studyof this decomposition approach to reliability modeling, see the paper by Duganand Trivedi [DUGA 1989].