Consider a random access memory card consisting of d VLSI chips, each contain-ing w

Chapter 3, Problem 4

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Consider a random access memory card consisting of d VLSI chips, each contain-ing w bits. Each chip supplies one bit position in a d-bit word for a total of w,d-bit words. Assuming a failure rate of per chip (and an exponential lifetimedistribution), derive the reliability expression R0(t) for the memory card. Sup-pose that we now introduce single error correction, so that up to one chip mayfail without a system failure. Note that this will require c extra chips where cmust satisfy the relation c log2(c + d + 1). (See Rao and Fujiwara [RAO 1989].)Derive the reliability expression R1(t). Plot R0(t) and R1(t) as functions of t onthe same plot. Derive expressions for the hazard functions h0(t) and h1(t), andplot these as functions of time t. For these plots assume d = 16 (hence c = 5)and = 10 per million hours.

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