An alternative proof of the IFRA property of some shock models

C. Derman and D. R. Smith

Naval Research Logistics Quarterly, 1980, vol. 27, issue 4, 703-707

Abstract: Let , where A (t)/t is nondecreasing in t, {P(k)1/k} is nonincreasing. It is known that H(t) = 1 — H(t) is an increasing failure rate on the average (IFRA) distribution. A proof based on the IFRA closure theorem is given. H(t) is the distribution of life for systems undergoing shocks occurring according to a Poisson process where P(k) is the probability that the system survives k shocks. The proof given herein shows there is an underlying connection between such models and monotone systems of independent components that explains the IFRA life distribution occurring in both models.

Date: 1980
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