Generalized Poisson Shock Models.
CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
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Suppose that shocks hit a device in accordance with a nonhomogeneous Poisson process with intensity function lambdat. The ith shock causes a damage X sub i. The X sub i are assumed to be independent and identically distributed positive random variables, and are also assumed independent of the counting process of shocks. Let Dx sub 1, ..., x sub n denote the total damage when n shocks having damages x sub 1, ..., x sub n have occurred. It has previously been shown that the first time that DX exceeds a critical threshold value is an increasing, failure rate average random variable whenever lambdat lambda and Dx sum over x sub i. This result is extended to the case where integral from 0 to t of lambdasdst is nondecreasing in t and Dx is a symmetric, nondecreasing function. The extension is obtained by making use of a recent closure result for increasing failure rate average stochastic processes.
- Statistics and Probability