Accession Number:

ADA058510

Title:

Generalized Poisson Shock Models.

Descriptive Note:

Research rept.,

Corporate Author:

CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER

Personal Author(s):

Report Date:

1978-04-01

Pagination or Media Count:

10.0

Abstract:

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.

Subject Categories:

  • Statistics and Probability
  • Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE