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Characteristic functions of stochastic integrals and reliability theory

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  • Gordon Antelman
  • I. Richard Savage

Abstract

This paper concerns reliability theoretic problems involving systems of n components subject to stochastic hazard rates with independent increments. General methods are given for finding the probabilities of service at specified times and the joint characteristic function of the system failure time and the component hazard rates at the time of failure. These methods involve evaluation of integrals of the form where u′ is an n‐component row vector, W(t) is an n by n matrix, and X(t) is an n‐component stochastic process with independent increments and X(0) = 0. Some illustrative applications to one component systems and multicomponents systems in series and in parallel are presented.

Suggested Citation

  • Gordon Antelman & I. Richard Savage, 1965. "Characteristic functions of stochastic integrals and reliability theory," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 199-222, September.
    • Handle: RePEc:wly:navlog:v:12:y:1965:i:3:p:199-222
    DOI: 10.1002/nav.3800120302
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    Cited by:

    1. Antonio Di Crescenzo & Franco Pellerey, 1998. "On lifetimes in random environments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(4), pages 365-375, June.

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