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Bayes Estimation of Reliability Using an Estimated Prior Distribution

Author

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  • W. J. Padgett

    (University of South Carolina, Columbia, South Carolina)

  • Chris P. Tsokos

    (University of South Florida, Tampa, Florida)

Abstract

Suppose that the conditional failure time distribution F ( t ∣ θ) depends on a random parameter θ whose probability distribution G (θ) is unknown. The unconditional failure time distribution is F G ( f ) = ∫ F ( t ∣ θ) dG (θ). In this paper we consider the estimation of G in reliability models when a priori information about the parameter θ is specified in the form of an initial guess, G 0 , of G . Utilizing the concepts of Dirichlet process priors on G , a Bayes estimate F̂ G of F G may be obtained based on k observed lifetimes from F G . Then an estimate Ĝ k of G is found from F̂ G using a linear programming approach. For the Weibull failure time distribution F ( t ∣ θ) with random scale parameter θ, the effect of using the estimated prior Ĝ k in Bayes estimation of reliability is studied by Monte Carlo simulations.

Suggested Citation

  • W. J. Padgett & Chris P. Tsokos, 1979. "Bayes Estimation of Reliability Using an Estimated Prior Distribution," Operations Research, INFORMS, vol. 27(6), pages 1142-1157, December.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:6:p:1142-1157
    DOI: 10.1287/opre.27.6.1142
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    Cited by:

    1. W. J. Padgett & S. D. Durham, 1989. "A model for critical crack size estimation in fatigue failure of gun barrels," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(2), pages 139-145, April.

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