Annals of Statistics

A Bayesian Nonparametric Approach to Reliability

R. L. Dykstra and Purushottam Laud

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It is suggested that problems in a reliability context may be handled by a Bayesian nonparametric approach. A stochastic process is defined whose sample paths may be assumed to be increasing hazard rates by properly choosing the parameter functions of the process. The posterior distribution of the hazard rates is derived for both exact and censored data. Bayes estimates of hazard rates and $\operatorname{cdf's}$ are found under squared error type loss functions. Some simulation is done and estimates graphed to better understand the estimators. Finally, estimates of the hazard rate from some data in a paper by Kaplan and Meier are constructed.

Article information

Ann. Statist., Volume 9, Number 2 (1981), 356-367.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62G99: None of the above, but in this section
Secondary: 62F15: Bayesian inference

Hazard rates increasing hazard rates Bayes estimates extended gamma process posterior process prior process


Dykstra, R. L.; Laud, Purushottam. A Bayesian Nonparametric Approach to Reliability. Ann. Statist. 9 (1981), no. 2, 356--367. doi:10.1214/aos/1176345401.

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