An engineering approach to Bayes estimation for the Weibull distribution

Bayesian enhanced strategic decision making for reliability.

Reliability analysis : Optimal inspection and maintenance schedules of failing systems

https://pure.rug.nl/ws/files/98787668/Optimum_maintenance_strategy_under_uncertainty_in_the_lifetime_distribution.pdf

Optimum maintenance strategy under uncertainty in the lifetime distribution

Cost benefits of postponing time-based maintenance under lifetime distribution uncertainty

This paper develops a Bayesian analysis of the scale and shape parameters in the Weibull distribution and the corresponding reliability function with respect to the usual life-testing procedures. For the scale parameter I¸, Bayesian estimates of I¸ and reliability are obtained for the uniform, exponential, and inverted gamma prior probability densities. Bhattacharya's results [J. Am. Stat. Assn. 62, 48-62 1967] for the one-parameter exponential life-testing distribution are reduced to a special case of these results. The paper develops a fully Bayesian analysis of both the scale and shape parameters I¸ and I¾ by assuming independent prior distributions; since in the latter case, analytical tractability is not possible, Bayesian estimates are obtained through a conjunction of a Monte Carlo simulation and numerical-integration techniques. In both cases, the paper carries out a computer simulation and makes a comparison between the Bayesian and the corresponding minimum-variance unbiased, or maximum likelihood, estimates. As expected, the Bayesian estimates are superior.

Chris P. Taokas

Papers

Bayesian Estimation of Life Parameters in the Weibull Distribution