Bayesian reliability analysis and the Higgins-Tsokos loss function

Carlos A.Molinares, Chris P.Tsokos

University of South Florida

Tampa, FL, 33620

Bayesian analysis of the reliability function for the three parameter Weibull distribution is developed with respect to the usual life testing procedure, with the scale parameter being treated as a random variable. The Bayesian estimates of the reliability functions are compared with respect to those obtained using the Higgins-Tsokos loss function, considering the general uniform, exponential, inverted gamma, and Jeffreys as prior densities. Bayesian estimates are obtained by numerical integration techniques. In all cases, a Monte-Carlo simulation is carried out to make the comparisons. The Higgins-Tsokos loss function used in conjunction with the Jeffreys' prior provided the best performance Bayesian estimate of the reliability function, giving a good approximation to the true reliability function. In addition, the Higgins-Tsokos loss function was found to be as robust as the square error loss function, and slightly more efficient.