Bayesian Confidence Bounds for the Weibull Failure Model

The following bounds are derived for the Weibull failure model when the parameter is being characterized by the inverted gamma and uniform probability density functions (pdf); they are lower and upper Bayes-confidence bounds for the scale parameter and lower bounds for the reliability function. To illustrate the results a Monte Carlo simulation was performed to obtain 90% and 95% Bayes-confidence bounds for the scale parameter and lower limits for the corresponding reliability function of the Weibull failure distribution. The consequences that one encounters when the following ``wrong'' priors have been chosen to characterize the random behavior of the scale parameter are investigated. The results are compared when the prior pdf of θ is uniform but inverted gamma was used, and vice versa.