Estimating the Shift to Wear-Out of Systems Having Exponential-Weibull Life Distributions

We develop a new family of life distributions, called the exponential-Weibull wear-out distributions, for systems whose failure rate function is a constant up to a change-point (wear-out point) and strictly increasing afterward. We derive properties of these wear-out distributions and develop a Bayes adaptive procedure for estimating the change point. Recursive formulas are given for determining the posterior probability that the change has occurred and its Bayes estimator. Results of numerical simulations are given to illustrate the properties of the adaptive procedure.