Application of a Bayesian approach to sequential life testing with an underlying Weibull model

摘要

An example is used to illustrate a new Bayesian approach to sequential life testing proposed in a previous work by De Souza (2002). The underlying sampling distribution was the Weibull model. The intended Bayesian sequential life testing approach uses a posterior probability statement that is continually updated as new test data become available. Since the underlying sampling distribution was the two-parameter Weibull model, in order to find a final expression for the posterior distribution, some numerical procedure had to be applied. For formulating the prior information on the scale parameter θ of the Weibull sampling model, we have used the Type Ⅱ Extreme Value distribution, and for formulating the prior information on the shape parameter β of the Weibull model, we have applied a Beta distribution, defined between two probabilistic limits (L, U). In a following article, we should present a truncation mechanism to the Bayesian sequential approach proposed in this paper.