Bayesian analysis of the lifetime performance index on the basis of progressively censored Weibull observations

ABSTRACT In manufacturing industries, indices such as the lifetime performance index ( ) are utilized to assess whether products’ quality meets the required level. This article deals with the Bayesian inferences about on the basis of progressively censored data when the product’s lifetime follows the Weibull distribution. The Bayesian analysis is based on a conjugate prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration. Two illustrative examples are studied to assess the sensitivity of results to the prior parameters and the underlying distribution of the observed data. Finally, a simulation study is conducted to carry out the performance of the obtained results.