Assessing the lifetime performance index of Weibull distributed products under progressive Type II censoring

Quality management is very important for many manufacturing industries. In the field of quality control, Process capability indices are defined to demonstrate whether product quality meets customer requirements. Usually, the process capability is calculated with product survival lifetime and hence a larger lifetime yields a better product quality. Montgomery [1] recommended using the capability index (lifetime performance index) for evaluating the lifetime performance of products. This paper deals with the Bayesian statistical inferences about the lifetime performance index when the available data are the progressively Type II censored data. Also, we suppose that the lifetimes of products follow the two-parameter Weibull distribution. The Bayesian statistical inferences are obtained based on a conjugate prior for the scale parameter and a discrete prior for the shape parameter of the Weibull distribution. Finally, an illustrative example is presented in order to illustrate all the methods of inference discussed here.