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

Quality management is very important formany manufacturing industries. In the field of qualitycontrol, Process capability indices are defined todemonstrate whether product quality meets customerrequirements. Usually, the process capability is calculatedwith product survival lifetime and hence a larger lifetimeyields a better product quality. Montgomery [1]recommended using the capability index (lifetimeperformance index) for evaluating the lifetime performanceof products. This paper deals with the Bayesian statisticalinferences about the lifetime performance index when theavailable data are the progressively Type II censored data.Also, we suppose that the lifetimes of products follow thetwo-parameter Weibull distribution. The Bayesianstatistical inferences are obtained based on a conjugateprior for the scale parameter and a discrete prior for theshape parameter of the Weibull distribution. Finally, anillustrative example is presented in order to illustrate all themethods of inference discussed here.

Keywords:

Quality management , lifetime performance index , Weibull distribution , Progressively Type II censored sample , Bayesian approach