Bayesian test of lifetime performance index for exponential products based on the progressively type II right censored sample

In the service (or manufacturing) industry, process capability indices (PCIs) are utilized to assess whether product quality meets a required level. The lifetime performance index (or the larger-the-better PCI) L C is frequently used to measure the potential and performance of a process, where L is the lower specification limit. And, progressively censoring scheme is quite useful in many practical situations where budget constraints are in place or there is a demand for rapid testing. In this paper, we construct two kinds of Bayesian estimators of L C based on the conjugate prior distribution and squarederror loss function under the exponential distribution with the progressively type II right censored sample. Further, two kinds of Bayesian estimators of L C are also utilized to develop the hypothesis testing for L C based on a credible interval in the condition of known L. Finally, we also give one numerical example to illustrate the use of the testing procedure under the given significance level. Moreover, the purchasers can then employ the new testing procedure to determine whether the product performance adheres to the required level.