Computational procedure of lifetime performance index of products for the Burr XII distribution with upper record values

Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. In practice, lifetime performance index (or the larger-the-better process capability indices (PCIs)) CL is a popular means to assess the performance and potential of their processes, where L is the lower specification limit. Moreover, record values often arise in industrial stress testing, meteorological analysis, hydrology, seismology, athletic events, and other similar situations. In this study, a two-stage maximum likelihood estimation applied to estimate lifetime performance index CL of non-normal processes. Further, this study will apply data transformation technology to construct a maximum likelihood estimator (MLE) of CL under the Burr XII distribution with the upper record values. The MLE of CL is then utilized to develop a hypothesis testing procedure in the condition of known L. Finally, we give simulation study and two examples to illustrate the use of the testing procedure under given significance level α.