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Process capability analysis has been widely applied in the ﬁeld of quality control to monitor the performance of industrial processes. Hence, lifetime performance index CL is used to measure the potential and performance of a process. In the present study, we construct a maximum likelihood estimator of CL under Burr Type III distribution based on the progressive Type II censored sample. The maximum likelihood estimator of CL is then utilized to develop the hypothesis testing procedure in the condition of known L. Finally, one practical example and Monte Carlo simulation are given to assess the behavior of the lifetime performance index under given significance level.
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