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Evaluating the lifetime performance is a vital topic in manufacturing process. This paper is devoted to evaluate the lifetime performance index CL for the three-parameter power Lomax distribution(POLO) under progressive first-failure type II right censoring sample with respect to a lower specification limit (L). The statistical inference concerning CL is conducted via obtaining the maximum likelihood of CL on the base of progressive first-failure censoring. The asymptotic normal distribution of the MLE of CL and the confidence interval are proposed. Moreover, the hypothesis testing of CL for evaluating the lifetime performance of POLO data is conducted. Providers can practice the innovative hypothesis testing to improve the process capability. Finally, two examples are given, one of them considering a real life data of the number of revolutions before failure of a ball bearing in endurance lifetime test and the other is a simulated example to illustrate the usage of the proposed procedure.

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