‎Process capability indices has been widely applied in industry to assess the performance of industrial processes‎. ‎For the larger-the-better lifetimes of products‎, ‎the lifetime performance index C_L is commonly considered by industrial managers‎. ‎This paper confines itself to the the Bayesian statistical inferences about C_L under the Pareto distribution with the progressively Type-II censored samples‎. ‎The Bayesian inferences are based on a conjugate continuous prior for the scale parameter and a discrete prior for the shape parameter of the distribution under consideration‎. ‎Two illustrative examples are given to demonstrate the sensitivity of results to the prior hyperparameters and the underlying distribution of the observations‎. ‎Finally‎, ‎a Monte Carlo simulation study is done to evaluate the behavior of the lifetime performance index C_L.

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