Evaluating the lifetime performance index of products based on progressively Type‐II censored Pareto samples: A new Bayesian approach.

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 CL$C_L$ is commonly considered by industrial managers. This paper confines itself to the the Bayesian statistical inferences about CL$C_L$ 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 CL$C_L$. [ABSTRACT FROM AUTHOR]