A computational algorithm for the evaluation on the lifetime performance index of products with Rayleigh distribution under progressive type I interval censoring

It is a very important topic these days to assessing the lifetime performance of products in manufacturing or service industries. Lifetime performance indices CL is used to measure the larger-the-better type quality characteristics to evaluate the process performance for the improvement of quality and productivity. The lifetimes of products are assumed to have Rayleigh distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample. The asymptotic distribution of this estimator is also developed. We use this estimator to build the new hypothesis testing algorithmic procedure with respect to a lower specification limit. Finally, two practical examples are given to illustrate the use of this testing algorithmic procedure to determine whether the process is capable.