Computational testing algorithmic procedure of assessment for lifetime performance index of products with Weibull distribution under progressive type I interval censoring

The assessing of the lifetime performance is a very important topic in manufacturing or service industries. Process capability indices had been widely used to evaluate the process performance to the continuous improvement of quality and productivity. The lifetimes of products are assumed to have Weibull distribution with a known shape parameter and the larger-the-better lifetime performance index is considered. 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 investigated. We use this estimator to develop 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.