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Lifetime performance indices  C Lis usually used as the measurement for the larger-the-better type quality characteristics to assess the process performance of products. The lifetimes of products are assumed to have Rayleigh distribution in this study. This research presents another approach to the hypothesis testing procedure for the index without the transformation of Rayleigh distribution to the exponential distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample and its asymptotic distribution of this estimator is also developed to build a new hypothesis testing procedure under a pre-assigned lower specification limit. A simulation study is done and the results show that the power performance of this approach is better than the existing one. Finally, two practical examples are given to illustrate the use of two testing algorithmic procedures to determine whether the process is capable.

Power comparison of the testing on the lifetime performance index for Rayleigh lifetime products under progressive type I interval censoring