Assessing the Lifetime Performance Index of Gamma Lifetime Products in the Manufacturing Industry

In the manufacturing (or service) industry, process capability indices (PCIs) are utilized to assess whether product quality meets a required level. The lifetime performance index (or the larger-the-better PCI) C_L is frequently used as a means of measuring product performance, where L is the lower specification limit. This study constructs the uniformly minimum variance unbiased estimator (UMVUE) of C_L based on a complete sample from a gamma distribution where the shape parameter α is given (or known) and the scale parameter λ is unknown. The UMVUE of C_L is then utilized to develop a novel hypothesis testing procedure in the condition of known L. Two practical examples illustrate the use of the testing procedure under a given significance level.