The Optimal Experimental Design of the Overall Lifetime Performance Index of Rayleigh Distribution Products Produced in Multiple Manufacturing Processes Under Progressive Type-I Interval Censoring

In response to the increasing quality demands of consumers amid technological advancements in manufacturing, manufacturers must manage the quality and lifespan of their products. In practical applications, various methods have been developed to assess product quality performance. This study employs process capability indices (PCIs) to evaluate product quality. This research explores scenarios involving products with multiple quality characteristics or multiple production lines under a Rayleigh lifetime distribution. Using the progressive Type-I interval censored sample, we assess whether the overall lifetime performance index meets a predetermined target. Given a specified significance level and statistical power, the minimum required sample size is derived. Under either fixed or unfixed total testing times, this study identifies the minimum number of observation intervals and the sample size that minimizes the total experimental cost, or the minimum number of observation intervals, equal-length interval time, and sample size. Finally, an illustrative practical example from two production lines is used to demonstrate how to apply the optimal experimental design proposed in this study to construct the progressive Type-I interval censored sample to test whether the overall lifetime performance index achieves the specified target.