Sampling design for the lifetime performance index of exponential lifetime distribution under progressive type I interval censoring

The lifetime performance index was used for the evaluation on the process performance to promote the quality and productivity especially with products following a one-parameter exponential distribution. Based on the hypothesis testing procedure using the maximum likelihood estimator as testing statistic, the sampling design is determined under different situations. For given power of hypothesis testing, the minimum sample size is determined and tabulated to reach the given power. When the termination time is fixed and the number of inspection intervals is not fixed, the required number of inspection intervals and sample size with minimum total cost are determined and tabulated. When the termination time is not fixed, the required number of inspection intervals, sample size and equal interval length to reach the minimum total cost are determined and tabulated. At last, one numerical example is given to illustrate the use of this sampling design to collect data and then implement the testing procedure to determine whether the process is capable.