Reliability sampling design for the lifetime performance index of Burr XII lifetime distribution under progressive type I interval censoring

For the lifetime of products following a Burr XII distribution, the lifetime performance index was measured to assess the performance of the manufacturing process under type I interval censoring. The sampling design is investigated to reach the given level of significance and power level. When the inspection interval length is fixed, the required number of inspection intervals and sample size are determined to reach the minimum total cost. When the termination time of experiment is not fixed, the required number of inspection intervals, sample size and equal interval length are determined to reach the minimum total cost. The optimal sampling design for different situations is tabulated for the practical use of users. At last, one practical example is given for illustrative aim to show the use of the optimal sampling design to collect data and then conduct the testing procedure to see if the process is capable.