Optimal and economic design of multiple deferred state repetitive group sampling plan for assuring mean life under a family of lifetime distributions

In this paper, a designing methodology of the multiple deferred (dependent) state repetitive group sampling plan is developed to ensure the mean lifetime of the products under the truncated life test, which follows a family of different lifetime distributions. An approach of two points on the operating characteristic curve is followed to obtain the optimal plan parameters with the known shape parameter values for various mean life ratios under different lifetime models. The proposed sampling plan is illustrated with a numerical example. The application of the proposed sampling plan is explained with a real-life example based on Burr XII distribution. Comparison is made among the performances of the proposed sampling plan using the different lifetime distributions; these performances are also compared with a single sampling plan using Burr XII distribution based on mean life assurance. Finally, an economic design of the proposed sampling plan is discussed, along with some cost models to minimize the total cost.