Optimal and economic design of repetitive group sampling plan based on new compounded bell Touchard exponential distribution

This paper presents a designing methodology of repetitive group sampling plan to ensure the median lifetime of the products based on a new-compounded model called complementary exponentiated bell Touchard exponential distribution. A non-linear optimization model is constructed to determine the optimal sampling plan parameters, minimizing the average sample number while maintaining the desired quality assurance levels. This study aims to focus on the advantages of the proposed plan by comparing the performance of the OC curve and average sample number with various exponential families of lifetime models. To elucidate the performance of the proposed plan in industrial scenarios, real-life applications are presented. The results revealed that it may provide a better fit than other related lifetime models. The effect of misspecification of shape parameters is investigated and a sensitivity analysis is performed to understand how much the proposed plan is impacted. Furthermore, to reduce the overall inspection cost of the product, the economic designing of the proposed plan is meticulously analyzed under a complementary exponentiated bell Touchard exponential lifetime model.