Acceptance Sampling Plans for Exponential- and Weibull-Distributed Lifetimes Under the Group Sampling Framework

Product lifetime is a critical quality characteristic of electronic products. Among various lifetime models, the Weibull distribution is one of the most flexible and widely used distributions in reliability analysis because it can describe different failure rate patterns through its shape parameter. In this study, the Weibull distribution is treated as the primary lifetime model, while the exponential distribution is included as a simpler benchmark model and as a special case of the Weibull distribution with shape parameter m = 1. Based on the lifetime performance index, this research applies the group sampling concept to design two lifetime acceptance sampling plans under these lifetime distributions. The optimal sampling plan parameters of the lifetime acceptance sampling plans are determined by minimizing the number of groups while satisfying the two-point principle of the operating characteristic curve. For practical purposes, the parameters of the proposed plan are tabulated for some combinations of quality levels with commonly used producer risk and consumer risk. Moreover, a comparative analysis of the two lifetime testing methods is presented, and the results show that Testing Method II proposed in this study can implement sampling inspection more efficiently. Finally, an example is used to illustrate the proposed methodology.