Some New Double and Multiple Acceptance Sampling Plans Using the X-gamma Distribution: Theory and Evaluation with Some Applications

This study develops double and multiple (three-stage) acceptance sampling plans based on the X-gamma distribution, a flexible model widely used in reliability engineering. The plans are built around truncated life tests, meaning testing stops either after a predetermined time or once a set number of failures occur. For the two-stage (double) sampling approach, we determine the smallest practical sample sizes and calculate the average sample number (ASN). We then expand the framework to a three-stage plan, outlining how it works and specifying the sample sizes needed at each step. To evaluate performance, we derive operating characteristic (OC) curves for all plan types, showing how well they distinguish between good and poor-quality lots across different quality levels. We also identify the minimum ratio of actual to specified mean life required to keep producer’s risk within acceptable limits. Additional efficiency metrics like average total inspection (ATI) and average outgoing quality (AOQ) are calculated to give a complete picture of how each plan performs in practice. Real-life numerical examples are included to walk through how these plans guide lot-acceptance decisions using the X-gamma model. Ultimately, this work gives quality control professionals reliable, distribution-specific tools for designing smarter, more efficient acceptance sampling procedures.