A SINGLE ACCEPTANCE SAMPLING PLAN FOR THE TRUNCATED LIFE TESTS BASED ON THE PERCENTILES OF ZECH DISTRIBUTION AND APPLICATIONS

Abstract

This study proposes a Single Acceptance Sampling Plan (SASP) for the truncated life test based
on the percentiles of Zech distribution. The methodology is designed to address quality
assessment in both industrial and biomedical contexts, thereby demonstrating the distribution’s
dual applicability across the two domains. The use of percentiles, over the conventional median,
provides a more flexible and informative approach in evaluating product reliability with the
lower and upper percentiles accounting for the early and late failures in improving decision-
making accuracy. This research constructs an efficient sampling scheme that minimizes the
required sample size while simultaneously satisfying consumer’s and producer’s risk. This is
achieved by formulating and solving constrained optimization problems tailored towards the
proposed plan. The performance of the SASP is examined through simulated datasets, arbitrarily
chosen parameter values, and real-life data. To validate its practical utility, the proposed plan is
benchmarked against SASPs derived from other lifetime distributions. Furthermore, the adoption
of multiple percentiles enhances the robustness of the plan, offering a significant improvement
over earlier models that focus solely on the median. Comparative study indicates that the
proposed SASP based on the Zech distribution consistently yields lower sample sizes and fewer
inspection cycles, thereby reducing both inspection time and cost.