Two-stage group acceptance sampling for the half exponential power distribution: Design, optimization, and validation

Abstract

Acceptance sampling plans based on truncated life tests offer a cost-effective mechanism for lot-disposition decisions by terminating the experiment at a pre-specified time and recording only the failure count, while Group Acceptance Sampling Plans (GASPs) further enhance efficiency by testing multiple items simultaneously across groups. This paper proposes a Two-Stage GASP for the Half Exponential Power Distribution (HEPD) under truncated life tests, constructed under the two-point operating characteristic criterion that simultaneously controls the producer's and consumer's risks. The failure probability under the truncated test is derived as a closed-form expression in the mean ratio and termination multiplier, and is shown to be independent of the scale parameter, a property that renders the resulting design tables universally applicable. Optimal design parameters are obtained by minimizing the Average Sample Number (ASN) at the consumer's quality level subject to both risk constraints, and comprehensive design tables are provided across the practical ranges of termination multiplier, mean ratio, and group size. The proposed plan achieves consistent ASN reductions of 18.4% to 41.1% relative to the single-stage GASP, with the largest savings at the most stringent consumer's risk and narrowest quality margin, while the producer's acceptance probability consistently exceeds 0.95, confirming that these gains arise from the two-stage structure rather than any relaxation of the risk constraints. The plan's practical utility is further demonstrated on two real-life data sets, the stress rupture life of Kevlar 49/epoxy strands and the plasma ferritin concentration of Australian athletes, in which it delivers a sound quality decision with materially smaller inspection effort than the single-stage alternative.