Acceptance Sampling Plans from Truncated Life Tests Based on the Generalized Birnbaum–Saunders Distribution

Abstract In this article, we develop acceptance sampling plans when the life test is truncated at a pre-fixed time. The minimum sample size necessary to ensure the specified median life is obtained by assuming that the lifetimes of the test units follow a generalized Birnbaum–Saunders distribution. The operating characteristic values of the sampling plans as well as producer's risk are presented. Two examples are also given to illustrate the procedure developed here, with one of them being based on a real data from software reliability. Keywords: Acceptance samplingBirnbaum–Saunders distributionConsumer's riskKurtosisLife testMinimum sample sizeProducer's riskMathematics Subject Classification: 62N0590B2562P3062H10 Acknowledgments This study was carried out with the support of research projects FONDECYT 1050862, FANDES C-13955/10, and DIPUV 42-2004, Chile. This article was written partially during the time that Dr. Víctor Leiva was doing a Postdoctoral Fellow in the Department of Mathematics and Statistics, McMaster University, Canada. He is especially grateful with the McMaster University, Canada, for its support. Notes Here, Φ(·) and Φ t (·) are the cdfs of the standard normal and Student-t distributions, respectively, and a t (α, β) is as given in (2), where and I x (a, b) is the incomplete beta function ratio (see Johnson et al., 1994 p. 364), given by