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Gamma Distribution in Acceptance Sampling Based on Life Tests

Shanti S. Gupta and Phyllis A. Groll
Journal of the American Statistical Association
Vol. 56, No. 296 (Dec., 1961), pp. 942-970
DOI: 10.2307/2282006
Stable URL: http://www.jstor.org/stable/2282006
Page Count: 29
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Gamma Distribution in Acceptance Sampling Based on Life Tests
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Abstract

The gamma distribution is assumed as a model for lifetime. The problem of acceptance sampling when the life test is truncated at a preassigned time is discussed. For various acceptance numbers, various confidence levels, and various values of the ratio of the fixed experiment time to the specified mean life, the tables of this paper give the minimum sample sizes necessary to assure the specified mean life. The operating characteristic functions of the sampling plans are obtained and these are graphed for a few selected cases. Producer's risk is discussed and a small table is given for the ratio of true mean life to a specified mean life which insures acceptance with a probability of P* = .95. An approximation is given for the minimum sample size problem. Failure rates for the gamma distribution are tabulated. The use of the tables is illustrated by examples in most cases.

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