Abstract
An acceptance sampling plan for Gompertz distribution under a truncated life test is developed. For different acceptance numbers, consumer’s confidence levels and values of the ratio of the experimental time to the specified mean lifetime, the minimum sample sizes required to ensure the specified mean lifetime are obtained. The operating characteristic function values and the associated producer’s risks are also presented. An example is provided to illustrate the acceptance sampling plan.
Highlights
Gompertz [1] introduced the Gompertz distribution to describe human mortality and establish actuarial tables
Gompertz distribution has attracted much attention. Some characteristics of this distribution are obtained by Pollard and Valkovics [5], Wu and Lee [6], Read [7], and Kunimura [8]
Saraçoǧlu et al [9] investigated the statistical inference for reliability and stress strength for Gompertz distribution
Summary
Gompertz [1] introduced the Gompertz distribution to describe human mortality and establish actuarial tables. Gompertz distribution has an exponentially increasing failure rate function and it is given by θet/σ /σ. The problem considered is that of finding the minimum sample size n necessary to ensure a certain mean lifetime based on the truncated life test. For a given acceptance sampling plan, the consumer’s risk and the producer’s risk are the probabilities that a bad lot is accepted and a good lot is rejected, respectively. Sobel and Tischendrof [12] studied acceptance sampling plans for exponential distribution. The acceptance sampling plans based on truncated life tests for the well-known Gom-pertz distribution have not been studied. This problem will be discussed in the paper.
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