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Planning time-censored inspection schemes for k-out-of-n systems with gamma distributed component lifetimes

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Abstract

The determination of the best inspection scheme for lot acceptance purposes is a prominent optimization problem arising in industrial reliability and quality control. Assuming that the component lifetime distribution is gamma, constrained optimization problems are stated and solved in order to find optimal acceptance sampling plans for k-out-of-n systems based on time-censored component reliability tests. The objective function to minimize is the required number of components to test, whereas the nonlinear constraints are related to the maximum risks that the producer and the consumer are disposed to tolerate at the corresponding acceptable and rejectable quality levels. The optimal decision criterion is based on the number of observed component failures until a specific censoring time. The proposed acceptance sampling plans are particularly useful when the reliability engineer is interested in determining the acceptability of a k-out-of-n system before assembly, especially when the assembled system is expensive to test. The results developed are illustrated by various numerical examples, including the analysis of a system of water pumps for cooling a reactor.

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Authors and Affiliations

  1. Departamento de Matemáticas, Estadística e Investigación Operativa, Universidad de La Laguna, 38071, Tenerife, Canary Islands, Spain

    Arturo J. Fernández

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  1. Arturo J. Fernández
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Correspondence to Arturo J. Fernández.

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Fernández, A.J. Planning time-censored inspection schemes for k-out-of-n systems with gamma distributed component lifetimes. Int J Adv Manuf Technol 89, 3139–3147 (2017). https://doi.org/10.1007/s00170-016-9301-1

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  • DOI: https://doi.org/10.1007/s00170-016-9301-1

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