Gamma Reliability Test Times With Minimal Costs and Limited Risks

Minimum-cost reliability test durations based on gamma failure count data are found by solving mixed integer nonlinear programming problems. The optimal numbers of test units and failures allowed are also determined. A linear combination of test time and sample size is minimized assuming that producer and consumer risks are controlled. A quite accurate approximation of the smallest feasible acceptance number is deduced in closed-form. Moreover, a fast and efficient iterative algorithm is presented in order to obtain the optimal reliability demonstration test plan, which provides the best criterion to decide the acceptability of submitted lots and production processes. Furthermore, some descriptive analyses of the proposed inspection schemes, as well as applications of the developed methodology to the manufacturing of deep groove ball bearings, semiconductor lasers, and water pumps, are provided for illustrative and comparative purposes.