Planning reliability demonstration tests with limited expected risks

Abstract

Optimal reliability demonstration test plans with controlled expected producer and consumer risks are computed. Device failure times follow Weibull distributions, whereas prior information on device reliability is described by limited beta models. Minimum-cost test durations, sample sizes and acceptance numbers are found by solving mixed integer nonlinear programming problems. Lower and upper bounds on the minimal feasible number of failures allowed, as well as a reasonable approximation, are first deduced. An iterative method is then presented for determining the optimal lot inspection plan. Numerical and graphical analyses and several applications in industrial manufacturing are also provided for illustrative and comparative purposes. The inclusion of substantial prior knowledge allows the reliability engineer to reduce test time, sample size and cost, and leads to improved risk assessments for both producers and consumers. The proposed approach also enables the practitioners the flexibility to define precise limits of the device reliability and to combine multiple experts’ opinions. In addition, the best plan can continually be updated as more subjective or objective information becomes available.