Designing a screening experiment with a reciprocal Weibull degradation rate

Degradation tests and design of experiments are powerful techniques to improve the reliability of highly reliable products. With respect to a resolution III experiment with a linearized degradation model where the degradation rate follows a lognormal distribution, Yu and Chiao addressed the problem of how to determine the optimal settings of decision variables such as the inspection frequency, the sample size, and the termination time for each run, which are influential to the precision of identifying significant factors and the experimental cost. In practical applications, Weibull and lognormal distributions are much alike. They may fit the lifetime data well. However, their predictions may lead to a significant difference. In this paper, we will deal with the optimal design of a resolution III experiment with a linearized degradation model where the degradation rate follows a reciprocal Weibull distribution. First, an intuitively appealing identification rule is proposed. Next, under the constraints of a minimum probability of correct decision and a maximum probability of incorrect decision of the proposed identification rule, the optimal test plan is derived by using the criterion of minimizing the total cost of experiment. An example is provided to demonstrate the proposed method. Finally, a simulation study is also provided to discuss the effects of mis-specification between the models of Yu and Chiao and the present paper on identification efficiency.