Optimal design of degradation tests in presence of cost constraint

Degradation test is a useful technique to provide information about the lifetime of highly reliable products. We obtain the degradation measurements over time in such a test. In general, the degradation data are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the failure time distribution can be estimated. However, in order to obtain a precise estimate of the percentile of failure time distribution, one needs to design an optimal degradation test. Therefore, this study proposes an approach to determine the number of units to test, inspection frequency, and termination time of a degradation test under a determined cost of experiment such that the variance of estimator of percentile of failure time distribution is minimum. The method will be applied to a numerical example and the sensitivity analysis will be discussed.