Optimal design for step-stress accelerated degradation testing based on D-optimality

Abstract

Accelerated Degradation Testing (ADT) is proposed as a means to obtain degradation data of products in a short time period and extrapolate the lifetime and reliability of products under use condition. There are two optimality criterion could be defined in designing an accelerated test plan. Criterion D : some testing planners are interest in the prediction of products' lifetime, so their objective is minimizing the variance (or asymptotic variance) of the MLE of parameter Θ which can include the quantiles and the mean of the lifetime distribution at a pre-specified stress level. Criterion II : if engineers are interest in the estimation of model parameters, their objective may be maximizing the determinant of the Fisher information matrix, which has a reciprocal relationship with variance-covariance matrix. This criterion is D-optimality, wherein the ‘information’ is maximized and the ‘variance’ is minimized at the same time. Criterion I for Step Stress Accelerated De gradation Testing (SSADT) planning is already proposed, however Criterion II (D-optimality) is seldom discussed. In this study, a method to optimal design for SSADT based on D-optimality is present. First, drift Brownian motion is applied to describe a typical SSADT problem. Next, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal plan gives sample size, total testing time, stress levels and testing time at each stress level. Finally, an example is used to illustrate this test planning method.