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Optimal Design for Step-Stress Accelerated Degradation Testing Based on D-Optimality

Abstract: 2011 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must first be obtained from the IEEE.

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 ␣: 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 Degradation 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.

Keywords: Accelerated Life Testing - Failure Rate - Product Reliability - RAMS 2011 Proceedings - Reliability Analysis/Prediction/Estimation

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