Robust Step-Stress Designs for Heteroscedastic Accelerated Life-Testing Models

• Activity Number: 653
• Type: Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Quality and Productivity Section
• Author(s): Xiaojian Xu*+
• Companies: Brock University
• Keywords: Heteroscedasticity ; Model misspecification ; Weibull distribution ; Shape-stress relationship ; Censoring ; Maximum likelihood estimation

Abstract

We discuss the optimal and robust designs of the experiments for accelerated life tests (ALT) with a step-stress plan. We take into account that not only the scale parameter but also the shape parameter of the underlying life distribution possibly vary when stress level changes. The optimal and robust designs are obtained in order to minimize the asymptotic variance of the estimator for the reliability of a product at the normal use stress level. Furthermore, we are aware that the possible departure from the model assumption may happen to the fitted life-stress relationship since there is no information provided for accessing the fitted model due to extrapolation. We consider both the fitted model and true model of the life-stress relationship being polynomials. The robust 3-step-stress plans have been found in order to minimize the squared asymptotic bias, asymptotic variance, and asymptotic mean squared error of the reliability estimates. The robust designs are derived for both complete data and censored data.