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Title: Optimal designs for multiple-step-stress accelerated life testing experiments when some testing constraints are required Authors:  Xiaojian Xu - Brock University (Canada) [presenting]
Abstract: Methods of designing accelerated life testing (ALT) experiments for the hazard rate prediction are investigated when a Cox proportional hazards (PH) model is utilized. We consider multiple step-stress ALT plans with time-censoring while certain practical testing requirements are needed. The maximum likelihood method is used for estimating the model parameters. The information matrix is derived, and the optimal stress levels and the optimal stress-changing times are determined under three optimality criteria: D-, A-, and Q-optimalities for the PH models with either a simple linear or a quadratic baseline hazard function. The efficiencies of our resulting optimal three-step-stress ALT plans are compared with their counterparts of optimal simple step-stress ALT plans. A practical simulation procedure is also provided and carried out to evaluate our resulting optimal three-step-stress ALT designs. Both asymptotic efficiency comparison and the simulation results have shown that the three-step-stress designs we have obtained with both an optimal middle stress level and two optimal stress changing times are more efficient than their competitors in terms of asymptotic variance, simulated bias, simulated variance, and simulated mean squared errors of the maximum likelihood estimator of the predicted hazard rate over a given period of time under normal design conditions.