| Products or materials are often tested at higher levels of stress than operational conditions to quickly obtain information on the life distribution or product performance under normal use. Such testing could save much time and money. In step-stress accelerated life test (SSALT), the stress for survival units is generally changed to a higher stress level at a pre-determined time. Determination of the stress change times is one of the most important design problems in SSALT.;In this dissertation research, we focus on the SSALT design problem for Weibull failure data because of its broad application in industry. The optimal simple SSALT, which involves only two stress levels, is first derived. Log-linear life stress relationship is assumed. Two different types of optimization criteria are presented, considering life estimate and reliability estimate. Optimal SSALT plan is proposed by minimizing the Asymptotic Variance (AV) of the desired life/reliability estimate.;In many applications and for various reasons, it is desirable to use more than one accelerating stress variable. Integration of Weibull failure data with multiple stress variables results in more complexity in the Fisher information matrix, and a more complicated problem to solve. Two stress variables are considered first, leading to the bivariate SSALT model. Bivariate SSALT model is then extended to a more generalized model: multi-variate SSALT, which includes k steps and m stress variables.;In addition to log-linear life-stress relationship, proportional hazards (PH) model is another widely used life-stress relationship for multiple stress variables. In this dissertation research, the baseline intensity function is defined at the highest stress levels to obtain a quick initial estimate of the parameters. PH model is assumed for all other stress levels. A simple SSALT design is considered first. The results are extended to multiple SSALT, which considers multiple steps, but only one stress variable. Optimal stress change times for each step are obtained. A more generalized case, multi-variate SSALT based on PH model is then proposed, including k steps and m stress variables. Fisher information matrix and AV of maximum likelihood estimation (MLE) are constructed. Optimal plan is designed to minimize the AV of MLE. |
