Modeling and planning accelerated life testing with proportional odds

Abstract

Accelerated life testing (ALT) is a method for estimating the reliability of products at normal operating conditions from the failure data obtained at the severe conditions. We propose an ALT model based on the proportional odds (PO) assumption to analyze failure time data and investigate the optimum ALT plans for multiple-stress-type cases based on the PO assumption. We present the PO-based ALT model and propose the parameter estimation procedures by approximating the general baseline odds function with a polynomial function. Numerical examples with experimental data and Monte Carlo simulation data verify that the PO-based ALT model provides more accurate reliability estimate for the failure time data exhibiting PO properties. The accuracy of the reliability estimates is directly affected by the reliability inference model and how the ALT is conducted. The latter is addressed in the literature as the design of ALT test plans. Design of ALT test plans under one type of stress may mask the effect of other critical types of stresses that could lead to the component's failure. The extended life of today's products makes it difficult to obtain enough failures in a reasonable amount of testing time using single stress type. Therefore, it is more realistic to consider multiple stress types. This is the first research that investigates the design of optimum ALT test plans with multiple stress types. We formulate nonlinear optimization problems to determine the optimum ALT plans. The optimization problem was solved with a numerical optimization method. Reliability practitioners could choose different ALT plans in terms of the stress loading types. In this dissertation we conduct the first investigation of the equivalency of ALT plans, which enables reliability practitioners to choose the appropriate ALT plan according to resource restrictions. The results of this research show that one can indeed develop efficient test plans that can provide accurate reliability estimate at design conditions in much shorter test duration than the traditional test plans. Finally, we conduct experimental testing using miniature light bulbs. The test units are subjected to different stress types. The results validate the applicability of the PO-based ALT models.