Step-stress Accelerated Life Tests - a Proportional Hazards Based Nonparametric Model

Using data from a simple Step-Stress Accelerated Life Testing (SSALT), a nonparametric Proportional Hazards (PH) model is proposed for obtaining Upper Confidence Bounds (UCBs) for the cumulative failure probability of a product under normal use conditions. The approach is nonparametric in the sense that most of the functions involved in the model do not assume any specific forms, except for certain verifiable conditions. Test statistics are introduced to verify assumptions about the model and to test the Goodness of Fit (GOF) of the proposed model to the data. A numerical example, using data simulated from the lifetime distribution of an existing parametric study on Metal-Oxide-Semiconductor capacitors, is used to illustrate the proposed methods. Discussions on how to determining the optimal stress levels and sample size are also given.