Non-parametric analysis of a proportional wearout model for accelerated degradation data

In analyzing the reliability of a product, the quantity of interest is usually the time-to-failure. However, many products may degrade before failure, and it is possible to record the actual degradation on units as a function of time. The time-to-failure is defined as the time when a unit reaches a particular level of degradation. This paper focuses on accelerated degradation models in life testing. A new model for accelerated degradation data called a proportional wearout model is proposed. The mean degradation curve and the acceleration factor for each stress level are estimated non-parametrically. A point estimate and a bootstrap confidence interval for the time-to-failure of the mean degradation curve under the usual use condition, t0, are obtained. A goodness-of-test that may be applied to this model and other degradation models is proposed. The proportional wearout model is fit to sliding metal wear data [W. Meeker, L. Escobar, Statistical Methods for Reliability Data, John Wiley and Sons, 1998], and the results are compared to the fit of the time-scale model used in [J. Shaiu, H. Lin, Analyzing accelerated degradation data by non-paramateric regression, IEEE Transactions on Reliability 48 (1999) 149–158]. It is shown that the proportional wearout model fits these data well but the time-scale model does not.