Interval estimation for Wiener processes based on accelerated degradation test data

Abstract

Degradation is a primary cause of failures for many materials and products. Although stochastic processes have been widely applied to degradation data, there is a lack of efficient and accurate methods for interval estimation of model parameters and reliability characteristics given limited degradation data. Using the method of generalized pivotal quantities, this study develops interval estimation procedures for fixed-effects and mixed-effects Wiener degradation processes based on accelerated degradation test data. The fixed-effects processes are common for mature products and the mixed-effects model is capable of capturing heterogeneities in an immature product. The constructed confidence intervals are shown to have exact, or asymptotically exact, frequentist coverage probabilities. Extensive simulations are conducted to compare the proposed procedures to other competing methods, including the large sample normal approximation, and the bootstrap. The simulation results reveal that the proposed intervals have satisfactory performance in terms of the coverage probability and the average interval length. The proposed interval estimation procedures are successfully applied to accelerated degradation data from commercial white LEDs.