Nonlinear general path models for degradation data with dynamic covariates

Degradation data have been widely used to estimate product reliability. Because of technology advancement, time-varying usage and environmental variables, which are called dynamic covariates, can be easily recorded nowadays, in addition to the traditional degradation measurements. The use of dynamic covariates is appealing because they have the potential to explain more variability in degradation paths. We propose a class of general path models to incorporate dynamic covariates for modeling of degradation paths. Physically motivated nonlinear functions are used to describe the degradation paths, and random effects are used to describe unit-to-unit variability. The covariate effects are modeled by shape-restricted splines. The estimation of unknown model parameters is challenging because of the involvement of nonlinear relationships, random effects, and shaped-restricted splines. We develop an efficient procedure for parameter estimations. The performance of the proposed method is evaluated by simulations. An outdoor coating weathering dataset is used to illustrate the proposed method. Copyright (c) 2015 John Wiley & Sons, Ltd.