Modeling and Estimation for Degradation Data With Initiation-Growth Correlations

Influenced by dynamic environmental factors, the degradation rates of products often vary with initial levels. However, most existing degradation models assume a fixed or zero starting point and treat it as independent of subsequent process, leading to biased failure-time predictions, poorly timed maintenance, and elevated costs or risks. To fill this gap, we propose a Wiener-process degradation model that explicitly links the random initial phase to its ongoing deterioration, allowing both the degradation rate and the failure threshold to adapt to the initial state. We derive explicit expressions for the lifetime and remaining useful life (RUL) distributions, along with confidence intervals for model parameters. To construct confidence intervals for reliability metrics and prediction intervals for RUL, we propose tailored generalized inference and objective Bayesian inference, which ensure accurate coverage even in small samples. Through simulations and a real-world case study, we demonstrate that our approach more accurately captures individual variability and delivers tighter, more reliable life-time forecasts than traditional models.