Partially observed competing degradation processes: modeling and inference

The aim of the present paper is the stochastic modeling and statistical inference of a component which deteriorates over time, for prediction purpose. The deterioration is due to defects which appear one by one and next independently propagate over time. The motivation comes from an application to passive components within electric power plants, where (measurable) flaw indications first initiate (one at a time) and next grow over time. The available data come from inspections at discrete times, where only the largest flaw indication is measured together with the total number of indications on each component. Although detected, too small indications cannot be measured, leading to censored observations. Taking into account this partial information coming from the field, a specific stochastic model is proposed, where the flaw indications initiate according to a Poisson process and next propagate according to competing independent gamma processes. A parametric estimation procedure is developed, tested on simulated data and then applied to the industrial case. The fitted model is next used to make some prediction over the future deterioration of each component and over its residual operating time until a specified critical degradation level is reached. Copyright © 2016 John Wiley & Sons, Ltd.