A stochastic framework to model deterioration in engineering systems

•A stochastic framework to model deterioration in engineering systems is proposed.•Modeling the effect of deterioration on both capacity and demand.•Modeling the dependence between the deterioration process and demand.•Modeling the combination of shock and gradual deterioration process.•A method is proposed to estimate total deterioration and the time to failure.

Almost every engineering system deteriorates over time due to exposure to extreme conditions and during routine use. Deterioration is a serious concern in engineering because it can considerably reduce the life and reliability of systems. In this work, we develop a novel general stochastic framework to model the deterioration process. We model the deterioration process as a combination of shock and gradual process. We account for the effects of deterioration on both capacity of a system and the imposed demands on the system. The framework accounts for two types of failure; demand exceeding capacity and accumulated damage exceeding allowable limit. An accurate and computationally efficient semi-analytical solution and an approximate solution are proposed to estimate the time to failure. We illustrate the steps in the proposed framework using two numerical examples. The proposed framework can be used to improve the reliability of systems and to optimize their performance.