Modeling ageing effects for multi-state systems with multiple components subject to competing and dependent failure processes

Abstract

This paper explores how the ageing process affects the two dependent and competing failure processes in the context of multi-state systems with multiple components. Ageing process is assumed to result in the decline of the product's intrinsic capacity to resist the exposed stresses. The state residence time is explicitly modeled with the consideration of the potential transition gap (the total number of states that the state transition process needs to stride across) and the cumulative ageing probability which is a measure of the likelihood that the product strength degrades. The random shock is assumed to cause abrupt changes in the one-step transition probabilities. The damage size is jointly determined by the shock magnitude and the cumulative ageing probability. Reliability analysis is conducted based on the continuous-time semi-Markov chain. Reliability functions for the degradation, abrupt failure, and competing failure processes are obtained respectively. An illustrative example of a multi-state transformer with four multi-state components is studied to demonstrate how the proposed method can be applied to the engineering practice.