A unified formalism for modeling and reliability estimation of degrading systems Riascos-Ochoa, Javier; Sánchez-Silva, Mauricio; Klutke, Georgia-Ann
We present a framework to model degradation on deteriorating systems, and to find easy-to- evaluate expressions for important reliability quantities. The model allows to combine multiple degradation mechanisms in the form of shock-based degradation with arbitrary shock sizes and progressive degradation (as deterministic drift plus a gamma process, among others). In addition, the proposed approach can be used to obtain expressions for the reliability function, the mean and n-moments of the deterioration process Xᵼ, and the probability density and moments of the lifetime L. In this paper we also present a novel numerical method to compute these expressions, which is highly efficient and accurate. Furthermore, several deterioration models are compared in terms of the calculated reliability quantities, and the feasible moments of the deterioration Xᵼ. The results demonstrate the generality, versatility, efficiency and accuracy of the proposed framework, which can open a new productive research field in the area of probabilistic degradation models.
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