On a Markov‐modulated shock and wear process

Abstract

Abstract:We present transient and asymptotic reliability indices for a single-unit system that is subject to Markov-modulated shocks and wear. The transient results are derived from the (transform) solution of an integro-differential equation describing the joint distribution of the cumulative degradation process and the state of the modulating process. Additionally, we prove the asymptotic normality of a properly centered and time-scaled version of the cumulative degradation at time t. This asymptotic result leads to a simple normal approximation for a properly centered and space-scaled version of the system's lifetime distribution. Two numerical examples illustrate the quality of the normal approximation.

A survey of maintenance and service logistics management: Classification and research agenda from a maritime sector perspective

“…As for aspect (ii), in the literature, modelling of the degradation process of systems operating in randomly varying environments has received large interest (see, e.g., [177,178,179,180,181]). These models assume that the deterioration status of systems under consideration evolves as a Markov chain and aim at deriving and computing reliability or availability of systems.…”

nSubpopulations experiencing stochastic degradation: reliability modeling, burn-in, and preventive replacement optimization

“…One of the predominant approaches to stochastic failure models is to descrie wear by a Lévy process, such as a Wiener process (Whitmore, 1995;Whitmore and Schenkelberg, 1997;Whitmore et al, 1998) or a gamma process (Lawless and Crowder, 2004;Padgett and Tomlinson, 2004;Park and Padgett, 2005;Liao et al, 2006). Other degradation-based approaches include using a stochastic process to model the failure rate (Aalen and Hakon, 2001) or dynamic operating environment (Kharoufeh, 2003;Kharoufeh and Cox, 2005;Kharoufeh and Mixon, 2009). Overviews of stochastic process-based failure models can be found in Singpurwalla (1995) and Lai and Xie (2006).…”

Condition-based maintenance policies for a combined wear and shock deterioration model with covariates

“…In comparison with Klutke and Yang (2002), Li and Luo (2005), Kharoufeh, Finkelstein, and Mixon (2006), Kharoufeh and Mixon (2009) and Xiang et al (2012), in our model both the wear and the shocks are affected by covariates. In our model, the shock magnitude is modeled by the generalized Pareto distribution, which can model the extreme shocks by adjusting the shock magnitude threshold parameter; see Hsing, Hüsler, and Leadbetter (1988) and van Noortwijk et al (2007).…”

“…In our model, the shock magnitude is modeled by the generalized Pareto distribution, which can model the extreme shocks by adjusting the shock magnitude threshold parameter; see Hsing, Hüsler, and Leadbetter (1988) and van Noortwijk et al (2007). In comparison with Klutke and Yang (2002), Li and Luo (2005), Kharoufeh et al (2006), Kharoufeh and Mixon (2009) and Xiang et al (2012), in our model the periodic inspection is extended to an aperiodic inspection and moreover the maintenance decision rule takes into account the environment state as in Zhao et al (2010) and Xiang et al (2012). Furthermore, we propose different maintenance policies based on the different deterioration sources.…”