Availability of periodically inspected systems with Markovian wear and shocks

Abstract

We analyze a periodically inspected system with hidden failures in which the rate of wear is modulated by a continuous-time Markov chain and additional damage is induced by a Poisson shock process. We explicitly derive the system's lifetime distribution and mean time to failure, as well as the limiting average availability. The main results are illustrated in two numerical examples.

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

“…Wang and Pham (2011) proposed an example of such deterioration where a battery supplying electric power degrades by both chemical reaction and overheating (overvoltage). Similarly to Kharoufeh et al (2006), in this study, we assume that the two deterioration sources are independent. The system failure occurs when the deterioration level DðtÞ exceeds a given threshold L.…”

“…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.…”

“…We study their application scope and efficiency and we analyze the sensitivity of their optimal decision parameters as in Moghaddam and Usher (2011). In contrast with Kharoufeh et al (2006), where the maintenance policy is evaluated based on reliability and availability measures, we evaluate the proposed maintenance policies by a cost criteria. A sensitivity analysis to cost variations is also carried out.…”

A modeling framework for deteriorating control system and predictive maintenance of actuators

“…It is described as the combination of two independent underlying processes which represent respectively a wear and a shock phenomena [21]. As a consequence the total damage at time t 4 0 may be written as…”