Availability of periodically inspected systems with Markovian wear and shocks

This paper tackles with the maintenance decision-making of gradually deteriorating control systems. The main feature of these systems is their ability within a closedloop to drive actuators in order to set the controlled process in a given state.Usually, the literature deals with the diagnosis of faults of a control system and the means for recovering system performances after their appearance. The controller reconfiguration is one of these means. The root cause of a fault is rarely argued nor its occurrence time. Before designing maintenance policies, this paper proposes a stochastic modeling framework of a degrading control system focusing on the actuator deterioration. It is assumed a close relationship between the controller setting, the actuator deterioration and finally its faulty situations. These latter are related to given degradation thresholds. Due to the stochastic nature of the deterioration, the corresponding hitting times are thus random. The obtained models allow to assess the conditional reliability of the actuator and then the prognosis of its residual useful life namely the RUL. This RUL is finally used to achieve two maintenance policies based upon the reconfiguration of the controller considered as a new maintenance action.Prepared using sagej.cls

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“…For that, the degradation model developed in Kharoufeh et al (2006); Kharoufeh (2003) is considered.…”

Section: Actuator Degradation Modelmentioning

confidence: 99%

Joint maintenance and controller reconfiguration policy for a gradually deteriorating control system

Langeron

Grall

Barros

2017

Proceedings of the Institution of Mechanical Engineers, Part O:

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“…, with respect to x, can be derived explicitly (see [24,25]). Let α be the initial distribution vector of the environment, e is a column vector of ones, and e i is a column vector whose ith entry is unity and all others are zero.…”

Section: The Cumulative Degradation Up To Time T Denoted By X(t) Ismentioning

confidence: 99%

“…Moreover, the LST of the nth moment of T x , conditioned on the initial state of the environment, is obtained by (see [25])…”

Section: : Approximate the Lifetime Distribution Function And Momentsmentioning

confidence: 99%

“…Kiessler et al [26] investigated the limiting average availability of a system whose time-varying wear rates are governed by a continuous-time Markov chain. Kharoufeh et al [25] extended the model of [26] by including damage-inducing shocks that arrive according to a timehomogeneous Poisson process and deriving the Laplace-Stieltjes transforms of transient reliability indices. Ebrahimi [12] considered a system whose degradation is comprised of a continuous wear component as well as jumps.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, we exploit phase-type (PH) distributions to approximate environment state holding times, thereby inducing a Markovian structure that is amenable to exact analysis by the methods described in [24,25]. We provide guidance on selecting an appropriate PH distribution approximation for each environment holding time.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic models for degradation-based reliability

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We present hybrid, degradation-based reliability models for a single-unit system whose degradation is driven by a semi-Markov environment. The primary objective is to develop a mathematical framework and associated computational techniques that unite environmental data and stochastic failure models to assess the current or future health of the system. By employing phase-type distributions, we construct a surrogate environment process that is amenable to analysis by exact Markovian techniques to obtain reliability estimates. By way of two numerical experiments, we illustrate the viability of our approach and assess the quality of the approximations. The numerical results indicate that remarkably accurate lifetime distribution and moment approximations are attainable.

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On a Markov‐modulated shock and wear process

Kharoufeh

Mixon

2009

Naval Research Logistics

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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.

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Availability of periodically inspected systems with Markovian wear and shocks

Cited by 26 publications

References 12 publications

Joint maintenance and controller reconfiguration policy for a gradually deteriorating control system

Joint maintenance and controller reconfiguration policy for a gradually deteriorating control system

Stochastic models for degradation-based reliability

On a Markov‐modulated shock and wear process

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