New Models and Measures for Reliability of Multi-state Systems

Liu, Yung-Wen; Kapur, Kailash C.

doi:10.1007/978-1-84800-131-2_28

Cited by 12 publications

(12 citation statements)

References 38 publications

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“…In order to describe the multiple states of the system, the Markov process, the semi-Markov process and the non-homogeneous continuous Markov process are usually adopted, as in Refs. 65,66 . However, some degradation processes may be non-Markovian.…”

Section: Rul Prediction Methods Based On Indirect Monitoring Datamentioning

confidence: 98%

A survey on life prediction of equipment

Zhou

Zhang

et al. 2015

Chinese Journal of Aeronautics

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Once in the hands of end users, such durable equipment as spacecraft, aircraft, ships, automobiles, computers, etc. are in a state of debugging, working or storage. In either state, availability, reliability and super-efficiency are the ultimate goals, which have been achieved through constant monitoring as well as regular, preventive, routine and corrective maintenance. Although some advanced instruments can visualize certain invisible malfunctioning phenomena into visible ones, deeply hidden troubles cannot be found unless monitoring and testing data are addressed using tools that process the data statistically, analytically and mathematically. Some state-of-theart trouble-shooting and life-predicting techniques and approaches are introduced in this paper. ª 2015 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

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Section: Rul Prediction Methods Based On Indirect Monitoring Datamentioning

confidence: 98%

A survey on life prediction of equipment

Zhou

Zhang

et al. 2015

Chinese Journal of Aeronautics

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“…Often, the use of common mathematical tools, such as MATLAB or MATHCAD and so on, may induce the problem of inaccuracy (Liu and Kapur 2008;Liu and Huang 2010). The bound approximation approach (Ding et al 2009) allows the determination of instantaneous state probabilities for a multi-state degraded system.…”

Section: Markov Reward Modelmentioning

confidence: 99%

“…In this scenario, the number of possible system states is increased, making it extremely difficult to solve the NHCTMM. Considering a non-repairable multi-state system, Liu and Kapur (2008) deduced the instantaneous dynamic probability of a multi-state system given the initial state p k (0) = 1, p i (0) = 0, 1 ≤ i ≤ k − 1. The instantaneous probability for the best state k can be written as:…”

Section: Markov Model Of Multi-state Degraded Componentsmentioning

confidence: 99%

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Optimization of preventive maintenance for a multi-state degraded system by monitoring component performance

Huang

Wang

2014

J Intell Manuf

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This study aims to construct an optimal preventive maintenance model for a multi-state degraded system under the condition that individual components or subsystems can be monitored in real time. Given the requirement of minimum system availability, the total maintenance cost is minimized by determining the maintenance activities of components in degraded states. The general non-homogeneous continuous-time Markov model (NHCTMM) and its analogous Markov reward model (NHCTMRM) are used to quantify the intensity of state transitions during the degradation process, allowing the determination of various performance indicators. The bound approximation approach is applied to solve the established NHCTMMs and NHCTMRMs, thus obtaining instantaneous system state probabilities to overcome their inherent computational difficulties. Furthermore, this study utilizes a genetic algorithm to optimize the proposed model. A simulation illustrates the feasibility and practicability of the proposed approach.

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“…Under this consideration, conventional mathematics cannot obtain explicit expressions of NHCTMM and NHCTMRM solutions. Often, using calculators as common mathematical tools, such as MATLAB or Mathcad, may induce the problem of inaccuracy [7][8][9][10]. Ding et al [9] developed the bound approximation approach that can solve the NHCTMMs efficiently.…”

Section: Introductionmentioning

confidence: 99%

A Time‐Replacement Policy for Multistate Systems with Aging Components under Maintenance, from a Component Perspective

Huang

Wang

2019

Mathematical Problems in Engineering

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This study aims for multistate systems (MSSs) with aging multistate components (MSCs) to construct a time-replacement policy and thereby determine the optimal time to replace the entire system. The nonhomogeneous continuous time Markov models (NHCTMMs) quantify the transition intensities among the degradation states of each component. The dynamic system state probabilities are therefore assessed using the established NHCTMMs. Solving NHCTMMs is rather complicated compared to homogeneous continuous time Markov models (HCTMMs) in determining reliability related performance indexes. Often, traditional mathematics cannot acquire accurate explicit expressions, in particular, for multiple components that are involved in designed system configuration. To overcome this difficulty, this study uses Markov reward models and the bound approximation approach to assess rewards of MSSs with MSCs, including such things as total maintenance costs and the benefits of the system staying in acceptable working states. Accordingly, we established a long-run expected benefit (LREB) per unit time, representing overall MSS performance through a lifetime, to determine the optimal time to replace the entire system, at which time the LREB values are maximized. Finally, a simulated case illustrates the practicability of the proposed approach.

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New Models and Measures for Reliability of Multi-state Systems

Cited by 12 publications

References 38 publications

A survey on life prediction of equipment

A survey on life prediction of equipment

Optimization of preventive maintenance for a multi-state degraded system by monitoring component performance

A Time‐Replacement Policy for Multistate Systems with Aging Components under Maintenance, from a Component Perspective

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