Economic and economic-statistical design of a multivariate Bayesian control chart for condition-based maintenance

Yin, Zhijian; Makiš, Viliam

doi:10.1093/imaman/dpp026

Cited by 33 publications

(11 citation statements)

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“…We also show in this paper that the optimal control policy for the threestate version of our model is a control limit policy. This provides a formal justification for the recent articles by Yin and Makis [38] and Kim et al, [20] who proposed Bayesian control charts for maintenance decision making, but did not prove that such a control policy is optimal. This also shows that the 2 control chart recently proposed by Wu and Makis [35] is in fact a suboptimal control policy.…”

Section: Introductionmentioning

confidence: 89%

Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

Kim

Makiš

2012

Stochastic Models

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We model a partially observable deteriorating system subject to random failure. The state process follows an unobservable continuous time homogeneous Markov chain. At equidistant sampling times vector-valued observations having multivariate normal distribution with statedependent mean and covariance matrix are obtained at a positive cost. At each sampling epoch a decision is made either to run the system until the next sampling epoch or to carry out full preventive maintenance, which is assumed to be less costly than corrective maintenance carried out upon system failure. The objective is to determine the optimal control policy that minimizes the long-run expected average cost per unit time. We show that the optimal preventive maintenance region is a convex subset of Euclidean space. We also analyze the practical threestate version of this problem in detail and show that in this case the optimal policy is a control limit policy. An efficient computational algorithm is developed for the three-state problem, illustrated by a numerical example.

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Section: Introductionmentioning

confidence: 89%

Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

Kim

Makiš

2012

Stochastic Models

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“…Wang extended the ideas presented in Makis and Yin and Makis and proposed a simulation‐based multivariate Bayesian (economic) control chart. The proposed control chart is very useful for monitoring real‐time condition‐based maintenance of complex systems.…”

Section: Bayesian Control Chartsmentioning

confidence: 99%

An Overview of Control Charts for High‐quality Processes

Ali

Pievatolo

Göb

2016

Quality & Reliability Eng

112

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Major difficulties in the study of high‐quality processes with traditional process monitoring techniques are a high false alarm rate and a negative lower control limit. The purpose of time‐between‐events control charts is to overcome existing problems in the high‐quality process monitoring setup. Time‐between‐events charts detect an out‐of‐control situation without great loss of sensitivity as compared with existing charts. High‐quality control charts gained much attention over the last decade because of the technological revolution. This article is dedicated to providing an overview of recent research and presenting it in a unifying framework. To summarize results and draw a precise conclusion from the statistical point of view, cross‐tabulations are also given in this article. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Rahim et al 29 developed the economic-statistical design model for the X chart when in-control times follow a Gamma (l,2) distribution. Some recent works an economic-statistical design of control charts are as follows: Kim et al, 30 Torng et al, 31 Chen et al, 32 Celano 33 , Faraz, 34 and Yin et al 35 Because there has been little work performed on the economic design of ACC, we provide a model for designing ACC that considers both economic and statistical criteria. In this article, we build an optimization model with an economic objective function and statistical constraints.…”

Section: S Hewhartmentioning

confidence: 99%

“…developed the economic‐statistical design model for the

\overset{X}{true}

chart when in‐control times follow a Gamma ( λ ,2) distribution. Some recent works an economic‐statistical design of control charts are as follows: Kim et al ., Torng et al ., Chen et al ., Celano, Faraz, and Yin et al …”

Section: Introductionmentioning

confidence: 99%

Economic‐Statistical Design of Acceptance Control Chart

Mohammadian

Amiri

2012

Quality & Reliability Eng

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Acceptance control charts are effective tools to monitor capable processes in which the fraction of the produced nonconforming items is very low. In these charts, some controlled changes in the process mean are allowed, and the production of a specified number of defectives is tolerated. Designing these acceptance control charts by considering the cost of sampling, detecting, and investigating out‐of‐control signals as well as the probable correction of assignable cause(s) can result in economic advantages. Moreover, the statistical properties of the control charts can be satisfied. In this article, an economic‐statistical model is developed to design acceptance control charts. An illustrative example is used to compare the results of economic versus economic‐statistical design of the acceptance control charts. In addition, a comprehensive sensitivity analysis is conducted on the basis of the parameters of the model. Copyright © 2012 John Wiley & Sons, Ltd.

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Economic and economic-statistical design of a multivariate Bayesian control chart for condition-based maintenance

Cited by 33 publications

References 0 publications

Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

Optimal Control of a Partially Observable Failing System with Costly Multivariate Observations

An Overview of Control Charts for High‐quality Processes

Economic‐Statistical Design of Acceptance Control Chart

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