The Lindstrom-Madden Method for Series Systems with Repeated Components

Optimal adaptive inspection and maintenance for redundant systems

Proceedings of the Institution of Mechanical Engineers Part O Journal of Risk and Reliability ◽

10.1177/1748006x211020151 ◽

2021 ◽

pp. 1748006X2110201

Author(s):

Chaochao Lin ◽

Matteo Pozzi

Keyword(s):

Engineering Systems ◽

Discounted Cost ◽

Markov Decision ◽

Inspection And Maintenance ◽

And Performance ◽

Partially Observable ◽

Series Systems ◽

Selection Of ◽

Redundant Systems

Optimal exploration of engineering systems can be guided by the principle of Value of Information (VoI), which accounts for the topological important of components, their reliability and the management costs. For series systems, in most cases higher inspection priority should be given to unreliable components. For redundant systems such as parallel systems, analysis of one-shot decision problems shows that higher inspection priority should be given to more reliable components. This paper investigates the optimal exploration of redundant systems in long-term decision making with sequential inspection and repairing. When the expected, cumulated, discounted cost is considered, it may become more efficient to give higher inspection priority to less reliable components, in order to preserve system redundancy. To investigate this problem, we develop a Partially Observable Markov Decision Process (POMDP) framework for sequential inspection and maintenance of redundant systems, where the VoI analysis is embedded in the optimal selection of exploratory actions. We investigate the use of alternative approximate POMDP solvers for parallel and more general systems, compare their computation complexities and performance, and show how the inspection priorities depend on the economic discount factor, the degradation rate, the inspection precision, and the repair cost.

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Use of Basu-Dhar bivariate geometric distribution in the analysis of the reliability of component series systems

International Journal of Quality & Reliability Management ◽

10.1108/ijqrm-05-2018-0115 ◽

2019 ◽

Vol 36 (4) ◽

pp. 569-586

Author(s):

Ricardo Puziol Oliveira ◽

Jorge Alberto Achcar

Keyword(s):

Bayesian Approach ◽

Geometric Distribution ◽

Bivariate Distribution ◽

Dependence Structure ◽

Series System ◽

Engineering Applications ◽

Data Set ◽

Content Type ◽

Bivariate Geometric Distribution ◽

Series Systems

Purpose The purpose of this paper is to provide a new method to estimate the reliability of series system by using a discrete bivariate distribution. This problem is of great interest in industrial and engineering applications. Design/methodology/approach The authors considered the Basu–Dhar bivariate geometric distribution and a Bayesian approach with application to a simulated data set and an engineering data set. Findings From the obtained results of this study, the authors observe that the discrete Basu–Dhar bivariate probability distribution could be a good alternative in the analysis of series system structures with accurate inference results for the reliability of the system under a Bayesian approach. Originality/value System reliability studies usually assume independent lifetimes for the components (series, parallel or complex system structures) in the estimation of the reliability of the system. This assumption in general is not reasonable in many engineering applications, since it is possible that the presence of some dependence structure between the lifetimes of the components could affect the evaluation of the reliability of the system.

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Design method of exact model matching control for finite Volterra series systems

International Journal of Control ◽

10.1080/002071797223758 ◽

1997 ◽

Vol 68 (1) ◽

pp. 107-124 ◽

Cited By ~ 8

Author(s):

Osamu Yamanaka ◽

Hiromitsu Ohmori ◽

Akira Sano

Keyword(s):

Volterra Series ◽

Design Method ◽

Model Matching ◽

Exact Model ◽

Series Systems

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Some new results on redundancy allocation in series systems

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2021.1931329 ◽

2021 ◽

pp. 1-18

Author(s):

Yinzhao Wei ◽

Sanyang Liu ◽

Xiaoliang Ling

Keyword(s):

Redundancy Allocation ◽

In Series ◽

Series Systems

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Modeling dependent series systems with q-Weibull distribution and Clayton copula

Applied Mathematical Modelling ◽

10.1016/j.apm.2020.12.042 ◽

2021 ◽

Vol 94 ◽

pp. 117-138

Author(s):

Meng Xu ◽

Jeffrey W. Herrmann ◽

Enrique Lopez Droguett

Keyword(s):

Weibull Distribution ◽

Clayton Copula ◽

Dependent Series ◽

Series Systems

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Optimal allocation of a coherent system with statistical dependent subsystems

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964821000437 ◽

2021 ◽

pp. 1-20

Author(s):

Bin Lu ◽

Jiandong Zhang ◽

Rongfang Yan

Keyword(s):

Hazard Rate ◽

Optimal Allocation ◽

Stochastic Order ◽

Sufficient Conditions ◽

Parallel Systems ◽

Coherent System ◽

Allocation Policy ◽

Usual Stochastic Order ◽

Series Systems ◽

Parallel Series

Abstract This paper studies the optimal allocation policy of a coherent system with independent heterogeneous components and dependent subsystems, the systems are assumed to consist of two groups of components whose lifetimes follow proportional hazard (PH) or proportional reversed hazard (PRH) models. We investigate the optimal allocation strategy by finding out the number $k$ of components coming from Group A in the up-series system. First, some sufficient conditions are provided in the sense of the usual stochastic order to compare the lifetimes of two-parallel–series systems with dependent subsystems, and we obtain the hazard rate and reversed hazard rate orders when two subsystems have independent lifetimes. Second, similar results are also obtained for two-series–parallel systems under certain conditions. Finally, we generalize the corresponding results to parallel–series and series–parallel systems with multiple subsystems in the viewpoint of the minimal path and the minimal cut sets, respectively. Some numerical examples are presented to illustrate the theoretical findings.

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