Uncertain Random Renewal Reward Process With Application to Block Replacement Policy

Yao, Kai; Zhou, Jian

doi:10.1109/tfuzz.2016.2544354

Cited by 22 publications

(6 citation statements)

References 35 publications

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“…Zhang et al ( 2013 ) proposed an uncertain delayed renewal process and a basic delayed renewal theorem. These three types of uncertain renewal processes have been extended in different directions (Yao & Gao, 2015 ; Yao & Zhou, 2016 , 2018a ; Yao, 2019 ), and the theoretical outcomes are exploited to determine systems’ block replacement strategies (Zhang & Guo, 2014 ; Ke & Yao, 2016 ), the optimal age replacement strategy for parts (Zhang & Guo, 2013 ) and the optimal replacement time for equipment (Yao & Ralescu, 2013 ).…”

Section: Discussion Of Development Historymentioning

confidence: 99%

A systematic review of uncertainty theory with the use of scientometrical method

Zhou

Jiang

Pantelous

et al. 2022

Fuzzy Optim Decis Making

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Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems.

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Section: Discussion Of Development Historymentioning

confidence: 99%

A systematic review of uncertainty theory with the use of scientometrical method

Zhou

Jiang

Pantelous

et al. 2022

Fuzzy Optim Decis Making

Self Cite

View full text Add to dashboard Cite

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“…In our paper, the lifetime of parts are assumed to be an uncertain variable, and the repair time to be a random variable in our repair policy; as a result, the interarrival times of replacements are uncertain random variables. Based on the chance theory (some concepts and properties of the uncertainty and chance theories are presented in Appendix), we propose a new type of extended renewal reward process with interarrival times consisted of random and uncertain variables, which is markedly different from classic uncertain random renewal reward process with random interarrival times, from Yao and Zhou (2016), to describe our optimal repair time policy.…”

Section: Extended Renewal Reward Processmentioning

confidence: 99%

“…Theorem 5. (Yao and Zhou, 2016) Let τ1,τ2,… be random rewards, and let ξ1,ξ2,… be uncertain interarrival times. Assume Nt is an uncertain renewal process with interarrival times ξ1,ξ2,… Then : is an uncertain random renewal reward process, andin the sense of convergence in distribution as t → ∞.…”

Section: Uncertain Theorymentioning

confidence: 99%

“…Yao and Gao (2015) proposed a concept of an uncertain random alternating renewal process and gave the limit chance distribution of the interval availability of the uncertain random alternating renewal system. And then, Yao and Zhou (2016) proposed the uncertain random reward process and applied to an uncertain random block replacement problem.…”

Section: Introductionmentioning

confidence: 99%

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Repair limit policy of aircraft component based on extended uncertain random renewal reward process

Zhang

Liu

et al. 2022

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PurposeThe purpose of this paper is to focus on an optimizing maintenance policy with repair limit time for a new type of aircraft component, in which the lifetime is assumed to be an uncertain variable due to no historical operation data, and the repair time is a random variable that can be described by the experimental data.Design/methodology/approachTo describe this repair limit time policy over an infinite time horizon, an extended uncertain random renewal reward theorem is firstly proposed based on chance theory, involves uncertain random interarrival times and stochastic rewards. Accordingly, the uncertain random programming model, which minimized the expected maintenance cost rate, is formulated to find the optimal repair limit time.FindingsA numerical example with sensitivity analysis is provided to illustrate the utility of the proposed policy. It provides a useful reference and guidance for aircraft optimization. For maintainers, it plays an important guiding role in engineering practice.Originality/valueThe proposed uncertain random renewal reward process proved useful for the optimization of maintenance strategy with maintenance limited time for a new type of aircraft components, which provides scientific support for aircraft maintenance decision-making for civil aviation enterprises.

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“…And the special cases such as the stationary increment process and the renewal process were discussed. Also, Yao and Zhou 39,40 proposed a special kind of uncertain random process, named the uncertain random renewal reward process, in which the renewal time and the rewards were defined as random variables and uncertain variables, respectively.…”

Section: Introductionmentioning

confidence: 99%

Uncertain process–based reliability and maintenance modeling for systems under mutually dependent degradation and shock processes

Zhang

2021

Quality & Reliability Eng

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For the systems that experience competing failure processes, an uncertain process–based degradation model is developed to describe the systems. The competing degradation process is composed of internal continuous degradation and external shocks, and the mutual dependence between them is considered. When the magnitude of the internal degradation exceeds the threshold, the soft failure occurs. While for the shock processes involving the randomness and the subjective information, we adopt the uncertain random renewal reward process to characterize it. Hard failure occurs when the damage of the shock process exceeds the strength threshold of the system. By using the belief reliability metric, the reliability of the degraded system is defined as the chance measure that neither soft failure nor hard failure occurs. And the effect of the degradation‐shock dependence on the system reliability is performed by the parametric studies. Then the proposed degradation model is introduced into the preventive maintenance strategy to minimize the average maintenance cost. Using the microelectromechanical systems as an example, the effectiveness of the constructed degradation model and maintenance strategy is illustrated, and the proposed model can characterize the system degradation process in a superior way to the stochastic process model. These methods can be applied to other similar degraded systems and provide support for maintenance decisions.

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Uncertain Random Renewal Reward Process With Application to Block Replacement Policy

Cited by 22 publications

References 35 publications

A systematic review of uncertainty theory with the use of scientometrical method

A systematic review of uncertainty theory with the use of scientometrical method

Repair limit policy of aircraft component based on extended uncertain random renewal reward process

Uncertain process–based reliability and maintenance modeling for systems under mutually dependent degradation and shock processes

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