Maximum Entropy Approach to Reliability of Multi-Component Systems with Non-Repairable or Repairable Components

Du, Yi-Mu; Chen, Jingfu; Guan, Xuefei; Sun, C. P.

doi:10.3390/e23030348

Cited by 7 publications

(4 citation statements)

References 32 publications

(42 reference statements)

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“…Due to the limit on currently accessible data, the verification of the developed model using other PBMs will be investigated in the future. The current modeling adopts a deterministic approach, and a probabilistic approach can also be employed for reliability analysis [ 46 , 47 , 48 ].…”

Section: Discussionmentioning

confidence: 99%

A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

et al. 2021

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This study develops a general temperature-dependent stress–strain constitutive model for polymer-bonded composite materials, allowing for the prediction of deformation behaviors under tension and compression in the testing temperature range. Laboratory testing of the material specimens in uniaxial tension and compression at multiple temperatures ranging from −40 ∘C to 75 ∘C is performed. The testing data reveal that the stress–strain response can be divided into two general regimes, namely, a short elastic part followed by the plastic part; therefore, the Ramberg–Osgood relationship is proposed to build the stress–strain constitutive model at a single temperature. By correlating the model parameters with the corresponding temperature using a response surface, a general temperature-dependent stress–strain constitutive model is established. The effectiveness and accuracy of the proposed model are validated using several independent sets of testing data and third-party data. The performance of the proposed model is compared with an existing reference model. The validation and comparison results show that the proposed model has a lower number of parameters and yields smaller relative errors. The proposed constitutive model is further implemented as a user material routine in a finite element package. A simple structural example using the developed user material is presented and its accuracy is verified.

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Section: Discussionmentioning

confidence: 99%

A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

et al. 2021

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“…Zhong et al studied the philosophical idea of failure science based on the practice of material fatigue and electrical and mechanical systems, and proposed the concept of "failurology", which means a science for failure [61,62]. In recent years, Sun has claimed that the theoretical basis of reliability analysis may require the assistance of the "applied theoretical physics" [63], and his team tried to interpret some reliability concepts such as time-variant hazard functions using the maximal entropy principle of statistical mechanics [64,65]. Unfortunately, all the above explorations did not result in a complete scientific theory system for reliability engineering till now.…”

Section: Posbist Reliability (Fuzzy Theory)mentioning

confidence: 99%

Belief Reliability: A Scientific Exploration of Reliability Engineering

Zhang,

Li,

et al. 2024

J. of Syst. Eng. Electron.

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This paper systematically introduces and reviews a scientific exploration of reliability called the belief reliability. Beginning with the origin of reliability engineering, the problems of present theories for reliability engineering are summarized as a query, a dilemma, and a puzzle. Then, through philosophical reflection, we introduce the theoretical solutions given by belief reliability theory, including scientific principles, basic equations, reliability science experiments, and mathematical measures. The basic methods and technologies of belief reliability, namely, belief reliability analysis, function-oriented belief reliability design, belief reliability evaluation, and several newly developed methods and technologies are sequentially elaborated and overviewed. Based on the above investigations, we summarize the significance of belief reliability theory and make some prospects about future research, aiming to promote the development of reliability science and engineering.

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“…We direct the reader to chapter 13 of Kapur (1998) for early applications of the standard method of maximum entropy to the discrete transportation problem. For more recent references to applications to a variety of problems in different fields, consider Abbas (2006), Larralde (2012), Zeibart et al (2013), Nguyen, Kreinovich, and Wu (2014), Lukits (2015), Salimi and Abbas (2017), Cuzzolin (2018), Lou and Cukier (2020), and Du, Chen, Guan, and Sun (2021). For applications to a related problem, namely, the determination of the copula underlying a joint distribution, consider Piantadosi et al (2012), AgaKouchak (2014), Borwein and Howlett (2019), Guo et al (2017), Fossaluzza et al (2018), and Yang, Li, and Y.P.and Huanga, G.H.…”

Section: Introductionmentioning

confidence: 99%

Joint probabilities under expected value constraints, transportation problems, maximum entropy in the mean

Gzyl

Mayoral

2023

Statistica Neerlandica

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Here we consider an application of the method of maximum entropy in the mean to solve an extension of the problem of finding a discrete probability distribution from the knowledge of its marginals. The extension consists of determining joint probabilities when, besides specifying the marginals, we specify the expected value of some given random variables. The proposed method can incorporate constraints as the the requirement that the joint probabilities have to fall within known ranges. To motivate, think of the marginal probabilities as demands or supplies, and of the joint probability as the fraction of the supplies to be shipped from the production sites to the demand sites, thus joint probabilities become transportation policies. Fixing the cost of a transportation policy is equivalent to requiring that the unknown probability yields a given value to some random variable, and prescribing the range for each unknown may have an economical interpretation.

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Maximum Entropy Approach to Reliability of Multi-Component Systems with Non-Repairable or Repairable Components

Cited by 7 publications

References 32 publications

A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

A General Temperature-Dependent Stress–Strain Constitutive Model for Polymer-Bonded Composite Materials

Belief Reliability: A Scientific Exploration of Reliability Engineering

Joint probabilities under expected value constraints, transportation problems, maximum entropy in the mean

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