Maximum entropy approach to reliability

Du, Yi-Mu; Ma, Yuhan; Wei, Yuan-Fa; Guan, Xuefei; Sun, C. P.

doi:10.1103/physreve.101.012106

Cited by 20 publications

(11 citation statements)

References 37 publications

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“…These results are reduced to the single-component case [2], which coincides with the reduction of the reliability block diagram in Figure 3.…”

Section: Homogeneous Hazard Assumptionsupporting

confidence: 79%

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

Chen

Guan

et al. 2021

Entropy

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The degradation and recovery processes are multi-scale phenomena in many physical, engineering, biological, and social systems, and determine the aging of the entire system. Therefore, understanding the interplay between the two processes at the component level is the key to evaluate the reliability of the system. Based on the principle of maximum entropy, an approach is proposed to model and infer the processes at the component level, and is applied to repairable and non-repairable systems. By incorporating the reliability block diagram, this approach allows for integrating the information of network connectivity and statistical moments to infer the hazard or recovery rates of the degradation or recovery processes. The overall approach is demonstrated with numerical examples.

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“…These results are reduced to the single-component case [2], which coincides with the reduction of the reliability block diagram in Figure 3.…”

Section: Homogeneous Hazard Assumptionsupporting

confidence: 79%

“…For high reliability-demanding systems or parts, the sample size is usually small. To alleviate the difficulty, the previous study [2] proposed a method based on the maximum entropy principle (MaxEnt) [3][4][5] to estimate the hazard rate function and the lifetime distribution with limited lifetime testing data of the whole system.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Guan

et al. 2021

Entropy

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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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“…The predictive models established based on scarce samples may highly depend on the chosen parameter estimation method [4,5]. In those cases, the probabilistic approach is usually preferred over the deterministic approach [6][7][8][9][10][11]. The Bayes rule provides a consistent and rational mathematical device to incorporate relevant information and prior knowledge for probabilistic inference.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Inference under Small Sample Sizes Using General Noninformative Priors

Wang

Huang

et al. 2021

Mathematics

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This paper proposes a Bayesian inference method for problems with small sample sizes. A general type of noninformative prior is proposed to formulate the Bayesian posterior. It is shown that this type of prior can represent a broad range of priors such as classical noninformative priors and asymptotically locally invariant priors and can be derived as the limiting states of normal-inverse-Gamma conjugate priors, allowing for analytical evaluations of Bayesian posteriors and predictors. The performance of different noninformative priors under small sample sizes is compared using the likelihood combining both fitting and prediction performances. Laplace approximation is used to evaluate the likelihood. A realistic fatigue reliability problem was used to illustrate the method. Following that, an actual aeroengine disk lifing application with two test samples is presented, and the results are compared with the existing method.

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Maximum entropy approach to reliability

Cited by 20 publications

References 37 publications

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

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

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

Bayesian Inference under Small Sample Sizes Using General Noninformative Priors

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