Belief Reliability Distribution Based on Maximum Entropy Principle

Zu, Tianpei; Kang, Rui; Wen, Meilin; Zhang, Qingyuan

doi:10.1109/access.2017.2779475

Cited by 26 publications

(11 citation statements)

References 10 publications

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“…Compared with existing uncertain random systems in [15,16,28], the reliability index in proposed models is also defined by chance distribution. For the continuous system subject to competing failure processes, the models in [17] suffer from the independent degradation process and shocks.…”

Section: Remarkmentioning

confidence: 99%

Uncertain Random Optimization Models Based on System Reliability

Xu¹,

Zhu²

2020

IJCIS

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The reliability of a dynamic system is not constant under uncertain random environments due to the interaction of internal and external factors. The existing researches have shown that some complex systems may suffer from dependent failure processes which arising from hard failure and soft failure. In this paper, we will study the reliability of a dynamic system where the hard failure is caused by random shocks which are driven by a compound Poisson process, and soft failure occurs when total degradation processes, including uncertain degradation process and abrupt degradation shifts caused by shocks, reach a predetermined critical value. Two types of uncertain random optimization models are proposed to improve system reliability where belief reliability index is defined by chance distribution. Then the uncertain random optimization models are transformed into their equivalent deterministic forms on the basis of 𝛼-path, and the optimal solutions may be obtained with the aid of corresponding nonlinear optimization algorithms. A numerical example about a jet pipe servo valve is put forward to illustrate established models by numerical methods. The results indicate that the optimization models are effective to the reliability of engineering systems. It is our future work to consider an interdependent competing failure model where degradation processes and shocks can accelerate each other.

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Section: Remarkmentioning

confidence: 99%

Uncertain Random Optimization Models Based on System Reliability

Xu¹,

Zhu²

2020

IJCIS

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“…Since the research on the probability measure-based reliability evaluation using TTF data is comprehensive and in-depth, scholars have focused on how to conduct reliability evaluation using limited TTF data based on the uncertain measure recently. Zu et al 20,21 proposed a maximum entropy approach and a graduation formula to construct belief reliability distributions. Li et al 22 used an uncertainty distribution to evaluate the reliability under type-I and type-II censoring.…”

Section: Introductionmentioning

confidence: 99%

Belief reliability evaluation with uncertain right censored time‐to‐failure data under small sample situation

Chen

et al. 2022

Quality & Reliability Eng

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Uncertain right censoring (URC) which describes the situation that the censoring settings of test units are unrelated to their failure time often occurs in practical life testing. Besides, in practical life testing, the small sample situation is also common since the test resources are usually limited, which brings epistemic uncertainties to reliability evaluations due to the lack of information. Under such situation, the large sample‐based probability theory is not appropriate anymore to conduct reliability evaluations. In this paper, the belief reliability evaluation is conducted with uncertain right censored time‐to‐failure (TTF) data under the small sample situation based on the belief reliability theory. Firstly, to deal with epistemic uncertainties, a truncated normal uncertainty distribution of lifetime is given, and the belief reliability evaluation is presented using the uncertain measure. Then, the corresponding uncertain statistics method for unknown parameter estimation is provided with objective measures. Finally, a simulation study and a practical case are used to illustrate the proposed method. The results show that the proposed method is suitable to deal with epistemic uncertainties and can achieve more accurate and stable mean time‐to‐failure (MTTF) results with uncertain right censored TTF data under the small sample situation compared to classical probability and Bayesian reliability methods.

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“…Zeng et al [34] developed mathematical foundation of belief reliability for coherent systems based on uncertainty theory. Zu et al [35] proposed an optimal model based on maximum entropy principle to estimate belief reliability distribution. Zhang et al [36] investigated some belief reliability indexes on the basis of the belief reliability metric based on chance theory to measure reliability of uncertain random systems.…”

Section: Introductionmentioning

confidence: 99%

Reliability Assessment of Random Uncertain Multi-State Systems

Yue

Zhao

2019

IEEE Access

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The random uncertain multi-state system is defined as a multi-state system consisting of multi-state components whose performance rates and the corresponding state probabilities are presented as uncertain variables. Reliability assessment of random multi-state systems with enough samples based on probability theory has been widely investigated. Nevertheless, in some real-world applications, only a few or even no samples are available to estimate the state probabilities and performance rates of multistate components or systems. To overcome the problem, by joint employment of probability theory and uncertainty theory, the reliability of a random uncertain multi-state system is analyzed in this paper. The state probabilities and performance rates of multi-state components are considered as uncertain variables. The uncertain universal generating function is introduced to evaluate the state probabilities and performance rates of the random uncertain multi-state systems. The uncertainty distributions, inverse uncertainty distributions, expected values and variances of the state probabilities, and performance rates for the system are discussed. An assessment technique for system reliability is proposed to compute the system reliability under the crisp user demand. A numerical example is presented to illustrate how to assess the state probabilities, performance rates, and reliability of the system.

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Belief Reliability Distribution Based on Maximum Entropy Principle

Cited by 26 publications

References 10 publications

Uncertain Random Optimization Models Based on System Reliability

Uncertain Random Optimization Models Based on System Reliability

Belief reliability evaluation with uncertain right censored time‐to‐failure data under small sample situation

Reliability Assessment of Random Uncertain Multi-State Systems

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