Extended composite importance measures for multi-state systems with epistemic uncertainty of state assignment

Xiahou, Tangfan; Liu, Yu; Jiang, Tao

doi:10.1016/j.ymssp.2018.02.021

Cited by 56 publications

(36 citation statements)

References 59 publications

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“…Many methods are presented to update the status with collected information, including Beyasian updating rule, Dempster combination rule, negation, dynamic model such as DEMATEL, neural model, and so on . The likelihood function is first defined as the product of probabilities.…”

Section: Preliminariesmentioning

confidence: 99%

A new soft likelihood function based on power ordered weighted average operator

Song

Deng

2019

Int J Intell Syst

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The likelihood function is widely used in data processing but the classical likelihood function is too strict to deal with data with extreme values in real applications.To address this issue, a soft likelihood function based on power ordered weighted average (POWA) operator for probability distribution is proposed. Compared with the existing soft likelihood functions, one of the main features of the proposed likelihood function is that the weighted mean is displayed by the geometric mean of the weighted probability products. As a result, the effect on final result caused by extreme data can be efficiently decreased. Numerical examples are used to illustrate the efficiency of the proposed soft likelihood function. K E Y W O R D S geometric mean, likelihood function, OWA operator, POWA operator, soft likelihood function | INTRODUCTIONDealing with uncertainty information plays an important role in real applications. 1-3 Many math tools, such as fuzzy sets, 4-6 rough sets, 7 Z-numbers, 8-11 belief structures, 12-14 D numbers 15-17 entropy function, 18,19 and evidence theory, 20-22 are presented to handle different types of uncertainty information. Among these tools, probability is heavily studied and is widely used in many applications, including decision making, 23-26 estimation, 27,28 and uncertain measurement. [29][30][31][32] One of the most used models in probability is the likelihood function, which is used when data are available to describe plausibility of a parameter value. [33][34][35] However, it is very strict in real applications since the original likelihood function made up with the probability product is too strict to show the compatibility probabilities for the different pieces of evidence since any piece of probabilities, which are low-value would greatly reduce the likelihood function.How to cite this article: Song Y, Deng Y. A new soft likelihood function based on power ordered weighted average operator. Int J Intell

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Section: Preliminariesmentioning

confidence: 99%

A new soft likelihood function based on power ordered weighted average operator

Song

Deng

2019

Int J Intell Syst

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“…respectively, whereR L la (t) andR U la (t) can be calculated by equations (27) and (28), respectively.…”

Section: Fuzzy Reliability Evaluation For a Multi-component Systemmentioning

confidence: 99%

“…Then, the a-cut level of the shape parameter of component l can be represented as h la (t) = ½h L la (t), h U la (t) with the lower bound In this example, all the fuzzy parameters are represented by TFNs and are tabulated in Table 2. Based on equations (27) and (28), the fuzzy survival probability of each component can be calculated under the internal degradation processes. As an illustration, the fuzzy survival probability of each component at time t = 10 months under the internal degradation processes is depicted in Figure 4.…”

Section: Case Studiesmentioning

confidence: 99%

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Reliability assessment for systems suffering competing degradation and random shocks under fuzzy environment

Tang

2019

Science Progress

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Reliability assessment of multi-component systems under competing degradation and random shocks has been intensively investigated in recent years. In most cases, the parameters associated with competing degradation and random shocks are represented by crisp values. However, due to insufficient data and vague judgments from experts, it may produce epistemic uncertainty with those parameters and they are befitting to be described as fuzzy numbers. In this article, the internal degradation is treated as a continuous monotonically increasing random process with respect to operating time, whereas the amount of cumulative damage produced by each external random shock is modeled by a geometric process. As components in a system suffer the same environmental condition, an external random shock will produce different amounts of cumulative damage to each component simultaneously. Each component fails when either the internal degradation or cumulative damage from the random shocks, whichever comes first, exceeds its corresponding random thresholds. Moreover, the parameters associated with the internal degradation and the random shocks are represented by triangular fuzzy numbers. The fuzzy reliability functions of components and the entire system are evaluated by a set of optimization models. A multi-component system, together with some comparative results, is presented to illustrate the implementation of the proposed method.

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“…Fuzzy UGF with fuzzy state probability function and performance rate was applied to evaluate fuzzy state probability of the MSS. Xiahou et al extended composite importance measures of MSSs by considering the epistemic uncertainty associated with component state assignment. The dynamic evidential network combined with the evidential Markov Chain and evidential network was proposed to calculate the system reliability and conditional reliability.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of multi‐state series systems with performance sharing mechanism under epistemic uncertainty

Qiu

Ming

2019

Quality & Reliability Eng

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For real engineering systems, it is sometimes difficult to obtain sufficient data to estimate the precise values of some parameters in reliability analysis. This kind of uncertainty is called epistemic uncertainty. Because of the epistemic uncertainty, traditional universal generating function (UGF) technique is not appropriate to analyze the reliability of systems with performance sharing mechanism under epistemic uncertainty. This paper proposes a belief UGF (BUGF)-based method to evaluate the reliability of multi-state series systems with performance sharing mechanism under epistemic uncertainty. The proposed BUGF-based reliability analysis method is validated by an illustrative example and compared with the interval UGF (IUGF)-based methods with interval arithmetic or affine arithmetic. The illustrative example shows that the proposed BUGF-based method is more efficient than the IUGF-based methods in the reliability analysis of multi-state systems (MSSs) with performance sharing mechanism under epistemic uncertainty.

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Extended composite importance measures for multi-state systems with epistemic uncertainty of state assignment

Cited by 56 publications

References 59 publications

A new soft likelihood function based on power ordered weighted average operator

A new soft likelihood function based on power ordered weighted average operator

Reliability assessment for systems suffering competing degradation and random shocks under fuzzy environment

Reliability analysis of multi‐state series systems with performance sharing mechanism under epistemic uncertainty

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