A failure rate interaction model for two-component systems based on copula function

Peng, Wei; Huang, Hong‐Zhong

doi:10.1177/1748006x16629855

Cited by 5 publications

(6 citation statements)

References 22 publications

(36 reference statements)

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“…In this paper, it is assumed that a whole machine has n fault-related system components and its reliability function is R(t i ), i = 1, 2, • • • , n and the joint reliability function of these system components is R(t 1 , t 2 , • • • , t n ). Based on the Copula theory and Sklar theorem [42][43][44], a Copula function can be uniquely determined. It is expressed as follows:…”

Section: Calculation Of the Fault Influence Degree Of Edges In The Same Level Based On The Copula Functionmentioning

confidence: 99%

Dynamic Analysis Method for Fault Propagation Behaviour of Machining Centres

Zhang

Liu

et al. 2021

Applied Sciences

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Fault propagation behaviour analysis is the basis of fault diagnosis and health maintenance. Traditional fault propagation studies are mostly based on a priori knowledge of a causality model combined with rule-based reasoning, disregarding the limitations of experience and the dynamic characteristics of the system that cause deviations in the identification of critical fault sources. Thus, this paper proposes a dynamic analysis method for fault propagation behaviour of machining centres that combines fault propagation mechanisms with model structure characteristics. This paper uses the design structure matrix (DSM) to establish the fault propagation hierarchy structure model. Considering the correlation of fault time, the fault probability function of a component is obtained and the fault influence degree of nodes are calculated. By introducing the Copula and Coupling degree functions, the fault influence degree of the edges between the same level and different levels are calculated, respectively. This paper constructs a fault propagation intensity model by integrating the edge betweenness and uses it as an index to analyze real-time fault propagation behaviour. Finally, a certain type of machining centre is taken as an example for specific application. This study can provide as a reference for the fault maintenance and reliability growth of a machining centre.

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Section: Calculation Of the Fault Influence Degree Of Edges In The Same Level Based On The Copula Functionmentioning

confidence: 99%

Dynamic Analysis Method for Fault Propagation Behaviour of Machining Centres

Zhang

Liu

et al. 2021

Applied Sciences

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“…Gu 14 used the Clayton Copula function to describe the failure correlation among the subsystem of computer numerical control (CNC) lathe, then obtained the cumulative failure distribution of CNC lathe without considering system maintenance. Peng 9 mentioned the phenomenon of time‐lag correlation is common and proposed reliability predict model of two components in the unrepairable system based on copula function. Copula function could express correlation with time‐lag, but is restricted strictly by monotonically increasing cumulative failure distribution function.…”

Section: Introductionmentioning

confidence: 99%

Reliability prediction used dynamic Bayesian networks for redundant system with time‐lag correlation

Liu

Zhou

Jia

et al. 2022

Quality & Reliability Eng

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In the reliability prediction process of a redundant system, active units and standby units are assumed independent generally. Due to the interaction among units, failure of the active unit gives the standby unit a potential interior shock, then the standby unit fails after a period of operation. Therefore, the correlation between the active unit and the standby unit is triggered by the failure of the active unit and also has time‐lag. In this paper, a correlation estimated method with two parameters is proposed based on cross‐correlation analysis, where the two parameters are time‐lag interval and time‐lag correlation coefficient, the discriminant conditions of independent, simultaneous correlation and time‐lag correlation are given. Subsequently, the Conditional Probability Table (CPT) of Dynamic Bayesian Network (DBN) is updated by adding time‐lag intervals and time‐lag correlation coefficients. Then, DBN is optimized into Time‐lag Dynamic Bayesian Network (TDBN). Meanwhile, the modeling process and calculated method of TDBN are given. To reduce the complexity of TDBN, the maximum time‐lag correlation coefficient and the time‐lag interval corresponding are regarded as the main parameters to estimate time‐lag correlation. Finally, through the simulation analysis and the case of Chinese train control system (CTCS‐3), it could be seen that the reliability prediction of TDBN is more accurate than DBN, TDBN improves the reliability prediction accuracy of train and driver interface module to 0.8135 either.

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“…In the field of failure interaction research, Murthy and Nguyen [31] first proposed the failure interaction between the components and studied the preventive replacement strategy of two-component systems in the case of type I and type II failure interactions. Peng et al [32] studied a twocomponent system and proposed a failure rate interaction model based on the copula function in the case of type II failure interaction. Liu et al [33] established a renewable and free replacement model based on the type I failure interaction, taking the warranty cost as the optimization goal.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Extended Warranty Cost for Multi-Component Products with Failure Interaction

Wang

Dong

Cheng

et al. 2021

Discrete Dynamics in Nature and Society

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In practice, the assumption of failure independence between components is seldom valid, especially for those complex systems with complicated failure mechanism. Users can decide whether to purchase extended warranty (EW) at the end of basic warranty, and there are many factors that influence this decision, such as product reliability and EW price. In order to solve the problem of EW pricing for multi-component systems with failure interaction reasonably, considering the failure interaction characteristics between components of the multi-component systems, under the condition of type II failure interaction, this paper constructed a dependent failure rate model and developed a EW cost model of two-component systems. Thus, after optimizing the preventive maintenance (PM) strategy, this paper obtained the optimal PM interval when EW cost is the lowest, which is a win-win strategy to reduce the EW price for manufacturers and users under the premise of ensuring the manufacturer's profit demand. Finally, the validity of the model was verified by a numerical example and sensitivity analysis for important parameters was presented.

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A failure rate interaction model for two-component systems based on copula function

Cited by 5 publications

References 22 publications

Dynamic Analysis Method for Fault Propagation Behaviour of Machining Centres

Dynamic Analysis Method for Fault Propagation Behaviour of Machining Centres

Reliability prediction used dynamic Bayesian networks for redundant system with time‐lag correlation

Optimization of Extended Warranty Cost for Multi-Component Products with Failure Interaction

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