Calculation of reliability function and remaining useful life for a Markov failure time process

Banjević, Dragan; Jardine, Andrew

doi:10.1093/imaman/dpi029

Cited by 145 publications

(88 citation statements)

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“…In this case, the known conditions are given: À T [ t 0 ;Z ðt 0 Þ ¼ j;´X 1 , X 2 ,…, X j-1 . According to the Law of Total Probability, Rðtjt 0 Þ is equal to: (12). The proof is shown in Appendix B.…”

Section: ) a New Componentmentioning

confidence: 97%

“…For instance,D 12 (7), which means the component is in state 1 at t 0 and state 2 at t. Also, in the area D 12 ,…”

Section: Determine Health Condition With Dga Informationmentioning

confidence: 99%

“…Accordingly, the model adopts the information on dissolved gas analysis (DGA) as covariate which affects the failure rates of power transformers. The MRL and conditional/unconditional SFs are calculated in [12] by a discrete Markov process and PHM for obtaining the additional insight on interactions between time-varying failure rates and reliability indices. Makis and Jardine [13] utilize a full parametric PHM and a timehomogeneous Markov chain to describe failure rates.…”

Section: Introductionmentioning

confidence: 99%

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Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

Wang

Shahidehpour

Guo

2017

J. Mod. Power Syst. Clean Energy

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The reliability of power transformers is subject to service age and health condition. This paper proposes a practical model for the evaluation of two reliability indices: survival function (SF) and mean residual life (MRL). In the proposed model, the periodical modeling of power transformers are considered for collecting the information on health conditions. The corresponding health condition is assumed to follow a continuous semi-Markov process for representing a state transition. The proportional hazard model (PHM) is introduced to incorporate service age and health condition into hazard rate. In addition, the proposed model derives the analytical formulas for and offers the analytical evaluation of SF and MRL. SF and MRL are calculated for new components and old components, respectively. In both cases, the proposed model offers rational results which are compared with those obtained from comparative models. The results obtained by the contrast of the proposed analytical method and the Monte Carlo method. The impact of different model parameters and the coefficient of variation (CV) on reliability indices are discussed in the case studies.

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Section: ) a New Componentmentioning

confidence: 97%

“…For instance,D 12 (7), which means the component is in state 1 at t 0 and state 2 at t. Also, in the area D 12 ,…”

Section: Determine Health Condition With Dga Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

Wang

Shahidehpour

Guo

2017

J. Mod. Power Syst. Clean Energy

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“…The proportional hazards models (PHM) and proportional intensity model (PIM), which are two statistical models in survival analysis, are useful tools for RUL estimation in combination with a trending model for the fault propagation process. Banjevic and Jardine [97] discussed RUL estimation for a Markov failure time process which includes a joint model of PHM and Markov property for the covariate evolution as a special case. Vlok et al [98] applied PIM with covariate extrapolation to estimate bearing residual life.…”

Section: Statistical Approachesmentioning

confidence: 99%

“…Advantages Disadvantages Statistical approaches [95][96][97][98][99][100][101][102][103] • Do not require condition monitoring • Population characteristics information enable longer-range forecast • Can be trained to recognize the types of faults…”

Section: Approachesmentioning

confidence: 99%

Machine Fault Diagnosis and Prognosis: The State of The Art

Tran¹,

Yang²

2009

International Journal of Fluid Machinery and Systems

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Machine fault diagnostic and prognostic techniques have been the considerable subjects of condition-based maintenance system in the recent time due to the potential advantages that could be gained from reducing downtime, decreasing maintenance costs, and increasing machine availability. For the past few years, research on machine fault diagnosis and prognosis has been developing rapidly. These publications covered in the wide range of statistical approaches to model-based approaches. With the aim of synthesizing and providing the information of these researches for researcher's community, this paper attempts to summarize and classify the recent published techniques in diagnosis and prognosis of rotating machinery. Furthermore, it also discusses the opportunities as well as the challenges for conducting advance research in the field of machine prognosis.

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A stochastic time scale based framework for system reliability under a Markovian dynamic environment

Jiang

Liu

2023

Naval Research Logistics

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Most engineering systems operate under stochastic dynamic environments. The variability and stochasticity of environmental conditions have a non‐negligible impact on the failure behavior of engineering systems. This article develops a reliability modeling and assessment framework for systems operating under a Markovian dynamic environment. The stochastic dynamic environment is characterized by a continuous‐time Markov chain. Using the cumulative exposure principle, the stochastic time scale, resulting from the cumulative effect of the Markovian dynamic environment, is computed via a Markov reward model. Based on the above settings, the system reliability model under the Markovian dynamic environment is developed. The maximum likelihood estimates and confidence intervals for the model parameters, including the transition rate matrix of the Markov chain, the reward rates of the Markov reward model, and the parameters of the baseline lifetime distribution, are obtained by utilizing the collected environment and lifetime data. The system reliability is then assessed with the estimated parameters. The effectiveness of the proposed framework are validated using simulation and through an application to a long‐term storage system. The results show that the unknown reliability model parameters can be accurately estimated, and the proposed model with the consideration of the cumulative effect of the Markovian dynamic environment can provide a more accurate reliability estimate than that without such a consideration.

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Calculation of reliability function and remaining useful life for a Markov failure time process

Cited by 145 publications

References 0 publications

Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

Applications of survival functions to continuous semi-Markov processes for measuring reliability of power transformers

Machine Fault Diagnosis and Prognosis: The State of The Art

A stochastic time scale based framework for system reliability under a Markovian dynamic environment

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