Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process

Rodríguez, Joanna; Lillo, Rosa E.; Ramírez‐Cobo, Pepa

doi:10.1016/j.ress.2014.10.020

Cited by 15 publications

(8 citation statements)

References 30 publications

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“…We have considered three inter-failure times because there are enough arrivals to establish correlations between the inter-failure times. On the other hand there are studies with more operational inter-failure times as [5] among others.…”

Section: The Data: Inter-failure Timesmentioning

confidence: 99%

“…In order to compare the MAP model developed in the previous section with the state of the art we choose the most recently model using the MAP methodology [5]. We apply to our data the 2-state non-stationary Markovian Arrival Process, in its canonical representation, denoted by M AP 2 .…”

Section: The 2-state Non-stationary Markovian Arrival Process (M Ap 2 )mentioning

confidence: 99%

“…In this sense the Markovian Arrival Process model (MAP) has the relevant property of dependence between consecutive inter-arrival times in a process with multiple events, that constitutes an effective tool for modeling the dependence in a multi-state process. In the literature several analysis with MAPs are found in Reliability such as analysis of an n-system under shocks and repairs [4] and the study of failures of an electrical N -component framework [5] among others.…”

Section: Introductionmentioning

confidence: 99%

“…The first method was developed by the authors in previous works ( [6], [7]). The second one is a recent model based on a non-stationary MAP of second order [5]. Our aim is to test our method comparing its performance versus some state of the art methodologies.…”

Section: Introductionmentioning

confidence: 99%

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Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

García-Mora

Santamaría

Rubio

2018

Journal of Computational and Applied Mathematics

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The most common assumptions in reliability studies are that failures occur independently and with the same distribution. However, these two assumptions are unrealistic in practice since inter-failure times are usually correlated and not identically distributed. In this sense the Markov Arrival Process (MAP) is an active research field for managing these features. We study two versions of the MAP approach. The first one is a model which we developed in previous works. The second one is based on a non-stationary MAP of second order. We compare the results of both models with simulated data.

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Section: The Data: Inter-failure Timesmentioning

confidence: 99%

Section: The 2-state Non-stationary Markovian Arrival Process (M Ap 2 )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

García-Mora

Santamaría

Rubio

2018

Journal of Computational and Applied Mathematics

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show abstract

“…The identifiability of the process is of crucial importance when inference is to be considered as we plan to do as future work. Either from a Bayesian viewpoint as in the work of Scott in year 1999 or in the work of Ramírez‐Cobo et al in year 2017 or from a moment‐matching method as in the work of Rodríguez et al, a statistical inference approach may be defined for fitting real data sets. On the other hand, the nonnegativity of the autocorrelation function of the batch sizes of the B M M P P 2 ( K ) is proven.…”

Section: Discussionmentioning

confidence: 99%

Findings about the BMMPP for modeling dependent and simultaneous data in reliability and queueing systems

Yera

Lillo

Ramírez‐Cobo

2018

Appl Stoch Models Bus & Ind

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The batch Markov‐modulated Poisson process (BMMPP) is a subclass of the versatile batch Markovian arrival process (BMAP), which has been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures, or risk events). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPPm(K ) is proven, where K is the maximum batch size and m is the number of states of the underlying Markov chain. This is a powerful result for inferential issues. On the other hand, some novelties related to the correlation and autocorrelation structures are provided.

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Performance Analysis of Shock Models Governed by a Discrete-Time Markovian Arrival Process

Nandi

Samanta

2018

J Indian Soc Probab Stat

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Failure modeling of an electrical N-component framework by the non-stationary Markovian arrival process

Cited by 15 publications

References 30 publications

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

Modeling dependence in the inter-failure times. An analysis in Reliability models by Markovian Arrival Processes

Findings about the BMMPP for modeling dependent and simultaneous data in reliability and queueing systems

Performance Analysis of Shock Models Governed by a Discrete-Time Markovian Arrival Process

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