A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

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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“…From (17), it can be concluded that q =q. Therefore, from (16),w = w and, consequently, D 1 =D 1 and D 2 =D 2 .…”

Section: Definitionmentioning

confidence: 95%

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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“…(1) The distribution for the k th working period from the beginning up states We suppose the system is in up states (U states) at the beginning. Let ( 1) k W   be the state occupancy probability vector at the start of the k th working period,…”

Section: Some Sojourn Time Distributions For Mrs-hds With Neglected Fmentioning

confidence: 99%

“…Reliability is an important feature of repairable systems [1]- [4]. In most existing literatures, reliability analysis is studied by modeling the repairable system as a Markov process (e.g., see [5]- [7]).…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of Markov history-dependent repairable systems with neglected failures

Zeng

Cui

et al. 2017

Reliability Engineering & System Safety

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Reliability analysis of Markov history-dependent repairable systems with neglected failures. Reliability Engineering and System Safety, 2017, 159, pp. Abstract:Markov history-dependent repairable systems refer to the Markov repairable systems in which some states are changeable and dependent on recent evolutional history of the system. In practice, many Markov history-dependent repairable systems are subjected to neglected failures, i.e., some failures do not affect system performances if they can be repaired promptly. In this paper, we develop a model based on the theory of aggregated stochastic processes to describe the history-dependent behavior and the effect of neglected failures on the Markov history-dependent repairable systems. Based on the developed model, instantaneous and steady-state availabilities are derived to characterize the reliability of the system. Four reliability-related time distributions, i.e., distribution for the k th working period, distribution for the k th failure period, distribution for the real working time in an effective working period, distribution for the neglected failure time in an effective working period, are also derived to provide a more comprehensive description of the system's reliability. Thanks to the power of the theory of aggregated stochastic processes, closed-form expressions are obtained for all the reliability indexes and time distributions. Finally, the developed indexes and analysis methods are demonstrated by a numerical example. 2 when evaluating the system's availability. For example, consider a failure in a water supply system that cut off the water supply to the end-users. If the failure is recovered in a relatively short period, e.g., several minutes, the end-users are possible to tolerate or even unaware of it. This kind of failure, which can be promptly repaired within the tolerance of the end-users, can therefore, be neglected when calculating the availability of the water supply system. Such failures are regarded as neglected failures and are commonly encountered in repairable systems. For instance, Zheng et al.[12] studied a single-unit Markov repairable system with repair time omission. Bao and Cui [13] considered series Markov repairable systems with neglected or delayed failures.Neglected failures also exist in MRS-HDS, e.g. the water distributed system, the power distributed networks, computer networks, etc. The introduction of changeable states, as a result of the neglected failures, makes standard Markov-process-based models incapable to capture the system's failure and repair behaviors. However, to the best of our knowledge, the effect of neglected failures on the reliability of MRS-HDS has not been considered before. To fill this gap, we develop a new model and associated reliability analysis method based on the theory of aggregated stochastic process and then derive some important reliability indexes for the system. Although a large number of literatures focused on obtaining reliability indexes for repairable systems (e.g.[14]-[16]), it is ...

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“…Also, Liu et al [10] has studied the system reliability in a cold standby repairable system with working vacations and vacation interruptions, where a matrix-analytic method is applied to derive the several important performance measures. Then Ardakan and Hamadani [1] investigated the reliability of the series-parallel systems with mixed redundancy strategy including the active and cold-standby components.…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis of standby systems with unreliable server and switching failure

Kuo

2016

Reliability Engineering & System Safety

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A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

Cited by 43 publications

References 41 publications

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

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

Reliability analysis of Markov history-dependent repairable systems with neglected failures

Comparative analysis of standby systems with unreliable server and switching failure

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