On the Use of Stochastic Processes in Modeling Reliability Problems

Birolini, Alessandro

doi:10.1007/978-3-642-46553-6

Cited by 94 publications

(24 citation statements)

References 5 publications

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“…Maintaining a high or required level of reliability and/or availability is often an essential requisite. Two redundant repairable systems have been studied extensively in the past (Birolini [1], Yearout et al [2], and detailed bibliography is found in Sztrik [3]). A number of authors have investigated two-unit redundant systems under different assumptions (see Goel and Shrivastava [4], Shi and Li [5], de Almeida and Campello de Souza [6], Gururajan and Srinivasan [7], Shi and Liu [8], Rajamanickam and Chandrasekar [9], Billinton and Pan [10], Sridharan and Mohanavadivu [11], Yadavalli et al [12], and Seo et al [13]).…”

Section: Introductionmentioning

confidence: 99%

On a repairable system with an unreliable service station—Bayesian approach

Lee

Hsu

et al. 2008

Computers & Mathematics with Applications

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a b s t r a c tSystem characteristics of a two-unit repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the service station is unreliable. Times to failure and times to repair of the operating units are assumed to follow exponential distributions. In addition, failure times and repair times of the service station also follow exponential distributions. When times to failure and times to repair of operating units, failure times and repair times of the service station are with uncertain parameters, a Bayesian approach is adopted to evaluate system characteristics. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and the steady-state availability. Some numerical experiments are performed to illustrate the results derived in this paper.

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Section: Introductionmentioning

confidence: 99%

On a repairable system with an unreliable service station—Bayesian approach

Lee

Hsu

et al. 2008

Computers & Mathematics with Applications

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“…Two unit standby redundant systems have been studied extensively in the past (Osaki and Nakagawa, 1976;Kumar and Agarwal, 1980;Srinivasan and Subramanian, 1980;Birolini, 1985;Yearout et al, 1986;Ravichandran, 1990). However the study of n(≥ 3) unit standby redundant systems, though very important, has received much less attention, possibly because of the built-in difficulties in analyzing such systems.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of a three unit warm standby redundant system with repair

Srinivasan

Subramanian

2006

Ann Oper Res

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Two-unit warm standby redundant systems have been investigated extensively in the past. The most general model is the one in which both the lifetime and repair time distributions of the units are arbitrary. However the study of standby systems with more than two units, though very important, has received much less attention, possibly because of the built-in difficulties in analyzing them. Such systems have been studied only when either the lifetime or the repair time is exponentially distributed. When both these distributions are general, the problem appears to be intractable even in the case of cold standby systems. The present contribution is an improvement in the state of art in the sense that a three unit warm standby system is shown to be capable of comprehensive analysis. In particular we show that there are imbedded renewal points that render the analysis possible. Using these imbedded renewal points we obtain the reliability and availability functions.

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Section: Introductionmentioning

confidence: 99%

“…In recent monographs Srinivasan and Subramanian [ 11 and Birolini [4] present the state of the art of such systems. The successful analysis of such a system depends on the complexity of the underlying stochastic process [4]. In the literature most of the analysis reported so far is confined to measures like stationary availability, mean time to system failure, and interval reliability in the stationary case [4].…”

Section: Introductionmentioning

confidence: 99%

“…The successful analysis of such a system depends on the complexity of the underlying stochastic process [4]. In the literature most of the analysis reported so far is confined to measures like stationary availability, mean time to system failure, and interval reliability in the stationary case [4]. The measure's steady-state availability and mean time to system failure are independent of the transform variable and hence are obtainable in easily computable form.…”

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confidence: 99%

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Transient analysis of multiple-unit reliability systems

Sharma

Ravichandran

Dass

1989

Naval Research Logistics

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A general Markovian model representing several multiple‐unit redundant repairable systems is proposed and its transient behavior is studied. Specifically, for multiple‐unit reliability system the reliability and availability functions are derived in an explicit form for the transient case. The stationary availability and mean time to system failure are deduced from the main results as special cases.

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On the Use of Stochastic Processes in Modeling Reliability Problems

Cited by 94 publications

References 5 publications

On a repairable system with an unreliable service station—Bayesian approach

On a repairable system with an unreliable service station—Bayesian approach

Reliability analysis of a three unit warm standby redundant system with repair

Transient analysis of multiple-unit reliability systems

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