A Bivariate Replacement Policy for a Cold Standby System Under Poisson Shocks

Wu, Qingtai; Zhang, Jin

doi:10.1080/01966324.2013.852489

Cited by 2 publications

(3 citation statements)

References 20 publications

(26 reference statements)

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“…Lemma 5 (see [6]). The operating time of the component in the th cycle is ( ) ; its distribution function is ( ) ( ); then…”

Section: Model Developmentmentioning

confidence: 99%

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Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

Chen¹,

Meng²,

Chen³

2014

Mathematical Problems in Engineering

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This paper considers the reliability analysis of a two-component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensityλ>0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.

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“…Lemma 5 (see [6]). The operating time of the component in the th cycle is ( ) ; its distribution function is ( ) ( ); then…”

Section: Model Developmentmentioning

confidence: 99%

“…The shock model, one kind of familiar models in the reliability theory, has been extensively studied [4]. Traditionally, there are three classic random shock models focused: extreme shock models, cumulative shock models, and -shock models [5,6]. Study the extreme shock models: the system fails when an individual shock is too large.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

Chen¹,

Meng²,

Chen³

2014

Mathematical Problems in Engineering

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“…They optimise their costs per unit time. Wu and Zhang [5] consider an infinite-horizon bivariate maintenance policy dependent on the interval length between preventive replacements and the number of component failures for a two-component cold-standby system subject to Poisson shocks. Coria et al [6] develop an analytical optimisation method based on a new hazard function for imperfect preventive maintenance policy over an infinite planning horizon.…”

Section: Introductionmentioning

confidence: 99%

Inspection and maintenance optimisation of multicomponent systems

Babishin¹

2021

Preprint

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The present research proposes methodology and mathematical models for optimisation of inspection and maintenance in complex multicomponent systems with finite planning horizon. Components are classified by failure types: hard-type and soft-type. The systems analysed are composed of either multiple identical hidden soft-type components in k-out-of-n redundant configuration, or a combination of hard-type and hidden soft-type components. Failures of hard-type components cause system failures. Failures of components in k-out-of-n systems and soft-type component failures are hidden and not discoverable until an inspection, but reduce the system’s reliability and performance. The systems are inspected either periodically, or non-periodically. They are also inspected opportunistically at the times of system failure (occurring at (k – n + 1)st component failures in k-out-of-n systems, or at hard failures in the systems composed of hard-type and soft-type components). Inspections have negligible duration. All components may undergo minimal repair, or corrective replacement, with hard-type components also having a possibility of preventive replacement under periodic inspections. We only consider minimal repair and corrective replacement under non-periodic inspections. We propose several models for joint optimisation of inspection and maintenance policies that result in the lowest total expected cost. Since soft failures are hidden, we generate expected values for the number of minimal repairs, number of replacements and downtime recursively. Due to multiple component interactions and system complexity, Monte Carlo simulation and genetic algorithms (GA) are used for optimisation. Using GA for optimisation allows to consider quasi-continuous inspection intervals due to improved computational efficiency compared to Monte Carlo simulation. Some of proposed models feature preventive component replacements and are applicable even for systems with hidden component failures. For k-out-of-n systems, we apply periodic model to series and parallel systems and compare the results. We provide expressions for expected number of system failures in terms of cost ratio and component failure intensity. We also provide a simplified expression for system reliability. In addition, we derive a formula for finding the planning horizon length based on expected number of system failures. It may be useful for planning the system’s operating horizon, at the system design stage and when analysing its performance.

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A Bivariate Replacement Policy for a Cold Standby System Under Poisson Shocks

Cited by 2 publications

References 20 publications

Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

Inspection and maintenance optimisation of multicomponent systems

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