Economic analysis of the M/M/R machine repair problem with warm standbys

Sivazlian, B. D.; Wang, K.H.

doi:10.1016/0026-2714(89)90007-3

Cited by 53 publications

(22 citation statements)

References 9 publications

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“…The M/M/R machine repair problem with warm spares considered by Sivazlian and Wang [4] is a special case of our model with v = 0, a 1 = a 2 and l = l 1 . Case 2: If R = 1, a 1 = a 2 and l = l 1 , our model becomes the M/M/1 machine repair problem with spare and server multiple vacations (or single vacation) considered by Gupta [14].…”

Section: Casementioning

confidence: 99%

“…Numerous machine repair problems have been proposed, for example, no-spare M/M/R model by Feller [2], cold-standby M/M/R model by Toft and Boothroyd [3], and warm-standby M/M/R model by Sivazlian and Wang [4]. Wang [5] further investigated the M/M/R machine repair problem with mixed-standby spare.…”

Section: Introductionmentioning

confidence: 98%

“…Recently, Wang and Lee [6] generalized Sivazlian and Wang [4] model to the M/M/R machine repair problem with cold-standby and multiple modes of failure. Cost (profit) models in the machine repair problem have been investigated by several authors including Ashcroft [7], Elsayed [8], Hilliard [9], Gross et al [10,11], Sivazlian and Wang [4], Wang [5], and Wang and Lee [6]. As for a vacation model, comprehensive and excellent surveys, including some applications, were examined by Doshi [12] and Takagi [13].…”

Section: Introductionmentioning

confidence: 99%

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Vacation policies for machine repair problem with two type spares

Wang

2007

Applied Mathematical Modelling

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This paper studies the machine repair problem consisting of M operating machines with two types of spare machines (S = S-1 + S-2) and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return and operate two vacation policies. First, the servers take vacations repeatedly until they find the repair facility has at least one waiting failed machine in the queue. Second, the servers do not take a vacation again and remain idle until the first arriving failed machine arrives, which starts a busy period in the repair facility. For both policies, the servers have two service rates for repair-slow and fast. The matrix geometric theory is used to find the steady-state probabilities of the number of failed machines in the system as well as the performance measures. Some special cases are given. A direct search algorithm is used to simultaneously determine the optimal values of the number of two types of spares and the number of servers while maintaining a minimum specified level of system availability. (c) 2006 Elsevier Inc. All rights reserved

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Section: Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Vacation policies for machine repair problem with two type spares

Wang

2007

Applied Mathematical Modelling

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“…Numerous machine repair problems have been proposed, for example, no-spare M/M/R model by Feller [1], cold-standby M/M/R model by Toft and Boothroyd [2], and warmstandby M/M/R model by Sivazlian and Wang [3]. Wang [4] further investigated the M/M/R machine repair problem with mixed-standby spare.…”

Section: Introductionmentioning

confidence: 98%

“…Recently, Wang and Lee [5] generalized Sivazlian and Wang [3] model to the M/M/R machine repair problem with cold-standby and multiple modes of failure. Cost (profit) models in the machine repair problem have been investigated by several authors including Ashcroft [6], Elsayed [7], Hilliard [8], Gross et al [9,10], Sivazlian and Wang [3], and Wang [4,5]. Jain et al [11] examined the reliability characteristics of a M/M/1 machine repair model with M operating and S warm spares, where the failed machines may renege when the server is busy.…”

Section: Introductionmentioning

confidence: 99%

An optimum maintenance strategy for machine repair problem with spares and server vacations

Liou

Lee

2006

Journal of Information and Optimization Sciences

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This paper studies the machine repair problem consisting of M operating machines with S spare machines, and R servers (repairmen) who leave for a vacation of random length when there are no failed machines queuing up for repair in the repair facility. At the end of the vacation the servers return to the repair facility. Two vacation policies of servers are considered. First, the servers take vacations repeatedly until they find the repair facility has at least one waiting failed machine in the queue. Second, the servers don't take a vacation again and remain idle until the first arriving failed machine arrives, which starts a busy period in the repair facility. For both policies, birth and death process is used to developed the steadystate probabilities of the number of failed machines in the system as well as the performance measures. Some special cases are given. A Cost model is developed to obtain the optimal values of the number of spares and the number of servers while maintaining a minimum specified level of system availability.

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Diffusion approximation to theG/G/R machine repair problem with warm standby spares

Sivazlian

Wang

1990

Naval Research Logistics

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The G/G/R machine repair problem with M operating machines, S warm standby spares, and R repairmen is studied as a diffusion process. The steady‐state equations are formulated as diffusion equations subject to two reflecting barriers. The approximate diffusion parameters of the diffusion equations are obtained (1) under the assumption that the input characteristics of the problem are defined only by their first two moments rather than their probability distribution function, (2) under the assumption of heavy traffic approximation, that is, when queues of failed machines in the repair stage are almost always nonempty, and (3) using well‐known asymptotic results from renewal theory. Expressions for the probability density functions of the number of failed machines in the system are obtained. A study of the derived approximate results, compared to some of the exact results, suggests that the diffusion approach provides a useful method for solving complex machine‐repair problems.

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Economic analysis of the M/M/R machine repair problem with warm standbys

Cited by 53 publications

References 9 publications

Vacation policies for machine repair problem with two type spares

Vacation policies for machine repair problem with two type spares

An optimum maintenance strategy for machine repair problem with spares and server vacations

Diffusion approximation to theG/G/R machine repair problem with warm standby spares

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