Repair Priority Effect on Availability of a 2-unit System

Mine, Hisashi; Kawai, Hiroyuki

doi:10.1109/tr.1979.5220620

Cited by 8 publications

(3 citation statements)

References 2 publications

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“…A lot of work has been done on reliability and cost analysis of various systems by various researchers including [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] who have analyzed these systems by considering various concepts like the Erlangian repair time, operating and rest periods, hardware/software faults, congestion of calls, availability, two types of repair facility, human failure, regenerative point technique, priority repair discipline, instruction, accident, patience time, chances of nonavailability of expert repairman, one big unit and two small identical units with priority for operation/repair to big unit, patience time, partial failures, and optimized maintenance of the diesel system in locomotives. In all such studies, the demand was fixed.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

Malhotra

Taneja

2014

Journal of Quality and Reliability Engineering

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The present paper analyzes a two-unit cold standby system wherein both units may become operative depending upon the demand. Initially, one of the units is operative while the other is kept as cold standby. If the operative unit fails or the demand increases to the extent that one operative unit is not capable of meeting the demand, the standby unit becomes operative instantaneously. Thus, both units may become operative simultaneously to meet the increased demand. Availability in three types of upstates is as follows: (i) when the demand is less than or equal to production manufactured by one unit; (ii) when the demand is greater than whatever produced by one unit but less than or equal to production made by two units; and (iii) when the demand is greater than the produces by two units. Other measures of the system effectiveness have also been obtained in general case as well as for a particular case. Techniques of semi-Markov processes and regenerative processes have been used to obtain various measures of the system effectiveness. 1 ( ) = ((1 − 3 22 * ( )) − 02 * ( ) 20 * ( )) × [ (1 − 9 66 * ( )) × (1 − 10 77 * ( ) − 57 * ( ) 75 * ( )) − 15 * ( ) 51 * ( ) (1 − 10 77 * ( )) Journal of Quality and Reliability Engineering 7 + (1 − 10 77 * ( )) × (− 16 * ( ) ( 51 * ( ) 8 65 * ( ) + 16 * ( ))) − 75 * ( ) 16 * ( ) × ( (8,10) 67 * ( ) + (9,10) 67 * ( )) + 61 * ( ) 57 * ( )] + 10 * ( ) × [(1 − 9 66 * ( )) × ((1 − 10 77 * ( )) − 57 * ( ) 75 * ( )) × ( 01 * ( ) (1 − 3 22 * ( )) + 02 * ( ) 4 21 * ( )) + 02 * ( ) (1 − 10 77 * ( )) × ( ( 51 * ( ) 8 65 * ( ) + 61 * ( )) + ( (3,9) 26 * ( ) + (4,9) 26 * ( )) + (1 − 9 66 * ( )) (4,8) 25 * ( ) 51 * ( )) − 51 * ( ) 75 * ( ) ( (8,10) 67 * ( ) + (9,10) 67 * ( )) × ( (3,9) 26 * ( ) + (4,9) 26 * ( )) − 51 * ( ) 75 * ( ) × (1 − 9 66 * ( ))

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Section: Introductionmentioning

confidence: 99%

Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

Malhotra

Taneja

2014

Journal of Quality and Reliability Engineering

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“…Many kinds of repairable parallel systems have been studied extensively according to different requirements in the past. For example, a 2-unit parallel system with priority repair was concerned in Mine and Kawai [17], then the optimality of Late Preemption Rule was shown and the effect of the rule on the availability of the system was investigated. Chung [3] presented a mathematical model of a repairable parallel system with standby units involving human error and common-cause failures, then developed Laplace trans-forms of state probabilities and steady-state availability of the system.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis of a random fuzzy repairable parallel system with two non-identical components

Liu

2014

Journal of Intelligent &Amp; Fuzzy Systems

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The repairable parallel system is an essential part of the maintenance support for high technology systems. The uncertain lifetimes and repair times of repairable parallel systems are usually treated as the stochastic variables, which have crisp parameters. However, in practice, the parameters may not be precisely represented due to lack of sufficient data. So in this paper, the lifetime and repair time of each component are assumed to have random fuzzy exponential distributions. Then a mathematical model of random fuzzy repairable parallel system composed by two non-identical components and one repair facility is established. Furthermore, the expressions of limiting availability and steady state failure frequency of the random fuzzy repairable parallel system are proposed, respectively. Finally, a numerical example is presented.

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“…Cold or warm standby systems, subjected to priority rules, have received considerable attention in previous literature see, e.g., [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] . As a variant, we introduce a duplex system consisting of a priority unit the p-unit with a back-up nonpriority unit the n-unit in 2 Journal of Applied Mathematics and Stochastic Analysis warm standby and attended by a repair facility.…”

Section: Introductionmentioning

confidence: 99%

On the Survival Time of a Duplex System: A Sokhotski‐Plemelj Problem

Vanderperre

2008

International Journal of Stochastic Analysis

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We analyze the survival time of a renewable duplex system characterized by warm standby and subjected to a priority rule. In order to obtain the Laplace transform of the survival function, we employ a stochastic process endowed with time-dependent transition measures satisfying coupled partial differential equations. The solution procedure is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we introduce a security interval related to a prescribed security level and a suitable risk criterion based on the survival function of the system. As an example, we consider the particular case of deterministic repair. A computer-plotted graph displays the survival function together with the security interval corresponding to a security level of 90%.

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Repair Priority Effect on Availability of a 2-unit System

Cited by 8 publications

References 2 publications

Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

Stochastic Analysis of a Two-Unit Cold Standby System Wherein Both Units May Become Operative Depending upon the Demand

Reliability analysis of a random fuzzy repairable parallel system with two non-identical components

On the Survival Time of a Duplex System: A Sokhotski‐Plemelj Problem

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