Cost Analysis of A System with Preventive Maintenance by Using the Kolmogorovâ€™s Forward Equations Method

El-Said, Khaled M.

doi:10.3844/ajassp.2008.405.410

Cited by 22 publications

(29 citation statements)

References 8 publications

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“…It is difficult to evaluate the transient solutions hence following El-said [14], and Haggag [15] we delete the rows and columns of absorbing state of matrix A and take the transpose to produce a new matrix, say Q . The expected time to reach an absorbing state is obtained from () …”

Section: Mean Time To System Failure For Systemmentioning

confidence: 99%

Mean Time to System Failure and Availability Modeling of a Repairable non Identical Three Unit Warm Standby Redundant System

Suleiman¹,

Yusuf

Bala

et al. 2012

International Journal of Basic and Applied Sciences

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Many authors have developed models on two units' cold standby system, but little or no attention is paid on series-parallel system involving four types of failures. In this study, measures of system effectiveness such as mean time to system failure (MTSF), steady state availability, busy period and profit function were discussed. The system is analyzed using Kolmogorov's forward equations method. The result has shown that MTSF, steady state availability and profit function increases with repair and decreases with failure rate.

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Section: Mean Time To System Failure For Systemmentioning

confidence: 99%

Mean Time to System Failure and Availability Modeling of a Repairable non Identical Three Unit Warm Standby Redundant System

Suleiman¹,

Yusuf

Bala

et al. 2012

International Journal of Basic and Applied Sciences

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“…It is difficult to evaluate the transient solutions, hence we follow [2], [3], [5], the procedure to develop the explicit expression for MTSF is to delete the seventh row and column of matrixT and take the transpose to produce a new matrix, say Q . The expected time to reach an absorbing state is obtained from…”

Section: Mean Time To System Failure Analysismentioning

confidence: 99%

“…Reference [4] examined the cost benefit analysis of series systems with cold standby components and repairable service station. Reference [5], [6] examined the cost analysis of two unit cold standby system involving preventive maintenance respectively. Reference [7] studied the cost and probabilistic analysis of series system with mixed standby components, and [8] studied cost benefit analysis of series systems with warm standby components involving general repair time where the server is not subject to breakdowns.…”

Section: Introductionmentioning

confidence: 99%

Some Reliability Measures of a Deteriorating System

Yusuf

Hussaini²,

Yakasai³

2013

International Journal of Applied Mathematical Research

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In this paper, we studied some reliability characteristics of a repairable 3-out-of-4 system with three modes: normal, deterioration and failure modes. The deterioration mode could be slow or fast. Failure and repair time are assumed to be exponential. We develop the explicit expressions for steady-state availability, busy period of repair man, profit function and mean time to system failure for the system using linear first order differential equations. Various cases are analyzed graphically to investigate the impact of system parameters on MTSF and profit function.

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“…Earlier researchers [1][2][3] have studied the cost analysis of two unit redundant systems with two types of repair. The researchers [4][5][6] have studied the cost analysis of different systems [7] .…”

Section: Introductionmentioning

confidence: 99%

Cost Analysis of a System Involving Common-Cause Failures and Preventive Maintenance

Haggag¹

2009

J. of Mathematics and Statistics

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Problem statement: Many authors have studied the cost analysis of a two-unit cold standby redundant system with two types of unit failure, but no attention was paid to the reliability of a system involving common-cause failures and preventive maintenance. Question was raised whether the preventive maintenance would be effective on the reliability and performance of the system. Determine the efficacy of preventive maintenance on the reliability and performance of the system. Approach: In this study, the Mean Time to System Failure (MTSF), steady state availability and the profit function of a two-unit cold standby repairable redundant system involving common-cause failures and preventive maintenance were discussed. We analyzed the system by using Kolmogorov's forward equations method. Some particular cases have also been discussed graphically. Results: The results indicated that the system with preventive maintenance is better than the system without preventive maintenance. Conclusion: These results indicated that the better maintenance of parts of the system originated better reliability and performance of the system.

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Cost Analysis of A System with Preventive Maintenance by Using the Kolmogorovâ€™s Forward Equations Method

Cited by 22 publications

References 8 publications

Mean Time to System Failure and Availability Modeling of a Repairable non Identical Three Unit Warm Standby Redundant System

Mean Time to System Failure and Availability Modeling of a Repairable non Identical Three Unit Warm Standby Redundant System

Some Reliability Measures of a Deteriorating System

Cost Analysis of a System Involving Common-Cause Failures and Preventive Maintenance

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