Pinnacle Engineering & Technology

(ISSN: 2360-9516)

March 2014, Vol.2 (2).

© Author(s) 2014. This work is distributed under the Creative Commons Attribution 3.0 License.

Research Article

 

Cost Analysis of Two-Similar-Unit Cold Standby System With three States Under Human Failure Using First Order Linear Differential Equations

Ahmed Khayar

Faculty of Science
Department of Mathematics
AL-Azhar University
Cairo, Egypt

Accepted 18 February, 2014; Available Online 2 March, 2014

Abstract:

Many authors have studied the two-similar unit redundant system with three states to evaluate various reliability parameters, but no attention was paid to the reliability evaluation due to human failure. Others have studied the two-dissimilar unit redundant system with three states to evaluate various reliability parameters, but they did not consider the cost function. This study determine the effect of human failures on the reliability of the system and determine the cost function. In this paper the MTTF, availability and cost analysis of a two-similar-unit cold standby system under human failure is discussed. The proposed system has been investigated under the assumption that each unit works in three different states: normal, partial failed ad total failure. The system suffer two types of failures: viz; unit failure and human failure. Failure and repair time distributions are exponential. Using first order linear differential equations the system characteristics have been obtained. Also the cost function of the system is obtained. A special case for the proposed system was given in which human error is not considered. The results indicated that the system without human failure is more greater than the system with human failure with respect to the MTSF, steady state availability and the profit. Conclusion: These results indicated that the system characteristics without human error are more greater than the system with human failure. We concluded that the system without human failure is better than the system with human failure with respect to the MTSF, steady state availability and the profit.

Keywords: Reliability , Cost analysis, Mean Time to System Failure (MTSF), steady-state availability, busy period, profit function, linear first order differential equations.

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