Pinnacle Engineering & Technology

(ISSN: 2360-9516)

January 2014, Vol.1 (2).

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

Research Article


Reliability Analysis of k-out of-n Repairable System Involving Human Error and Common-cause Failure

M.Y. Haggag1* & Ahmed Khayar2

1&2Faculty of Science
Department of Mathematics
AL-Azhar University
Cairo, Egypt

Accepted 8 January, 2014; Available Online 18 January, 2014


Earlier research workers have studied the reliability behavior of k-out of-n systems with dependent failure and standby support, but no attention was paid to the reliability evaluation due to human and common-cause failure. Question was raised whether the repair due to human error and common-cause failure would be effective on the reliability and performance of the system. In this paper, a mathematical model of k-out of-n repairable system is studded with standby units involving human and common-cause failure to evaluate availability, steady state availability, MTTF and cost function with and without repair. Using supplementary variable technique, Laplace transforms of various state probabilities are obtained. Some particular cases have been discussed. Numerical computation and graphs also have been drawn. Also three particular cases are developed. Results have shown that system with repair is better in terms of system effectiveness than system without repair. we conclude that system with repair is more effective than system without repair due to both human error and common-cause failure.

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