An alternative approach to reliability analysis of cold standby systems. (English) Zbl 1349.60136
Summary: An alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.
MSC:
| 60K15 | Markov renewal processes, semi-Markov processes |
| 60K20 | Applications of Markov renewal processes (reliability, queueing networks, etc.) |
Keywords:
availability; cold standby systems; Laplace transform; matrix renewal function; semi-Markov processesReferences:
| [1] | Cinlar E., Introduction to Stochastic Processes (1975) |
| [2] | DOI: 10.1016/0026-2714(85)90443-3 · doi:10.1016/0026-2714(85)90443-3 |
| [3] | DOI: 10.1016/S0026-2714(82)80191-1 · doi:10.1016/S0026-2714(82)80191-1 |
| [4] | DOI: 10.1016/j.ress.2011.06.004 · doi:10.1016/j.ress.2011.06.004 |
| [5] | DOI: 10.1007/978-1-4612-0161-8 · doi:10.1007/978-1-4612-0161-8 |
| [6] | DOI: 10.1016/j.mcm.2009.10.019 · Zbl 1190.90061 · doi:10.1016/j.mcm.2009.10.019 |
| [7] | DOI: 10.1016/0026-2714(89)90017-6 · doi:10.1016/0026-2714(89)90017-6 |
| [8] | DOI: 10.1016/0026-2714(89)90006-1 · doi:10.1016/0026-2714(89)90006-1 |
| [9] | DOI: 10.1016/0026-2714(87)90620-2 · doi:10.1016/0026-2714(87)90620-2 |
| [10] | DOI: 10.1109/24.75325 · Zbl 0729.90935 · doi:10.1109/24.75325 |
| [11] | DOI: 10.1016/j.amc.2011.05.089 · Zbl 1231.60069 · doi:10.1016/j.amc.2011.05.089 |
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