Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model
A semi-Markov process with four states, has been applied for modeling two dissimilar unit cold standby systems. At the moment that operating unit fails, the standby unit is switched to operate by using a switching device that is available with unknown probability alpha1. It is also assumed that the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Springer
2013-09-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
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| Online Access: | https://www.atlantis-press.com/article/9048.pdf |
| _version_ | 1811335970754134016 |
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| author | M. Fathizadeh K. Khorshidian |
| author_facet | M. Fathizadeh K. Khorshidian |
| author_sort | M. Fathizadeh |
| collection | DOAJ |
| description | A semi-Markov process with four states, has been applied for modeling two dissimilar unit cold standby systems. At the moment that operating unit fails, the standby unit is switched to operate by using a switching device that is available with unknown probability alpha1. It is also assumed that the failure rate of unit i has the general form hi(t)= alpha2i + alpha2i+1 tbeta1-1, i=1,2, where alpha2...alpha5 are non-negative unknown parameters. In favor of semi-Markov structure of the system, maximum likelihood and the Bayes estimators of the unknown parameters alpha = (alpha1, alpha2...alpha5)are obtained while betai are non-negative known constants. Furthermore, the estimators are obtained for systems with similar units. Finally, to compare the results a simulation study is done. |
| first_indexed | 2024-04-13T17:32:24Z |
| format | Article |
| id | doaj.art-a7c15e1391f348c48f18afe2adc11e4d |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-04-13T17:32:24Z |
| publishDate | 2013-09-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-a7c15e1391f348c48f18afe2adc11e4d2022-12-22T02:37:31ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872013-09-0112310.2991/jsta.2013.12.3.3Parameters Estimation in a General Failure Rate Semi-Markov Reliability ModelM. FathizadehK. KhorshidianA semi-Markov process with four states, has been applied for modeling two dissimilar unit cold standby systems. At the moment that operating unit fails, the standby unit is switched to operate by using a switching device that is available with unknown probability alpha1. It is also assumed that the failure rate of unit i has the general form hi(t)= alpha2i + alpha2i+1 tbeta1-1, i=1,2, where alpha2...alpha5 are non-negative unknown parameters. In favor of semi-Markov structure of the system, maximum likelihood and the Bayes estimators of the unknown parameters alpha = (alpha1, alpha2...alpha5)are obtained while betai are non-negative known constants. Furthermore, the estimators are obtained for systems with similar units. Finally, to compare the results a simulation study is done.https://www.atlantis-press.com/article/9048.pdfBayesian estimationCold standby systemsMaximum likelihoodSemi-Markov process |
| spellingShingle | M. Fathizadeh K. Khorshidian Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model Journal of Statistical Theory and Applications (JSTA) Bayesian estimation Cold standby systems Maximum likelihood Semi-Markov process |
| title | Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model |
| title_full | Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model |
| title_fullStr | Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model |
| title_full_unstemmed | Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model |
| title_short | Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model |
| title_sort | parameters estimation in a general failure rate semi markov reliability model |
| topic | Bayesian estimation Cold standby systems Maximum likelihood Semi-Markov process |
| url | https://www.atlantis-press.com/article/9048.pdf |
| work_keys_str_mv | AT mfathizadeh parametersestimationinageneralfailureratesemimarkovreliabilitymodel AT kkhorshidian parametersestimationinageneralfailureratesemimarkovreliabilitymodel |