Laplace-Stieltjes transform of the system mean lifetime via geometric process model
Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calcula...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-01-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2016-0034 |
| _version_ | 1828916214264496128 |
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| author | Gökdere Gökhan Gürcan Mehmet |
| author_facet | Gökdere Gökhan Gürcan Mehmet |
| author_sort | Gökdere Gökhan |
| collection | DOAJ |
| description | Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a solution to the problem. In this paper, we have designed a system which consists of two components that can be repairable with the aging property. Firstly, the Laplace-Stieltjes transform of the system is formed. Later, the mean operating time of the system is calculated by means of Laplace-Stieltjes transform. The system’s repair policy is evaluated depending on the geometric process. This property provides the aging of the system. We also provide special systems with different marginal lifetime distributions to illustrate the theoretical results in this study. |
| first_indexed | 2024-12-13T20:28:24Z |
| format | Article |
| id | doaj.art-347eaa43f0584ab5a603c908dcd662b9 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-13T20:28:24Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-347eaa43f0584ab5a603c908dcd662b92022-12-21T23:32:29ZengDe GruyterOpen Mathematics2391-54552016-01-0114138439210.1515/math-2016-0034math-2016-0034Laplace-Stieltjes transform of the system mean lifetime via geometric process modelGökdere Gökhan0Gürcan Mehmet1Department of Statistics, Fırat University, 23119 Elazıǧ, TurkeyDepartment of Statistics, Fırat University, 23119 Elazıǧ, TurkeyOperation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a solution to the problem. In this paper, we have designed a system which consists of two components that can be repairable with the aging property. Firstly, the Laplace-Stieltjes transform of the system is formed. Later, the mean operating time of the system is calculated by means of Laplace-Stieltjes transform. The system’s repair policy is evaluated depending on the geometric process. This property provides the aging of the system. We also provide special systems with different marginal lifetime distributions to illustrate the theoretical results in this study.https://doi.org/10.1515/math-2016-0034cold standby systemlaplace-stieltjes transformsystem mean lifetimegeometric process62k0565r1090b25 |
| spellingShingle | Gökdere Gökhan Gürcan Mehmet Laplace-Stieltjes transform of the system mean lifetime via geometric process model Open Mathematics cold standby system laplace-stieltjes transform system mean lifetime geometric process 62k05 65r10 90b25 |
| title | Laplace-Stieltjes transform of the system mean lifetime via geometric process model |
| title_full | Laplace-Stieltjes transform of the system mean lifetime via geometric process model |
| title_fullStr | Laplace-Stieltjes transform of the system mean lifetime via geometric process model |
| title_full_unstemmed | Laplace-Stieltjes transform of the system mean lifetime via geometric process model |
| title_short | Laplace-Stieltjes transform of the system mean lifetime via geometric process model |
| title_sort | laplace stieltjes transform of the system mean lifetime via geometric process model |
| topic | cold standby system laplace-stieltjes transform system mean lifetime geometric process 62k05 65r10 90b25 |
| url | https://doi.org/10.1515/math-2016-0034 |
| work_keys_str_mv | AT gokderegokhan laplacestieltjestransformofthesystemmeanlifetimeviageometricprocessmodel AT gurcanmehmet laplacestieltjestransformofthesystemmeanlifetimeviageometricprocessmodel |