Analysis of a deteriorating system with delayed repair and unreliable repair equipment
In this article, we mainly consider a repairable degradation system consisting of a single component, a repairman, and repair equipment. Suppose that the system cannot be repaired immediately after failure and cannot be repaired “as good as new.” Herein, the repair equipment may fail during repair a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-09-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0052 |
| _version_ | 1811236549950439424 |
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| author | Li Yan-Ling Xu Gen Qi Chen Hao |
| author_facet | Li Yan-Ling Xu Gen Qi Chen Hao |
| author_sort | Li Yan-Ling |
| collection | DOAJ |
| description | In this article, we mainly consider a repairable degradation system consisting of a single component, a repairman, and repair equipment. Suppose that the system cannot be repaired immediately after failure and cannot be repaired “as good as new.” Herein, the repair equipment may fail during repair and the system will replace a new one after failures. In particular, the repair time follows the general distribution. Under the above assumptions, a partial differential equation model is established through the geometric process and supplementary variable technique. By Laplace transform, we obtain the availability of the system, and from the expression one can see that the availability of the system will tend to zero after running for a long time. Therefore, we further study a replacement policy NN based on the failed times of the system. We give the explicit expression of the system average cost C(N)C\left(N) and obtain the optimal replacement policy N∗{N}^{\ast } by minimizing the average cost rate C(N∗)C\left({N}^{\ast }). That is, the system will be replaced when the failure number of the system reaches N∗{N}^{\ast }. Furthermore, the extended degenerate system is proposed by assuming that the system is not always successive degenerative after repair, and then the optimal replacement policy is studied. Finally, the numerical analysis is given to illustrate the theoretical results. |
| first_indexed | 2024-04-12T12:10:07Z |
| format | Article |
| id | doaj.art-622f9f6d00ce4bc58f8de29b23f2c98b |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-12T12:10:07Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-622f9f6d00ce4bc58f8de29b23f2c98b2022-12-22T03:33:36ZengDe GruyterOpen Mathematics2391-54552022-09-0120186387710.1515/math-2022-0052Analysis of a deteriorating system with delayed repair and unreliable repair equipmentLi Yan-Ling0Xu Gen Qi1Chen Hao2School of Mathematics and Statistics, Qinghai Nationalities University, Xining, 810007, P. R. ChinaSchool of Mathematics, Tianjin University, Tianjin, 300350, P. R. ChinaSchool of Mechanical and Electrical Engineering, Beijing Institute of Technology, Beijing, 100081, P. R. ChinaIn this article, we mainly consider a repairable degradation system consisting of a single component, a repairman, and repair equipment. Suppose that the system cannot be repaired immediately after failure and cannot be repaired “as good as new.” Herein, the repair equipment may fail during repair and the system will replace a new one after failures. In particular, the repair time follows the general distribution. Under the above assumptions, a partial differential equation model is established through the geometric process and supplementary variable technique. By Laplace transform, we obtain the availability of the system, and from the expression one can see that the availability of the system will tend to zero after running for a long time. Therefore, we further study a replacement policy NN based on the failed times of the system. We give the explicit expression of the system average cost C(N)C\left(N) and obtain the optimal replacement policy N∗{N}^{\ast } by minimizing the average cost rate C(N∗)C\left({N}^{\ast }). That is, the system will be replaced when the failure number of the system reaches N∗{N}^{\ast }. Furthermore, the extended degenerate system is proposed by assuming that the system is not always successive degenerative after repair, and then the optimal replacement policy is studied. Finally, the numerical analysis is given to illustrate the theoretical results.https://doi.org/10.1515/math-2022-0052deteriorating systemlaplace transformavailabilityextended geometric processreplacement policytp391 |
| spellingShingle | Li Yan-Ling Xu Gen Qi Chen Hao Analysis of a deteriorating system with delayed repair and unreliable repair equipment Open Mathematics deteriorating system laplace transform availability extended geometric process replacement policy tp391 |
| title | Analysis of a deteriorating system with delayed repair and unreliable repair equipment |
| title_full | Analysis of a deteriorating system with delayed repair and unreliable repair equipment |
| title_fullStr | Analysis of a deteriorating system with delayed repair and unreliable repair equipment |
| title_full_unstemmed | Analysis of a deteriorating system with delayed repair and unreliable repair equipment |
| title_short | Analysis of a deteriorating system with delayed repair and unreliable repair equipment |
| title_sort | analysis of a deteriorating system with delayed repair and unreliable repair equipment |
| topic | deteriorating system laplace transform availability extended geometric process replacement policy tp391 |
| url | https://doi.org/10.1515/math-2022-0052 |
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