A Time-Inhomogeneous Prendiville Model with Failures and Repairs
We consider a time-inhomogeneous Markov chain with a finite state-space which models a system in which failures and repairs can occur at random time instants. The system starts from any state <i>j</i> (operating, <i>F</i>, <i>R</i>). Due to a failure, a transition...
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MDPI AG
2022-01-01
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| Online Access: | https://www.mdpi.com/2227-7390/10/2/251 |
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| author | Virginia Giorno Amelia G. Nobile |
| author_facet | Virginia Giorno Amelia G. Nobile |
| author_sort | Virginia Giorno |
| collection | DOAJ |
| description | We consider a time-inhomogeneous Markov chain with a finite state-space which models a system in which failures and repairs can occur at random time instants. The system starts from any state <i>j</i> (operating, <i>F</i>, <i>R</i>). Due to a failure, a transition from an operating state to <i>F</i> occurs after which a repair is required, so that a transition leads to the state <i>R</i>. Subsequently, there is a restore phase, after which the system restarts from one of the operating states. In particular, we assume that the intensity functions of failures, repairs and restores are proportional and that the birth-death process that models the system is a time-inhomogeneous Prendiville process. |
| first_indexed | 2024-03-10T01:01:47Z |
| format | Article |
| id | doaj.art-a792ebdb497a4026bca26071bae8acc3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:01:47Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a792ebdb497a4026bca26071bae8acc32023-11-23T14:34:41ZengMDPI AGMathematics2227-73902022-01-0110225110.3390/math10020251A Time-Inhomogeneous Prendiville Model with Failures and RepairsVirginia Giorno0Amelia G. Nobile1Dipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Salerno, ItalyDipartimento di Informatica, Università degli Studi di Salerno, Via Giovanni Paolo II n. 132, 84084 Salerno, ItalyWe consider a time-inhomogeneous Markov chain with a finite state-space which models a system in which failures and repairs can occur at random time instants. The system starts from any state <i>j</i> (operating, <i>F</i>, <i>R</i>). Due to a failure, a transition from an operating state to <i>F</i> occurs after which a repair is required, so that a transition leads to the state <i>R</i>. Subsequently, there is a restore phase, after which the system restarts from one of the operating states. In particular, we assume that the intensity functions of failures, repairs and restores are proportional and that the birth-death process that models the system is a time-inhomogeneous Prendiville process.https://www.mdpi.com/2227-7390/10/2/251continuous-time ehrenfest modelfirst-passage time densitiesproportional intensity functionsasymptotic behaviors |
| spellingShingle | Virginia Giorno Amelia G. Nobile A Time-Inhomogeneous Prendiville Model with Failures and Repairs Mathematics continuous-time ehrenfest model first-passage time densities proportional intensity functions asymptotic behaviors |
| title | A Time-Inhomogeneous Prendiville Model with Failures and Repairs |
| title_full | A Time-Inhomogeneous Prendiville Model with Failures and Repairs |
| title_fullStr | A Time-Inhomogeneous Prendiville Model with Failures and Repairs |
| title_full_unstemmed | A Time-Inhomogeneous Prendiville Model with Failures and Repairs |
| title_short | A Time-Inhomogeneous Prendiville Model with Failures and Repairs |
| title_sort | time inhomogeneous prendiville model with failures and repairs |
| topic | continuous-time ehrenfest model first-passage time densities proportional intensity functions asymptotic behaviors |
| url | https://www.mdpi.com/2227-7390/10/2/251 |
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