Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy
A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time <i>u</i> an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that...
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| Format: | Article |
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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/8/1203 |
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| author | Antonio Di Crescenzo Patrizia Di Gironimo Suchandan Kayal |
| author_facet | Antonio Di Crescenzo Patrizia Di Gironimo Suchandan Kayal |
| author_sort | Antonio Di Crescenzo |
| collection | DOAJ |
| description | A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time <i>u</i> an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time <i>t</i> the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at <inline-formula> <math display="inline"> <semantics> <mrow> <mi>x</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, which is finalized to measure the goodness of the replacement procedure. The characterization and the properties of the differential entropy of the system lifetime are also discussed. Finally, an example of application to the firing activity of a stochastic neuronal model is provided. |
| first_indexed | 2024-03-10T18:18:46Z |
| format | Article |
| id | doaj.art-59a3eb90c3eb4089a01bded6e74f3660 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:18:46Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-59a3eb90c3eb4089a01bded6e74f36602023-11-20T07:30:54ZengMDPI AGMathematics2227-73902020-07-0188120310.3390/math8081203Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential EntropyAntonio Di Crescenzo0Patrizia Di Gironimo1Suchandan Kayal2Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano (SA), ItalyDipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano (SA), ItalyDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha 769008, IndiaA suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time <i>u</i> an item is planned to be replaced by another one having the same age but a different lifetime distribution. We investigate the past lifetime of this system, given that at a larger time <i>t</i> the system is found to be failed. Subsequently, we perform some stochastic comparisons between the random lifetimes of the single items and the doubly truncated random variable that describes the system lifetime. Moreover, we consider the relative ratio of improvement evaluated at <inline-formula> <math display="inline"> <semantics> <mrow> <mi>x</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </semantics> </math> </inline-formula>, which is finalized to measure the goodness of the replacement procedure. The characterization and the properties of the differential entropy of the system lifetime are also discussed. Finally, an example of application to the firing activity of a stochastic neuronal model is provided.https://www.mdpi.com/2227-7390/8/8/1203reliabilityreplacement modelstochastic ordersdifferential entropystochastic neuronal model |
| spellingShingle | Antonio Di Crescenzo Patrizia Di Gironimo Suchandan Kayal Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy Mathematics reliability replacement model stochastic orders differential entropy stochastic neuronal model |
| title | Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy |
| title_full | Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy |
| title_fullStr | Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy |
| title_full_unstemmed | Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy |
| title_short | Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy |
| title_sort | analysis of the past lifetime in a replacement model through stochastic comparisons and differential entropy |
| topic | reliability replacement model stochastic orders differential entropy stochastic neuronal model |
| url | https://www.mdpi.com/2227-7390/8/8/1203 |
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