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Article

Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy

1
Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II n.132, I-84084 Fisciano (SA), Italy
2
Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha 769008, India
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(8), 1203; https://doi.org/10.3390/math8081203
Received: 25 June 2020 / Revised: 17 July 2020 / Accepted: 18 July 2020 / Published: 22 July 2020
(This article belongs to the Special Issue Stochastic Processes in Neuronal Modeling)
A suitable replacement model for random lifetimes is extended to the context of past lifetimes. At a fixed time u 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 t 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 x ( u , t ) , 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. View Full-Text
Keywords: reliability; replacement model; stochastic orders; differential entropy; stochastic neuronal model reliability; replacement model; stochastic orders; differential entropy; stochastic neuronal model
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MDPI and ACS Style

Di Crescenzo, A.; Di Gironimo, P.; Kayal, S. Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy. Mathematics 2020, 8, 1203. https://doi.org/10.3390/math8081203

AMA Style

Di Crescenzo A, Di Gironimo P, Kayal S. Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy. Mathematics. 2020; 8(8):1203. https://doi.org/10.3390/math8081203

Chicago/Turabian Style

Di Crescenzo, Antonio, Patrizia Di Gironimo, and Suchandan Kayal. 2020. "Analysis of the Past Lifetime in a Replacement Model through Stochastic Comparisons and Differential Entropy" Mathematics 8, no. 8: 1203. https://doi.org/10.3390/math8081203

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