On the Computation of Some Interval Reliability Indicators for Semi-Markov Systems

Guglielmo D’Amico, Raimondo Manca, Filippo Petroni and Dharmaraja Selvamuthu
Additional contact information
Guglielmo D’Amico: Department of Economics, University “G. d’Annunzio” of Chieti-Pescara, 66013 Pescara, Italy
Raimondo Manca: MEMOTEF Department, University of Rome, “La Sapienza”, 00185 Rome, Italy
Filippo Petroni: Department of Management, Marche Polytechnic University, 60121 Ancona, Italy
Dharmaraja Selvamuthu: Department of Mathematics, Indian Institute of Technology Delhi, New Delhi 110016, India

Mathematics, 2021, vol. 9, issue 5, 1-23

Abstract: In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered duration-dependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To make the computation of the window availability, an explicit formula was derived involving duration-dependent transition probabilities and the interval reliability function. Both interval reliability and availability functions were evaluated considering the local behavior of the system through the recurrence time processes. The results are illustrated through a numerical example. They show that the considered indicators can describe the duration effects and the age of the multi-state system and be useful in real-life problems.

Keywords: recurrence time processes; reliability; availability; non-homogeneous system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/5/575/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/5/575/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:5:p:575-:d:512649

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().