DISTRIBUTIONS OF RANDOM VARIABLES INVOLVED IN DISCRETE CENSORED δ-SHOCK MODELS

dc.authorscopusid 6602310120
dc.authorscopusid 8203625300
dc.contributor.author Chadjiconstantinidis, Stathis
dc.contributor.author Eryilmaz, Serkan
dc.contributor.other Industrial Engineering
dc.date.accessioned 2024-07-05T15:23:24Z
dc.date.available 2024-07-05T15:23:24Z
dc.date.issued 2023
dc.department Atılım University en_US
dc.department-temp [Chadjiconstantinidis, Stathis] Univ Piraeus, Dept Stat & Insurance Sci, 80 Karaoli & Dimitriou Str, Piraeus 18534, Greece; [Eryilmaz, Serkan] Atilim Univ, Dept Ind Engn, TR-06830 Ankara, Turkiye en_US
dc.description.abstract Suppose that a system is affected by a sequence of random shocks that occur over certain time periods. In this paper we study the discrete censored delta-shock model, delta <= 1 , for which the system fails whenever no shock occurs within a -length time period from the last shock, by supposing that the interarrival times between consecutive shocks are described by a first-order Markov chain (as well as under the binomial shock process, i.e., when the interarrival times between successive shocks have a geometric distribution). Using the Markov chain embedding technique introduced by Chadjiconstantinidis et al. (Adv. Appl. Prob. 32, 2000), we study the joint and marginal distributions of the system's lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system. The joint and marginal probability generating functions of these random variables are obtained, and several recursions and exact formulae are given for the evaluation of their probability mass functions and moments. It is shown that the system's lifetime follows a Markov geometric distribution of order (a geometric distribution of order under the binomial setup) and also that it follows a matrix-geometric distribution. Some reliability properties are also given under the binomial shock process, by showing that a shift of the system's lifetime random variable follows a compound geometric distribution. Finally, we introduce a new mixed discrete censored delta -shock model, for which the system fails when no shock occurs within a -length time period from the last shock, or the magnitude of the shock is larger than a given critical threshold . gamma > 0. Similarly, for this mixed model, we study the joint and marginal distributions of the system's lifetime, the number of shocks, and the number of periods in which no shocks occur, up to the failure of the system, under the binomial shock process. en_US
dc.identifier.citationcount 1
dc.identifier.doi 10.1017/apr.2022.72
dc.identifier.endpage 1170 en_US
dc.identifier.issn 0001-8678
dc.identifier.issn 1475-6064
dc.identifier.issue 4 en_US
dc.identifier.scopus 2-s2.0-85153857623
dc.identifier.startpage 1144 en_US
dc.identifier.uri https://doi.org/10.1017/apr.2022.72
dc.identifier.uri https://hdl.handle.net/20.500.14411/2313
dc.identifier.volume 55 en_US
dc.identifier.wos WOS:001168005000007
dc.identifier.wosquality Q3
dc.institutionauthor Eryılmaz, Serkan
dc.language.iso en en_US
dc.publisher Cambridge Univ Press en_US
dc.relation.publicationcategory Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı en_US
dc.rights info:eu-repo/semantics/closedAccess en_US
dc.scopus.citedbyCount 5
dc.subject Censored delta-shock model en_US
dc.subject mixed censored delta-shock model en_US
dc.subject Markov chain en_US
dc.subject reliability en_US
dc.subject waiting time en_US
dc.subject Markov chain imbedding technique en_US
dc.subject discrete compound geometric distribution en_US
dc.subject geometric distribution of order delta en_US
dc.subject matrix-geometric distribution en_US
dc.title DISTRIBUTIONS OF RANDOM VARIABLES INVOLVED IN DISCRETE CENSORED δ-SHOCK MODELS en_US
dc.type Article en_US
dc.wos.citedbyCount 4
dspace.entity.type Publication
relation.isAuthorOfPublication 37862217-5541-47e3-9406-e21aa38e7fdf
relation.isAuthorOfPublication.latestForDiscovery 37862217-5541-47e3-9406-e21aa38e7fdf
relation.isOrgUnitOfPublication 12c9377e-b7fe-4600-8326-f3613a05653d
relation.isOrgUnitOfPublication.latestForDiscovery 12c9377e-b7fe-4600-8326-f3613a05653d

Files

Collections