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Öğe A new mixed ?-shock model with a change in shock distribution(Springer, 2023) Chadjiconstantinidis, Stathis; Tuncel, Altan; Eryilmaz, SerkanIn this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well.Öğe Assessment of Shock Models for a Particular Class of Intershock Time Distributions(Springer, 2022) Kus, Coskun; Tuncel, Altan; Eryilmaz, SerkanIn this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems' lifetimes are obtained in a matrix form. Survival functions of the systems are approximated based on the Laplace-Stieltjes transforms. The results are applied for the reliability evaluation of a certain repairable system consisting of two components.Öğe Computational results on the compound binomial risk model with nonhomogeneous claim occurrences(Elsevier Science Bv, 2014) Tuncel, Altan; Tank, FatihThe aim of this paper is to give a recursive formula for non-ruin (survival) probability when the claim occurrences are nonhomogeneous in the compound binomial risk model. We give recursive formulas for non-ruin (survival) probability and for distribution of the total number of claims under the condition that the claim occurrences are nonhomogeneous. (C) 2013 Elsevier B.V. All rights reserved.Öğe Computing the Signature of a Generalized k -Out-of-n System(Ieee-Inst Electrical Electronics Engineers Inc, 2015) Eryılmaz, Serkan; Tuncel, AltanA generalized k-out-of-n system which is denoted by ((n(1), ... , n(N)), f, k) consists N of modules ordered in a line or a circle, and the ith module is composed of n(i) components in parallel. (n(i) >= 1, i = 1, ... , N). The system fails iff there exist at least failed components or at least k consecutive failed modules. In this paper, we compute the signature of this system when n(1) = ... = n(N) = n, and present illustrative examples to demonstrate its application. Simulation based computation of the signature is provided when the modules have different numbers of components.Öğe Generalizing the survival signature to unrepairable homogeneous multi-state systems(Wiley, 2016) Eryilmaz, Serkan; Tuncel, AltanThe notion of signature has been widely applied for the reliability evaluation of technical systems that consist of binary components. Multi-state system modeling is also widely used for representing real life engineering systems whose components can have different performance levels. In this article, the concept of survival signature is generalized to a certain class of unrepairable homogeneous multi-state systems with multi-state components. With such a generalization, a representation for the survival function of the time spent by a system in a specific state or above is obtained. The findings of the article are illustrated for multi-state consecutive-k-out-of-n system which perform its task at three different performance levels. The generalization of the concept of survival signature to a multi-state system with multiple types of components is also presented. (C) 2016 Wiley Periodicals, Inc.Öğe Lebesgue integrali ve bazı istatistiksel uygulamaları(Kırıkkale Üniversitesi, 2007) Tuncel, Altan; Koca, KerimBu çalısma dört bölümden olusmaktadır. Birinci bölümde çalısmanın amacı ve kullanılan kaynaklar hakkında ön bilgiler verilmistir. kinci bölümde gerekli temel kavramlar verilmis, daha sonra Lebesgue integrali, Riemann integrali ve Lebesgue- Stieltjes integrali, statistikteki uygulamaları incelenmistir. Dördüncü bölüm ise Tartısma ve Sonuç'a yer verilmistir. Anahtar Kelimeler: Ölçü, Lebesgue Ölçüsü, Lebesgue ntegrali, Lebesgue-Stieltjes Ölçüsü, Lebesgue-Stieltjes ntegrali, Beklenen DegerÖğe ? new mixed ?-shock model with a change in shock distribution(Institute for Ionics, 2023) Chadjiconstantinidis, Stathis; Tuncel, Altan; Eryilmaz, SerkanIn this paper, reliability properties of a system that is subject to a sequence of shocks are investigated under a particular new change point model. According to the model, a change in the distribution of the shock magnitudes occurs upon the occurrence of a shock that is above a certain critical level. The system fails when the time between successive shocks is less than a given threshold, or the magnitude of a single shock is above a critical threshold. The survival function of the system is studied under both cases when the times between shocks follow discrete distribution and when the times between shocks follow continuous distribution. Matrix-based expressions are obtained for matrix-geometric discrete intershock times and for matrix-exponential continuous intershock times, as well. © 2022, The Author(s) under exclusive licence to Sociedad de Estadística e Investigación Operativa.Öğe Residual Lifetime Of System With Cold Standby Unit(2017) Tuncel, AltanIn this paper, we define and study two different residual life random variables corresponding to single unit system equipped with cold standby unit. We obtain the conditional survival functions when the lifetimes Of active and standby units are dependent. Some properties of the associated mean residual life functions are also investigated. Graphical illustrations are presented to observe time dependent behaviors of associated mean residual life functions.Öğe Some bivariate Schur-constant distributions and application to life insurance(Elsevier, 2025) Tuncel, Altan; Aslan, Tugba AktasSchur-constant models play a particular role when modelling time in fields such as actuarial science, insurance, reliability and survival models. These models describe random lifetimes with a certain dependence. In this study, a relation between proportional hazard rate distributions and Schur-constant models is established. Bivariate Schur-constant models, whose marginals are proportional hazard rate distributed, are introduced. Then, the dependency analysis in life insurances is performed through Schur-constant and copula models. It is revealed that there are differences in pricing when individuals' future lifetimes are dependent.Öğe Some results on the extreme distributions of surplus process with nonhomogeneous claim occurrences(Hacettepe Univ, Fac Sci, 2015) Tank, Fatih; Tuncel, AltanIn this paper; survival (non-ruin) probability after a definite time period of an insurance company is studied in a discrete time model based on non-homogenous claim occurrences. Furthermore, distributions of the minimum and maximum levels of surplus in compound binomial risk model with non-homogeneous claim occurrences are obtained and some of its characteristics are given.Öğe SURVIVAL PROBABILITIES FOR COMPOUND BINOMIAL RISK MODEL WITH DISCRETE PHASE-TYPE CLAIMS(2016) Tuncel, Altan[Abstract Not Available]Öğe Survival Probabilities For Compound Binomial Risk Model With Discrete Phase-Type Claims(2016) Tuncel, AltanDue to having useful properties in approximating to the otherdistributions and mathematically tractable, phase type distributions are commonly used in actuarial risk theory. Claim occurrence time and individualclaim size distributions are modelled by phase type distributions in literature.This paper aims to calculate the survival probabilities of an insurance company under the assumption that compound binomial risk model where theindividual claim sizes are distributed as discrete Phase Type distribution.Öğe System reliability under delta-shock model(Taylor & Francis Inc, 2018) Tuncel, Altan; Eryilmaz, Serkandelta-shock model is one of the widely studied shock models in reliability. Under this model, the system fails when the time between two consecutive shocks falls below a fixed threshold . In this paper, the survival function and the mean time to failure of the system are obtained when the times between successive shocks follow proportional hazard rate model.
