# Murat OzkutIzmir University of Economics · Deparment of Mathematics

Murat Ozkut

PhD

## About

15

Publications

1,956

Reads

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129

Citations

Citations since 2017

Introduction

Current research interests are reliability, stochastic modeling, and applied probability.

Additional affiliations

February 2019 - June 2021

September 2017 - January 2019

September 2015 - December 2017

Education

September 2009 - June 2015

## Publications

Publications (15)

This paper is about the reliability modeling of a linear consecutive k-out-of- n system that consists of two types of dependent components. The survival function and mean time to failure of such a system are expressed using copulas. Extensive numerical findings are provided for Clayton and Gumbel-type copulas. The survival and mean time to failure...

This paper is a short review of classical and recent results on Marshall–Olkin shock models and their applications in reliability analysis. The classical Marshall–Olkin shock model was introduced in Marshall and Olkin (J Am Stat Assoc 62:30–44, 1967). The model describes a joint distribution of lifetimes of two components of a system subjected to t...

This paper is concerned with two optimization problems for a k-out-of- n system consisting of dependent components such as finding the number of elements in the system that minimize the system’s mean cost rate and the system’s optimal replacement time. In previous studies, either system consisting of independent components or parallel systems, a pa...

We consider an (n−k+1)-out-of-n concomitant system consisting of n components each having two subcomponents. This system functions if and only if at least (n−k+1) of the first subcomponents function, and the second subcomponents of working first components also function. The reliability of the proposed system is derived. The effect of dependent sub...

This paper is concerned with two optimization problems for a parallel system that consists of dependent components. First, the problem of finding the number of elements in the system that minimizes the mean cost rate of the system is considered. The second problem is concerned with the optimal replacement time of the system. Previous work assumes t...

In this paper, a new shock model called Marshall–Olkin run shock model is defined and studied. According to the model, two components are subject to shocks that may arrive from three different sources, and component i fails when it is subject to k consecutive critical shocks from source i or k consecutive critical shocks from source 3, i=1,2. Relia...

We consider coherent systems subjected to Marshall-Olkin type shocks coming at random times and destroying components of the system. The paper combines two important models, coherent systems and Marshall-Olkin type shocks and studies the mean residual life (MRL) and the mean inactivity time (MIT) functions of coherent systems that is subjected to r...

In this paper, the influence of a cold standby component on a coherent system is studied. A method for computing the system reliability of coherent systems with a cold standby component based on signature is presented. Numerical examples are presented. Reliability and mean time to failure of different systems are computed.

In classical Marshall–Olkin type shock models and their modifications a system of two or more components is subjected to shocks that arrive from different sources at random times and destroy the components of the system. With a distinctive approach to the Marshall–Olkin type shock model, we assume that if the magnitude of the shock exceeds some pre...

In the classical Marshall–Olkin model, the system is subjected to two types of shocks coming at random times, and destroying components of the system. In statistics and reliability engineering literature, there are numerous papers dealing with various extensions of this model. However, none of these works takes into account the system structure, i....

A system can be classified with respect to the physical arrangement of its components
and the functioning principle. A circular consecutive k-within-m-out-of-n:F system consists
of n circularly ordered components and fails if and only if there are m consecutive
components that include among them at least k failed components. A circular consecutive...

The aim of this paper is to propose a portfolio selection model which takes into account the investors preferences for higher return moments such as skewness and kurtosis. In the presence of skewness and kurtosis, the portfolio selection problem can be characterized with multiple conflicting and competing objective functions such as maximizing expe...

## Projects

Project (1)

Birnbaum importance was firstly introduced in 1969, such that among other importance measures Birnbaum importance has an important role. A lot of work has been done for Birnbaum importance in consecutive-systems. We can study on Birnbaum importance for linear (circular) m-consecutive-k-out-of-n systems which is the generalized version of consecutive k-out-of-n systems. Some equations on Birnbaum importance can be proposed and by using these equations, the ranking of components based on Birnbaum importance in the system can be given.