Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
This paper is about the reliability modeling of a linear consecutive k-out-of- n system that cons... more 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 behaviors are explored in connection with the value of Kendall’s correlation coefficient.
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
This paper is concerned with two optimization problems for a k-out-of- n system consisting of dep... more 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 particular case of the present study, was examined. In particular, we numerically examine how the components’ dependence affects the optimal number of units and replacement time for the system, minimizing mean cost rates. We consider when the components are exchangeable and dependent, that is, the system consists of dependent components. For three vastly used Clayton, Gumbel, and FGM copula functions, comparative numerical results are presented.
We consider an ( n − k + 1 ) -out-of- n concomitant system consisting of n components each having... more 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 subcomponents on the system reliability relative to independent subcomponents is discussed. The system with two subcomponents is extended to the system with m subcomponents. Comparative numerical results and graphical representations are provided.
The aim of this paper is to propose a portfolio selection model which takes into account the inve... more 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 expected return and skewness, and minimizing risk and kurtosis, simultaneously. By constructing polynomial goal programming, in which investor preferences for skewness and kurtosis incorporated, a Turkish Stock Market example will be presented for the period from January 2005 to December 2010.
ABSTRACT In the classical Marshall–Olkin model, the system is subjected to two types of shocks co... more ABSTRACT 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.e., in existing shock models usually the system structure is not considered. In this work, we consider a new shock model involving the system structure. More precisely, we consider a coherent system which is subjected to Marshall–Olkin type shocks. We investigate the reliability, and mean time to failure (MTTF) of such systems subjected to shocks coming at random times. Numerical examples and graphs are provided, and an extension to a general model is discussed.
Journal of Computational and Applied Mathematics, 2014
ABSTRACT In classical Marshall–Olkin type shock models and their modifications a system of two or... more ABSTRACT 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 predefined threshold, then the component, which is subjected to this shock, is destroyed; otherwise it survives. More precisely, we assume that the shock time and the magnitude of the shock are dependent random variables with given bivariate distribution. This approach allows to meet requirements of many real life applications of shock models, where the magnitude of shocks is an important factor that should be taken into account. A new class of bivariate distributions, obtained in this work, involve the joint distributions of shock times and their magnitudes. Dependence properties of new bivariate distributions have been studied. For different examples of underlying bivariate distributions of lifetimes and shock magnitudes, the joint distributions of lifetimes of the components are investigated. The multivariate extension of the proposed model is also discussed.
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
This paper is about the reliability modeling of a linear consecutive k-out-of- n system that cons... more 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 behaviors are explored in connection with the value of Kendall’s correlation coefficient.
Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
This paper is concerned with two optimization problems for a k-out-of- n system consisting of dep... more 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 particular case of the present study, was examined. In particular, we numerically examine how the components’ dependence affects the optimal number of units and replacement time for the system, minimizing mean cost rates. We consider when the components are exchangeable and dependent, that is, the system consists of dependent components. For three vastly used Clayton, Gumbel, and FGM copula functions, comparative numerical results are presented.
We consider an ( n − k + 1 ) -out-of- n concomitant system consisting of n components each having... more 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 subcomponents on the system reliability relative to independent subcomponents is discussed. The system with two subcomponents is extended to the system with m subcomponents. Comparative numerical results and graphical representations are provided.
The aim of this paper is to propose a portfolio selection model which takes into account the inve... more 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 expected return and skewness, and minimizing risk and kurtosis, simultaneously. By constructing polynomial goal programming, in which investor preferences for skewness and kurtosis incorporated, a Turkish Stock Market example will be presented for the period from January 2005 to December 2010.
ABSTRACT In the classical Marshall–Olkin model, the system is subjected to two types of shocks co... more ABSTRACT 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.e., in existing shock models usually the system structure is not considered. In this work, we consider a new shock model involving the system structure. More precisely, we consider a coherent system which is subjected to Marshall–Olkin type shocks. We investigate the reliability, and mean time to failure (MTTF) of such systems subjected to shocks coming at random times. Numerical examples and graphs are provided, and an extension to a general model is discussed.
Journal of Computational and Applied Mathematics, 2014
ABSTRACT In classical Marshall–Olkin type shock models and their modifications a system of two or... more ABSTRACT 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 predefined threshold, then the component, which is subjected to this shock, is destroyed; otherwise it survives. More precisely, we assume that the shock time and the magnitude of the shock are dependent random variables with given bivariate distribution. This approach allows to meet requirements of many real life applications of shock models, where the magnitude of shocks is an important factor that should be taken into account. A new class of bivariate distributions, obtained in this work, involve the joint distributions of shock times and their magnitudes. Dependence properties of new bivariate distributions have been studied. For different examples of underlying bivariate distributions of lifetimes and shock magnitudes, the joint distributions of lifetimes of the components are investigated. The multivariate extension of the proposed model is also discussed.
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Papers by Murat Ozkut