On some generalized ageing orderings
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In this paper, some generalized partial orderings that compare probability distributions with the exponential distribution are found to be very useful to understand the phenomenon of ageing, and they describe the same kind of phenomenon of some generalized ageing classes.Abstract:
Some partial orderings that compare probability distributions with the exponential distribution are found to be very useful to understand the phenomenon of ageing. Here, we introduce some new generalized partial orderings which describe the same kind of phenomenon of some generalized ageing classes. We give some equivalent conditions for each of the orderings. Inter-relations among the generalized orderings have also been discussed.read more
Citations
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Journal ArticleDOI
Stochastic Ageing and Dependence for Reliability
TL;DR: This book aims to introduce simulation techniques for practitioners in the financial and risk management industry at an intermediate level by having extensive simulation examples using S–PLUS or Visual Basics.
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Relative Ageing of Series and Parallel Systems With Statistically Independent and Heterogeneous Component Lifetimes
TL;DR: The system with homogeneous componentlifetimes is proved to age relatively faster than that with component lifetimes following the proportional hazard rates (reversed hazard rates) model in terms of the reversed hazard rate (hazard rate).
Journal ArticleDOI
Iterated failure rate monotonicity and ordering relations within gamma and weibull distributions
Idir Arab,Paulo Eduardo Oliveira +1 more
TL;DR: In this paper, the Gamma and Weibull distributions are verified using the relative convexity of the tail functions of the distribution functions, and a method that allows for explicit usage is introduced.
Posted Content
On Relative Ageing of Coherent Systems with Dependent Identically Distributed Components
Nil Kamal Hazra,Neeraj Misra +1 more
Abstract: Relative ageing describes how a system ages with respect to another one. The ageing faster orders are the ones which compare the relative ageings of two systems. Here, we study ageing faster orders in the hazard and the reversed hazard rates. We provide some sufficient conditions for proving that one coherent system dominates another system with respect to ageing faster orders. Further, we investigate whether the active redundancy at the component level is more effective than that at the system level with respect to ageing faster orders, for a coherent system. Furthermore, a used coherent system and a coherent system made out of used components are compared with respect to ageing faster orders.
Journal ArticleDOI
On relative ageing of coherent systems with dependent identically distributed components
Nil Kamal Hazra,Neeraj Misra +1 more
TL;DR: In this paper, the ageing faster orders were used to compare the relative ageing of two coherent systems, and sufficient conditions for one coherent system to dominate another with respect to aging faster orders was provided.
References
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Book
Statistical Theory of Reliability and Life Testing: Probability Models
Richard E. Barlow,Frank Proschan +1 more
TL;DR: A number of new classes of life distributions arising naturally in reliability models are treated systematically and each provides a realistic probabilistic description of a physical property occurring in the reliability context, thus permitting more realistic modeling of commonly occurring reliability situations.
Journal ArticleDOI
Methods of Measuring the Concentration of Wealth
TL;DR: In this article, the authors present methods of measuring the concentration of wealth in the United States, and present a method for measuring the distribution of wealth among individuals in the USA, in terms of wealth concentration.
Book
Stochastic Ageing and Dependence for Reliability
TL;DR: A panoramic view of theory and applications of Ageing and dependence in the use of mathematical methods in reliability and survival analysis is provided in this paper, which serves as a reference for professors and researchers involved in reliability analysis.
Journal ArticleDOI
Some Criteria for Aging
Maurice C. Bryson,M. M. Siddiqui +1 more
TL;DR: In this article, the concept of "aging" is discussed in terms of the entity's survival time distribution, and a set of seven criteria for aging is established, based on these quantities, and the chain of implications among the criteria is developed.
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