Journal ArticleDOI
On relative aging comparisons of coherent systems with identically distributed components
Nil Kamal Hazra,Neeraj Misra +1 more
TLDR
In this article, sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders are given. And the proposed sufficient conditions are satisfied for k-out-of-n systems.Abstract:
The relative aging is an important notion which is useful to measure how a system ages relative to another one. Among the existing stochastic orders, there are two important orders describing the relative aging of two systems, namely, aging faster orders in the cumulative hazard and the cumulative reversed hazard rate functions. In this paper, we give some sufficient conditions under which one coherent system ages faster than another one with respect to the aforementioned stochastic orders. Further, we show that the proposed sufficient conditions are satisfied for k-out-of-n systems. Moreover, some numerical examples are given to illustrate the applications of proposed results.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.
Journal ArticleDOI
Ordering and aging properties of systems with dependent components governed by the Archimedean copula
Tanmay Sahoo,Nil Kamal Hazra +1 more
TL;DR: This paper considers the systems that are formed by dependent and identically distributed components, where the dependency structures are described by Archimedean copulas, and investigates whether a system of used components performs better than a used system with respect to different stochastic orders.
Journal ArticleDOI
Characterizations of Lifetime Distributions Using Two Relative Reliability Measures
Ghadah A. Alomani,Mohamed Kayid +1 more
TL;DR: In this article , a general characterization property considering two new dynamic relative reliability measures is obtained, which are expressed as the ratio of hazard rates and as a ratio of reversed hazard rates, and evaluated partially at some sequential random times following a specific distribution.
Journal ArticleDOI
Stochastic Comparisons of General Proportional Mean Past Lifetime Frailty Model
TL;DR: In this article, the unconditional cumulative distribution and density functions of the lifetime variable are derived from a general proportional mean past lifetime frailty model, and the effects of the baseline variable and the frailty variable on the proposed model are studied.
Journal ArticleDOI
Ordering results of second order statistics from random and non-random number of random variables with Archimedean copulas
Bin Lu,Rongfang Yan +1 more
TL;DR: In this article, the second largest order statistics of homogeneous samples coupled by Archimedean copula were investigated, and the reversed hazard rate and likelihood ratio orders were established.
References
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Book
An Introduction to Copulas
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Journal ArticleDOI
Statistical Theory of Reliability and Life Testing Probability Models
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.
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
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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