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Comparing Lifetimes of Series and Parallel Systems with Heterogeneous Fréchet Components

Longxiang Fang, Yanqin Wang
2017 Symmetry  
In this paper, we discuss stochastic comparisons of lifetimes of series and parallel systems with heterogeneous Fréchet components in terms of the usual stochastic order, reversed hazard rate order and  ...  The partial results established here extend some well-known results in the literature of Gupta et al.  ...  Author Contributions: Longxiang Fang and Yanqin Wang conceived and designed this paper, and contributed equally to this work. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym9010010 fatcat:my2zmdr4e5empgejc56lqacoce

Stochastic Comparison of Parallel Systems with Log-Lindley Distributed Components under Random Shocks [article]

Shovan Chowdhury, Amarjit Kundu
2019 arXiv   pre-print
Recently, Chowdhury and Kundu [6] compared two parallel systems of heterogeneous independent log-Lindley distributed components using the concept of vector majorization and related orders.  ...  Under the same set-up, this paper derives some results related to usual stochastic ordering between two parallel systems when each component receives a random shock.  ...  This paper compares the lifetimes of two parallel systems having heterogeneous log-Lindley distributed components under random shocks.  ... 
arXiv:1804.04103v2 fatcat:gqobnmeaffhcbnzpqhab5wuzgu

Stochastic comparisons of series and parallel systems with heterogeneous components [article]

Esmaeil Bashkar and Hamzeh Torabi and Majid Asadi
2017 arXiv   pre-print
In this paper, we discuss stochastic comparisons of parallel systems with independent heterogeneous exponentiated Nadarajah-Haghighi (ENH) components in terms of the usual stochastic order, dispersive  ...  In the presence of the Archimedean copula, we study stochastic comparison of series dependent systems in terms of the usual stochastic order.  ...  In particular, X 1:n and X n:n correspond to the lifetimes of series and parallel systems, respectively.  ... 
arXiv:1704.06329v1 fatcat:ianq3suqmrhudgpeaqofngmozi

Stochastic Comparison of Parallel Systems with Log-Lindley Distributed Components [article]

Shovan Chowdhury, Amarjit Kundu
2016 arXiv   pre-print
In this paper, we study stochastic comparisons of parallel systems having log-Lindley distributed components.  ...  These comparisons are carried out with respect to reversed hazard rate and likelihood ratio ordering.  ...  This concept is used in the context of optimal component allocation in parallel-series as well as in series-parallel systems, allocation of standby in series and parallel systems, and so on, see, for instance  ... 
arXiv:1608.06903v1 fatcat:hs3rkkr2hbhmfflvhe7dy7iyf4

f-Majorization with Applications to Stochastic Comparison of Extreme Order Statistics

Esmaeil Bashkar, Hamzeh Torabi, Ali Dolati, Felix Belzunce
2018 Journal of Statistical Theory and Applications (JSTA)  
We discuss stochastic comparisons of series systems with independent heterogeneous exponentiated scale components in terms of the usual stochastic order and the hazard rate order.  ...  independent samples following the Frèchet distribution and scale model.  ...  Acknowledgement We would like to express our deep appreciation to referees and Dr Javanshiri for their helpful comments that improved this paper.  ... 
doi:10.2991/jsta.2018.17.3.8 fatcat:co5v3x5ejvbwrnj2glu4ma77va

A new notion of majorization with applications to the comparison of extreme order statistics [article]

Esmaeil Bashkar and Hamzeh Torabi and Ali Dolati and Felix Belzunce
2017 arXiv   pre-print
We discuss stochastic comparisons of series systems with independent heterogeneous exponentiated scale components in terms of the usual stochastic order and the hazard rate order.  ...  independent samples following the Frechet distribution and scale model.  ...  In this section, we discuss stochastic comparisons of series and parallel systems with Frèchet distributed components in terms of the hazard rate order and the reverse hazard rate order.  ... 
arXiv:1704.03656v1 fatcat:rtlggbqup5b5ngnxdgdywyroau

Ordering extremes of interdependent random variables

Rui Fang, Xiaohu Li
2017 Communications in Statistics - Theory and Methods  
Specifically, sample extremes X 1:n and X n:n denote the system lifetimes of series and parallel structure, respectively.  ...  In the context of reliability, random variables X 1 , · · · , X n usually represent component lifetimes, and thus the kth smallest observation, X k:n defines the lifetime of a (n − k + 1)-out-of-n system  ...  Example 3.2(ii) is motivated by one reviewer, and the likelihood ratio order in Theorem 3.8 and Example 3.9 are due to the encouragement of the other reviewer and the Associate editor.  ... 
doi:10.1080/03610926.2017.1371754 fatcat:7jfbcxwx6bbn5n44zkgnqzre6a

Stochastic comparison study of the general family of PHR and PRHR distributions [article]

Madhurima Datta, Nitin Gupta
2020 arXiv   pre-print
Some stochastic ordering results for sample minimum and maximum with dependency based on Archimedean copula has also been studied by varying the location parameters.  ...  In this paper, we have obtained conditions on parameters that result in dispersive ordering and star ordering among two unequal sets of random variables from Proportional hazard rate and Proportional reversed  ...  The next theorems establishes the conditions under which a series system (parallel) can be compared with another series (parallel) system, where all the component lifetimes are dependent and the baseline  ... 
arXiv:2002.12436v1 fatcat:rv6slcjd25b4vcnlf6e4hqe3uq

Design of quasibrittle materials and structures to optimize strength and scaling at probability tail: an apercu

Zdeněk P. Bažant
2019 Proceedings of the Royal Society A  
This yields a size-dependent Gauss-Weibull distribution of lifetime. Close agreement with numerous published test data is achieved.  ...  However, as generally agreed, engineering structures, such as bridges, aircraft or microelectromechanical systems must be designed for tail probability of failure less than 10-6 per lifetime.  ...  Figure 5 . 5 (a) Parallel coupling (bundle) and (b) series coupling (chain); (c) simple hierarchical model combining series and parallel couplings; (d) idealized fracture process zone with illustration  ... 
doi:10.1098/rspa.2018.0617 pmid:31105447 pmcid:PMC6501650 fatcat:zdwmsknwnjefxhu7uppouwgvha

PRISMS-Fatigue computational framework for fatigue analysis in polycrystalline metals and alloys

Mohammadreza Yaghoobi, Krzysztof S. Stopka, Aaditya Lakshmanan, Veera Sundararaghavan, John E. Allison, David L. McDowell
2021 npj Computational Materials  
The performance and flexibility of this framework is demonstrated with various examples that assess the driving force for fatigue crack formation of microstructures with different crystallographic textures  ...  Results indicate that the multilevel parallelism scheme of PRISMS-Fatigue is more efficient and scalable than ABAQUS for large-scale fatigue simulations.  ...  In PRISMS-Fatigue, PBCs are implemented using a set of linear constraints. These constraints are defined on three components of opposing faces, parallel edges, and vertices.  ... 
doi:10.1038/s41524-021-00506-8 fatcat:vo2ctvorwjehfeckml4qojb2oy

Imprecise reliability: An introductory overview [chapter]

Lev V. Utkin, Frank P. A. Coolen
2007 Studies in Computational Intelligence  
The main aim of this paper is to define what imprecise reliability is, and discuss a variety of problems that can be solved by means of a framework of imprecise probabilities.  ...  From this point of view, various branches of reliability analysis are considered, including analysis of monotone systems, repairable systems, multi-state systems, structural reliability, software reliability  ...  Suppose that the following information is available about components of a two-component series system.  ... 
doi:10.1007/978-3-540-37372-8_10 fatcat:mb224zwiwff77idp5xwr5b2v5q

Porous polymeric monoliths: design and preparation towards environmental applications

2019 Biointerface Research in Applied Chemistry  
Polymeric monoliths are porous substrates comprised of suitable monomer(s) beside a crosslinking agent and a radical initiator.  ...  Immobilizing nanoparticles; mainly the metallic ones onto the surface of the polymeric monolith enhances the efficiency of these columns and expands their application fields.  ...  Some heterogeneous globular structure of phase-separated polymer may emerge, with some aggregates in the mold with various sizes, shapes and morphology [16, 17, 36] .  ... 
doi:10.33263/briac94.027036 fatcat:cy7zsc4gnbfuxbkdjozc4ydq64

Stochastic comparisons on sample extremes of dependent and heterogenous observations

Rui Fang, Chen Li, Xiaohu Li
2016 Statistics (Berlin)  
Later, Khaledi and Kochar [10] strengthened the result of Dykstra et al. [13] to a heterogeneous exponential sample and a homogeneous one with common geometric average of all parameters.  ...  For example, concerning two exponential samples with heterogeneous hazards and homogeneous average hazard, respectively, Dykstra et al. [13] proved that the maximum of the heterogeneous one is larger than  ...  Disclosure statement No potential conflict of interest was reported by the authors.  ... 
doi:10.1080/02331888.2015.1119151 fatcat:6gservsrsrcmjfkw5wzauvquhq

USING THE Q-WEIBULL DISTRIBUTION FOR RELIABILITY ENGINEERING MODELING AND APPLICATIONS [article]

Meng Xu
2019
Moreover, in terms of system reliability, the q-Weibull distribution can model dependent series systems and can be modified to model dependent parallel systems.  ...  This research proposes using the q-Weibull distribution to directly model failure time of a series system composed of dependent components that are described by Clayton copula and discusses the connection  ...  of series and parallel systems with dependence.  ... 
doi:10.13016/1xsh-jrje fatcat:mvr5kjnvnjdnrf3droptdmrzn4

Chapter 7 Earnings Functions, Rates of Return and Treatment Effects: The Mincer Equation and Beyond [chapter]

James J. Heckman, Lance J. Lochner, Petra E. Todd
2006 Handbook of the Economics of Education  
reaching a peak of 58% in 1990 (compared with 50% for whites in 1990).  ...  Individuals with s years of schooling must decide whether to quit school and receive lifetime earnings of Y s , or continue on in school for an additional year and receive an expected lifetime earnings  ...  The bandwidth used is equal to 5. 160 For some of the Census years, there is a problem of nonrandom sampling with sampling weights provided in the data.  ... 
doi:10.1016/s1574-0692(06)01007-5 fatcat:h3mz67tdovhovjyyi2mvtkpqmi
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