Abstract
This study aims to investigate the reliability properties of the systems constituted of three identical components that are dependent of each other. Besides this, it is studied to compare between the lifetimes of such systems in the sense of hazard rate ordering. Illustrative examples are given by considering some trivariate exponential distributions that are commonly used in reliability literature for the joint distribution of the component lifetimes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barlow R, Proschan F (1975) Statistical theory of reliability and life testing. Holt, Rinehart and Winston, New York
Basu AP (1997) Multivariate exponential distributions with constant failure rates. J Multivariate Anal 61:159–169
Franco M, Vivo JM (2009) A multivariate lifetime model based on generalized exponential distributions. In: The XIII international conference, application stochastic. Model D.A., Vilnius, Lithuania, pp 378–381
Galambos J, Kotz S (1978) Characterizations of probability distributions: a unified approach with an emphasis on exponential and related models, lecture notes in mathematics, Springer-Verlag, Berlin
Georges P et al (2001) multivariate survival modelling: a unified aapproach with copulas. Groupe de Recherche Oṕerationnelle, Cŕedit Lyonnais, Working Paper
Johnson NL, Kotz S (1977) On some generalized farlie-gumbel-morgenstern distributions-II regression, correlation and further generalizations. Commun Stat Theor Meth 6(6):485–496
Joo S, Mi J (2010) Some properties of Hazard rate functions of systems with two components. J Stat Plan Infer 140(2):444–453
Kotz S et al (2000) Continuous multivariate distributions: models and applications, Second Edition edn. John Wiley and Sons, New York, p 752
Lai CD, Xie M (2006) Stochastic ageing and dependence for reliability. Springer, New York
Marshall AW, Olkin I (1967) A multivariate exponential distribution. J Am Stat Assoc 62(317):30–44
Navarro J, Shaked M (2006) Hazard rate ordering of order statistics and systems. J Appl Probab 43(2):391–408
Navarro J et al (2006a) Reliability properties of systems with exchangeable components and exponential conditional distributions. Test 15(2):471–484
Navarro J et al (2006b) Systems with exchangeable components and gumbel exponential distributions. In: Advances in distribution theory, order statistics and inference. Statistics for Industry and Technology. Birkhäuser, Boston, MA, pp 291–306
Navarro J, Lai CD (2007) Ordering properties of systems with two dependent components. Commun Stat Theor 36(3):645–655
Regina C, Elandt-Johnson (1976) Conditional failure time distributions under competing risk theory with dependent failure times and proportional hazard rates. Scand Actuar J. pp 37–51
Sarhan AM, Balakrishnan N (2007) A new class of bivariate distributions and its mixture. J Multivariate Anal 98:1508–1527
Shaked M, Shanthikumar JG (1994) Stochastic orders and their applications. Academic Press, San Diego
Acknowledgments
This paper is dedicated to the memory of our advisor emeritus Professor Yalcin Tuncer who passed away suddenly on August 18, 2011.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Yılmaz, M., Potas, N., Topçu, B. (2015). Reliability Properties of Systems with Three Dependent Components. In: Erçetin, Ş., Banerjee, S. (eds) Chaos, Complexity and Leadership 2013. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-09710-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-09710-7_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09709-1
Online ISBN: 978-3-319-09710-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)