Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T12:03:15.337Z Has data issue: false hasContentIssue false
  • English
  • Français

Stochastic comparisons of interfailure times under a relevation replacement policy

Part of: Sufficiency and information Distribution theory - Probability

Published online by Cambridge University Press:  04 April 2017

Miguel A. Sordo  and
Georgios Psarrakos
Miguel A. Sordo*
Affiliation:
University of Cádiz
Georgios Psarrakos*
Affiliation:
University of Piraeus
*
* Postal address: Department of Statistics and Operation Research, University of Cádiz, 11510 Puerto Real, Cádiz, Spain. Email address: [email protected]
** Postal address: Department of Statistics and Insurance Science, University of Piraeus, 18534 Piraeus, Greece. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We provide some results for the comparison of the failure times and interfailure times of two systems based on a replacement policy proposed by Kapodistria and Psarrakos (2012). In particular, we show that when the first failure times are ordered in terms of the dispersive order (or, the excess wealth order), then the successive interfailure times are ordered in terms of the usual stochastic order (respectively, the increasing convex order). As a consequence, we provide comparison results for the cumulative residual entropies of the systems and their dynamic versions.

Keywords

Stochastic orderdispersive orderexcess wealth orderincreasing convex ordercumulative residual entropy

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 62B10: Information-theoretic topics
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 134 - 145
Copyright
Copyright © Applied Probability Trust 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Asadi, M. and Zohrevand, Y. (2007).On the dynamic cumulative residual entropy.J. Statist. Planning Infer. 137,1931–1941.CrossRefGoogle Scholar
Baratpour, S. (2010).Characterizations based on cumulative residual entropy of first-order statistics.Commun. Statist. Theory Meth. 39,3645–3651.Google Scholar
Baratpour, S. and Habibi Rad, A. (2016).Exponentiality test based on the progressive type II censoring via cumulative entropy.Commun. Statist. Simul. Comput. 45,2625–2637.CrossRefGoogle Scholar
Barlow, R. E. and Proschan, F. (1975).Statistical Theory of Reliability and Life Testing.Holt, Rinehart and Winston,New York.Google Scholar
Baxter, L. A. (1982).Reliability applications of the relevation transform.Naval Res. Logistics 29,321–330.CrossRefGoogle Scholar
Belzunce, F., Martínez-Riquelme, C. and Mulero, J. (2016a).An Introduction to Stochastic Orders.Elsevier,Amsterdam.Google Scholar
Belzunce, F., Martínez-Riquelme, C., Ruiz, J. M. and Sordo, M. A. (2016b).On sufficient conditions for the comparisons in the excess wealth order and spacings.J. Appl. Prob. 53,33–46.CrossRefGoogle Scholar
Belzunce, F., Pellerey, F., Ruiz, J. M. and Shaked, M. (1997).The dilation order, the dispersion order, and orderings of residual lives.Statist. Prob. Lett. 33,263–275.CrossRefGoogle Scholar
Bickel, P. J. and Lehmann, E. L. (1976).Descriptive statistics for nonparametric models. III. Dispersion.Ann. Statist. 4,1139–1158.CrossRefGoogle Scholar
Burkschat, M. and Navarro, J. (2014).Asymptotic behavior of the hazard rate in systems based on sequential order statistics.Metrika 77,965–994.Google Scholar
Chamany, A. and Baratpour, S. A. (2014).A dynamic discrimination information based on cumulative residual entropy and its properties.Commun. Statist. Theory Meth. 43,1041–1049.Google Scholar
Di Crescenzo, A. and Longobardi, M. (2009).On cumulative entropies.J. Statist. Planning Infer. 139,4072–4087.CrossRefGoogle Scholar
Di Crescenzo, A. and Longobardi, M. (2015).Some properties and applications of cumulative Kullback–Leibler information.Appl. Stoch. Models Bus. Ind. 31,875–891.Google Scholar
Di Crescenzo, A. and Toomaj, A. (2015).Extensions of the past lifetime and its connections to the cumulative entropy.J. Appl. Prob. 52,1156–1174.Google Scholar
Kapodistria, S. and Psarrakos, G. (2012).Some extensions of the residual lifetime and its connection to the cumulative residual entropy.Prob. Eng. Inf. Sci. 26,129–146.CrossRefGoogle Scholar
Krakowski, M. (1973).The relevation transform and a generalization of the gamma distribution function.Rev. F. Automat. Inf. 7,107–120.Google Scholar
López-Dí, M., Sordo, M. A. and Suárez-Llorens, A. (2012).On the L p -metric between a probability distribution and its distortion.Insurance Math. Econom. 51,257–264.Google Scholar
Müller, A. and Stoyan, D. (2002).Comparison Methods for Stochastic Models and Risks.John Wiley,Chichester.Google Scholar
Navarro, J. and Psarrakos, G. (2017).Characterizations based on generalized cumulative residual entropy functions.Commun. Statist. Theory Meth. 46,1247–1260.Google Scholar
Navarro, J., Del Águila, Y. and Asadi, M. (2010).Some new results on the cumulative residual entropy.J. Statist. Planning Infer. 140,310–322.Google Scholar
Nelsen, R. B. (1999).An Introduction to Copulas (Lectures Notes Statist. 139).Springer,New York.Google Scholar
Psarrakos, G. and Navarro, J. (2013).Generalized cumulative residual entropy and record values.Metrika 76,623–640.CrossRefGoogle Scholar
Rao, M. (2005).More on a new concept of entropy and information.J. Theoret. Prob. 18,967–981.CrossRefGoogle Scholar
Rao, M., Chen, Y., Vemuri, B. C. and Wang, F. (2004).Cumulative residual entropy: a new measure of information.IEEE Trans. Inf. Theory 50,1220–1228.Google Scholar
Shaked, M. and Shanthikumar, J. G. (2007).Stochastic Orders.Springer,New York.Google Scholar
Yang, J., Zhuang, W. and Hu, T. (2014). L p -metric under the location independent-risk ordering of random variables.Insurance Math. Econom. 59,321–324.Google Scholar