A note on likelihood ratio ordering between parallel systems with two exponential components

Volume 19, Issue 4, pp 251--257 http://dx.doi.org/10.22436/jmcs.019.04.05

Publication Date: July 07, 2019 Submission Date: January 02, 2019 Revision Date: May 30, 2019 Accteptance Date: June 23, 2019

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Authors

Emanuel Emanouilidis - School of Computer Science, Kean University, Union, NJ, 07083, USA. Jiantian Wang - School of Mathematical Science, Kean University, Union, NJ, 07083, USA.

Abstract

With the aid of computer programming, we obtain a result on stochastic comparison of the lifetime of two parallel systems with two exponential components in terms of likelihood ratio ordering. This result reveals a more comprehensive picture on stochastic ordering between parallel systems and thus provides a relatively satisfied answer to an open problem raised in [N. Balakrishnan, P. Zhao, Probab. Engrg. Inform. Sci., \(\bf 27\) (2013), 403--443].

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Keywords

• Parallel system
• stochastic comparison
• likelihood ratio order

MSC

•  90B25
•  60E15

References

• [1] N. Balakrishnan, P. Zhao, Ordering properties of order statistics from heterogeneous populations: a review with an emphasis of some recent developments, Probab. Engrg. Inform. Sci., 27 (2013), 403--443
  • View Article
  • MathSciNet
  • Google Scholar


• [2] P. J. Boland, E. El-Neweihi, F. Proschan, Applications of hazard rate ordering in reliability and order statistics, J. Appl. Probab., 31 (1994), 180--192
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] R. Dykstra, S. Kochar, J. Rojo, Stochastic comparisons of parallel systems of heterogeneous exponential components, J. Statist. Plann. Inference, 65 (1997), 203--211
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] B. Khaledi, S. C. Kochar, Stochastic orderings among order statistics and sample spacings, in: Uncertainty and optimality, 2002 (2002), 167--203
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] S. Kochar, J. Rojo, Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions, J. Multivariate Anal., 59 (1996), 272--281
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] S. Kochar, M. C. Xu, Stochastic comparisons of parallel systems when components have proportional hazard rates, Probab. Engrg. Inform. Sci., 21 (2007), 597--609
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] H. Laniado, R. E. Lillo, Allocation policies of redundancies in two-parallel–series and two-series–parallel systems, IEEE Trans. Reliab., 63 (2014), 223--229
  • View Article
  • Google Scholar


• [8] A. M. Müller, D. Stoyan, Comparison Methods for Stochastic Models and Risks, John Wiley & Sons, Chichester (2002)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] M. Shaked, J. G. Shanthikumar, Stochastic Orders, Springer, New York (2007)
  • View Article
  • MathSciNet
  • Google Scholar


• [10] R. F. Yan, G. F. Da, P. Zhao, Further Results for Parallel Systems with Two Heterogeneous Exponential Components, Statistics, 47 (2013), 1128--1140
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] P. Zhao, N. Balakrishnan, Some characterization results for parallel systems with two heterogeneous exponential components, Statistics, 45 (2011), 593--604
  • View Article
  • MathSciNet
  • Google Scholar