A note on likelihood ratio ordering between parallel systems with two exponential components
- School of Computer Science, Kean University, Union, NJ, 07083, USA.
- School of Mathematical Science, Kean University, Union, NJ, 07083, USA.
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].
- Parallel system
- stochastic comparison
- likelihood ratio order
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
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
R. Dykstra, S. Kochar, J. Rojo, Stochastic comparisons of parallel systems of heterogeneous exponential components, J. Statist. Plann. Inference, 65 (1997), 203--211
B. Khaledi, S. C. Kochar, Stochastic orderings among order statistics and sample spacings, in: Uncertainty and optimality, 2002 (2002), 167--203
S. Kochar, J. Rojo, Some new results on stochastic comparisons of spacings from heterogeneous exponential distributions, J. Multivariate Anal., 59 (1996), 272--281
S. Kochar, M. C. Xu, Stochastic comparisons of parallel systems when components have proportional hazard rates, Probab. Engrg. Inform. Sci., 21 (2007), 597--609
H. Laniado, R. E. Lillo, Allocation policies of redundancies in two-parallelseries and two-seriesparallel systems, IEEE Trans. Reliab., 63 (2014), 223--229
A. M. Müller, D. Stoyan, Comparison Methods for Stochastic Models and Risks, John Wiley & Sons, Chichester (2002)
M. Shaked, J. G. Shanthikumar, Stochastic Orders, Springer, New York (2007)
R. F. Yan, G. F. Da, P. Zhao, Further Results for Parallel Systems with Two Heterogeneous Exponential Components, Statistics, 47 (2013), 1128--1140
P. Zhao, N. Balakrishnan, Some characterization results for parallel systems with two heterogeneous exponential components, Statistics, 45 (2011), 593--604