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

Volume 19, Issue 4, pp 251--257
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].

### Keywords

• Parallel system
• stochastic comparison
• likelihood ratio order

•  90B25
•  60E15

### References

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