[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
Main Menu
Home::
Journal Information::
Articles archive::
For Authors::
For Reviewers::
Registration::
Ethics Considerations::
Contact us::
Site Facilities::
::
Search in website

Advanced Search
..
Receive site information
Enter your Email in the following box to receive the site news and information.
..
Indexing and Abstracting



 
..
Social Media

..
Licenses
Creative Commons License
This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).
 
..
Similarity Check Systems


..
:: ::
Back to the articles list Back to browse issues page
A New Method for Proving the Preservation of IFR Property in Discrete Order Statistics
Mahdi Alimohammadi * , Rezvan Gharebaghi
Abstract:   (242 Views)
It was proved about 60 years ago that if a continuous random variable X has an increasing failure rate  then its order statistics will also be increasing failure rate, and this problem remained unproved for the discrete case until recently a proof method using an integral inequality was provided. In this article, we present a completely different method to solve this problem.
Keywords: ‎Order statistics‎, ‎Failure rate ‎function, Convexity
Full-Text [PDF 262 kb]   (85 Downloads)    
Type of Study: Research | Subject: Reliability
Received: 2024/11/16 | Accepted: 2025/04/30
References
1. Alimohammadi, M., Alamatsaz, M.H. and Cramer, E. (2016), Convolutions and Generalization of Logconcavity: Implications and Applications, Naval Research Logistics, 63(2), 109-123. [DOI:10.1002/nav.21679]
2. Alimohammadi, M., Balakrishnan, N. and Simon, T. (2024), An Inequality for Log-concave Functions and Its Use in the Study of Failure Rates, Probability in the Engineering and Informational Sciences, 38(4), 695-704. [DOI:10.1017/S0269964824000056]
3. Alimohammadi, M. and Navarro, J. (2024), Resolving an Old Problem on the Preservation of the IFR Property Under the Formation of k-out-of-n Systems with Discrete Distributions, Journal of Applied Probability, 61(2), 644-653. [DOI:10.1017/jpr.2023.63]
4. Barlow, R.E. and Proschan, F. (1975), Statistical Theory of Reliability and Life Testing, New York: Holt, Rinehart and Winston.
5. David, H.A. and Nagaraja, H.N. (2004), Order Statistics, John Wiley & Sons. [DOI:10.1002/0471667196.ess6023]
6. Dembińska, A. (2018), On Reliability Analysis of k-out-of-n Systems Consisting of Heterogeneous Components with Discrete Lifetimes, IEEE Transactions on Reliability, 67(3), 1071-1083. [DOI:10.1109/TR.2018.2837080]
7. Esary, J.D. and Proschan, F. (1963), Relationship Between System Failure Rate and Component Failure Rates, Technometrics, 5(2), 183-189. [DOI:10.1080/00401706.1963.10490074]
8. Rockafellar, R. (1970), Convex Analysis, Princeton University Press, New Jersey. [DOI:10.1515/9781400873173]
9. Roy, D. and Gupta, R.P. (1992), Classifications of Discrete Lives, Microelectronics Reliability, 32(10), 1459-1473. [DOI:10.1016/0026-2714(92)90015-D]
10. Shaked, M., Shanthikumar, J.G., and Valdez-Torres, J.B. (1995), Discrete Hazard Rate Functions, Computers & Operations Research, 22(4), 391-402. [DOI:10.1016/0305-0548(94)00048-D]
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA


XML   Persian Abstract   Print



Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Back to the articles list Back to browse issues page
مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

Persian site map - English site map - Created in 0.06 seconds with 45 queries by YEKTAWEB 4710