RESEARCH PAPER
Further Results on Relative Aging Orders and Comparison of Record Statistics
1
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Submission date: 2024-03-19
Final revision date: 2024-06-26
Acceptance date: 2024-08-29
Online publication date: 2024-08-30
Publication date: 2024-08-30
Corresponding author
Mohamed Kayid
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Eksploatacja i Niezawodność – Maintenance and Reliability 2025;27(1):192756
HIGHLIGHTS
- Improve the study and understanding of relative aging ordering properties to compare lifetime distributions.
- Highlight the difference between relative aging orders and other well-known stochastic orders in literature.
- Compare items that are close to each other during aging.
- Investigate the preservation properties of two well-known faster aging orders under the upper and lower record values.
KEYWORDS
TOPICS
ABSTRACT
In reliability engineering, relative aging is an important notion useful for measuring how a system ages relative to another. In recent years, the reliability properties of record statistics used for statistical modeling, such as shock models, have been investigated. This study presents new findings regarding aging faster orders. Several implications of relative aging orders are presented, including further inequalities arising from these stochastic orders. We apply two faster aging orders by comparing distributions using their cumulative hazard rate functions and cumulative reversed hazard rate functions in the upper and lower record values, respectively. In addition, we compare the record statistics in the two-sample problem. The extent to which the aging-induced faster orders are preserved in the record statistics resulting from sequences of independent and identically distributed random lifetimes is investigated. Finally, examples are provided to illustrate these concepts.
ACKNOWLEDGEMENTS
The author thanks two anonymous reviewers for their constructive comments and suggestions which lead to this improved version. This work is supported by Researchers Supporting Project number (RSP2025R392), King Saud University, Riyadh, Saudi Arabia.
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| eISSN: | 2956-3860 |
| ISSN: | 1507-2711 |
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