Preservation properties of some relative aging classes under $ (n-k+1) $-out-of-$ n $ systems

Mohamed Kayid; Mansour Shrahili; Mohamed Kayid; Mansour Shrahili

doi:10.3934/math.20241428

AIMS Mathematics

2024, Volume 9, Issue 10: 29474-29495. doi: 10.3934/math.20241428

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Research article

Preservation properties of some relative aging classes under $ (n-k+1) $-out-of-$ n $ systems

Mohamed Kayid ,
Mansour Shrahili ^,

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 26 August 2024 Revised: 04 October 2024 Accepted: 14 October 2024 Published: 17 October 2024
MSC : 62E10, 62E15, 62N05

In this paper, we focus on two relative aging classes, namely increasing (decreasing) relative failure rate and increasing (decreasing) failure rate relative to average failure rate. We studied some reliability properties and connections with other classes of lifetime distributions. The main objective of this paper was to investigate the preservation properties of decreasing relative failure rate class and decreasing failure rate relative to average failure rate class under the structure of ($ n-k+1 $)-out-of-$ n $ system. We give some examples of parametric distributions to evaluate the correctness of the results.
- relative aging,
- stochastic order,
- aging intensity,
- classes of life distributions,
- hazard rate,
- DFRA
Citation: Mohamed Kayid, Mansour Shrahili. Preservation properties of some relative aging classes under $ (n-k+1) $-out-of-$ n $ systems[J]. AIMS Mathematics, 2024, 9(10): 29474-29495. doi: 10.3934/math.20241428

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Abstract

In this paper, we focus on two relative aging classes, namely increasing (decreasing) relative failure rate and increasing (decreasing) failure rate relative to average failure rate. We studied some reliability properties and connections with other classes of lifetime distributions. The main objective of this paper was to investigate the preservation properties of decreasing relative failure rate class and decreasing failure rate relative to average failure rate class under the structure of ($ n-k+1 $)-out-of-$ n $ system. We give some examples of parametric distributions to evaluate the correctness of the results.

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