Reliability and aging properties of novel nonparametric lifetime distribution classes

Mohamed Kayid; Mutairah Alanazi; Mohamed Kayid; Mutairah Alanazi

doi:10.3934/math.2025878

AIMS Mathematics

2025, Volume 10, Issue 8: 19693-19711. doi: 10.3934/math.2025878

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Reliability and aging properties of novel nonparametric lifetime distribution classes

Mohamed Kayid ^,,
Mutairah Alanazi

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

Received: 05 July 2025 Revised: 06 August 2025 Accepted: 13 August 2025 Published: 27 August 2025
MSC : 62N05, 62G05, 62G30

This paper introduces novel nonparametric classes of lifetime distributions characterized by the shape of the failure rate function. Particular reputable parametric distributions are examined to lie within these novel classes. Preservation property of one of these classes under order statistics is established. An empirical estimator of the failure rate ratio is proposed and in a simulation study, its attributes are explored. Then, a data set of strength of glass fibers is analyzed.
- failure rate function,
- empirical estimation,
- relative aging,
- order statistics,
- nonparametric class,
- aging properties
Citation: Mohamed Kayid, Mutairah Alanazi. Reliability and aging properties of novel nonparametric lifetime distribution classes[J]. AIMS Mathematics, 2025, 10(8): 19693-19711. doi: 10.3934/math.2025878

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Abstract

This paper introduces novel nonparametric classes of lifetime distributions characterized by the shape of the failure rate function. Particular reputable parametric distributions are examined to lie within these novel classes. Preservation property of one of these classes under order statistics is established. An empirical estimator of the failure rate ratio is proposed and in a simulation study, its attributes are explored. Then, a data set of strength of glass fibers is analyzed.

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