Abstract
This study introduces the Odd-Exponential-Ailamujia (OEA) distribution, a novel extension of the Ailamujia distribution via the T-X family, offering enhanced flexibility for modeling complex lifetime data in reliability and survival analysis. Key statistical properties, including moments, moment-generating function, characteristic function, mean residual life, and mean waiting time, are derived using binomial and Taylor series expansions, transforming intractable integrals into computable forms and enabling precise approximation of distributional behavior. The hazard rate function exhibits diverse shapes (increasing, decreasing, or unimodal), controlled by parameters, making the proposed model adaptable to varied failure patterns. Applied to aircraft windshield failure data, the OEA distribution demonstrates superior fit over competing models through goodness-of-fit tests, various plots of reliability measures, 3D surface interactions, and heatmaps revealing parameter-driven correlations. Efficient Python implementation to ensures scalable inference. The OEA distribution emerges as a robust, versatile tool for reliability engineering, survival modeling, and probabilistic forecasting, effectively capturing real-world failure dynamics.
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The data supporting the findings of this study are available within the article and from publicly accessible online sources. All datasets used for analysis and validation are properly cited and can be accessed through the references provided in the manuscript.
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Acknowledgements
Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R404), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
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T.A. conceptualized the study framework and contributed to the theoretical formulation of the proposed distribution. Q.R. developed the OEA distribution, performed the statistical analysis, implemented the Pythonbased simulations, and wrote the main manuscript text. M.A. assisted in the refinement of methodology, model validation, and result interpretation. M.A.M. contributed to manuscript revision, improved figure presentation, and enhanced the overall clarity of the work. H.A.E.K. provided supervision, critical give a deeper look intots, and final review of the paper. All authors read and approved the final manuscript.
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Alballa, T., Ramzan, Q., Amin, M. et al. The development and implementation of odd-exponential-ailamujia distribution in python: properties and application in reliability engineering. Sci Rep (2026). https://doi.org/10.1038/s41598-025-30574-5
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DOI: https://doi.org/10.1038/s41598-025-30574-5
