A Novel Neutrosophic Fuzzy Approach for Stress-Strength Reliability Analysis of Ailamujia Distributions Under Parameter Uncertainty
DOI:
https://doi.org/10.13052/jrss0974-8024.1929Keywords:
Ailamujia distribution, stress-strength reliability, fuzzy reliability, neutrosophic statistics, hybrid model, parameter uncertainty, interval estimationAbstract
In this study, a hybrid framework is proposed that combines fuzzy logic with neutrosophic statistics to deal with the issue of parameter uncertainty in stress-strength reliability analysis of systems that are governed by the Ailamujia distribution. The proposed framework is an extension of the conventional binary reliability model in that it incorporates a fuzzy reliability concept that considers the degree of exceedance of strength over stress rather than the conventional binary concept of exceedance/non-exceedance. To deal with the indeterminate scale parameters that arise in practice, the proposed framework is extended to a neutrosophic framework to arrive at interval estimates of reliability that reflect the imprecise nature of real-world problems. The objectives of this study are to arrive at the fuzzy reliability model, extend it to a neutrosophic framework, and finally examine the performance of the proposed framework through extensive simulation studies. Additionally, the practicality of the proposed model is also examined through a case study of component reliability in mechanical systems.
Downloads
References
K. F. H. Alhasan and F. Smarandache, “Neutrosophic reliability analysis of systems,” Neutrosophic Sets and Systems, vol. 42, pp. 1–12, 2021.
M. Aslam, “Design of a new Z-test for the uncertainty of Covid-19 events under Neutrosophic statistics,” BMC Medical Research Methodology, vol. 22, no. 1, p. 99, 2022.
F. Smarandache, “Introduction to Neutrosophy, Neutrosophic Set, Neutrosophic Probability, Neutrosophic Statistics and Their Applications to Decision Making,” in Neutrosophic Paradigms: Advancements in Decision Making and Statistical Analysis: Neutrosophic Principles for Handling Uncertainty, Cham: Springer Nature Switzerland, 2025, pp. 3–21.
S. K. Singh et al., “On the estimation of stress strength reliability parameter of inverted exponential distribution,” International Journal of Scientific World, vol. 3, no. 1, pp. 98–112, 2015.
M. Kumar and S. B. Singh, “A novel fuzzy reliability method for the marine power plant under different intuitionistic fuzzy environments,” Life Cycle Reliability and Safety Engineering, vol. 13, no. 4, pp. 467–482, 2024.
F. Smarandache, Neutrosophy: Neutrosophic Probability, Set, and Logic. American Research Press, 1998.
F. Smarandache, Introduction to Neutrosophic Statistics. Sitech & Education Publishing, 2014.
L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 3–28, 1978.
N. Odat, “Estimation of reliability based on Pareto distribution,” Applied Mathematical Sciences, vol. 4, no. 53–56, pp. 2743–2748, 2010.
K. S, Chauhan, and S. Tomer. Stress and Strength Reliability Estimation for the Inverse Family of Distributions using Bayesian Analysis. Journal of Reliability and Statistical Studies, vol. 19, no. 2, pp. 241–262, 2026,
S. M. Ghania, K. R. M. Mahmoud, and A. M. Hashmi, “A reliability study of renewable energy resources and their integration with utility grids,” Engineering, Technology & Applied Science Research, vol. 12, no. 5, pp. 9078–9086, 2022. doi: 10.48084/etasr.5090.
O. Bouketir, A. Saib, and A. Fenni, “A fuzzy logic-based greenhouse smart system for sustainable tomato production in Algeria,” Engineering, Technology & Applied Science Research, vol. 15, no. 4, pp. 24110–24116, 2025. doi: 10.48084/etasr.10856.
N. Odat, “Estimation of the stress-strength reliability for Kumaraswamy distribution,” International Journal of Applied Mathematics, vol. 55, no. 10, pp. 3298–3303, 2025.
N. Odat, “Fuzzy Reliability Estimation for Benktander Distribution,” International Journal of Neutrosophic Science, vol. 27, no. 1, pp. 147–158, 2026. DOI: https://doi.org/10.54216/IJNS.270115.
N. Odat, “Estimation of the stress–strength Reliability for Benktander Distribution,” International Journal of Neutrosophic Science, vol. 26, no. 4, pp. 137–142, 2025. DOI: https://doi.org/10.54216/IJNS.260413.
M. Aslam, “Neutrosophic Chi-Square Test for Analyzing Population Variances with Uncertain Data,” Journal of Statistical Theory and Practice, vol. 19, no. 2, p. 25, 2025.
S. A. Lone, Q. Ramzan, and L. A. AL-Essa, “The exponentiated Ailamujia distribution: properties and application,” Alexandria Engineering Journal, vol. 108, pp. 1–15, 2024.
T. Alballa, Q. Ramzan, M. Amin, and L. A. AL-Essa, “The development and implementation of odd-exponential-Ailamujia distribution in Python: properties and application in reliability engineering,” Scientific Reports, vol. 16, p. 7015, 2026.
M. M. Mansour, E. A. El-Sherpieny, R. E. Mohamed, and H. M. Aljohani, “Statistical analysis of the induced Ailamujia lifetime distribution with engineering and biomedical applications,” Mathematics, vol. 13, no. 20, p. 3307, 2025.
N. Odat, “Neutrosophic reliability analysis using the Kumaraswamy distribution: A robust framework for uncertain data,” European Journal of Pure and Applied Mathematics, vol. 18, no. 4, p. 7098, 2025.
A. Muhammad, R. A. Bantan, A. Shafiq, and M. Elgarhy, “Properties and applications of neutrosophic Burr XII distribution,” International Journal of Computational Intelligence Systems, vol. 18, no. 1, pp. 1–11, 2025.
M. Savkoviæ, V. Paunoviæ, C. Caiazzo, and N. Komatina, “Neutrosophic failure mode and effect analysis—Elimination and choice translating reality method for prioritizing failure modes,” Journal of Engineering Management and Systems Engineering, vol. 4, no. 4, 2025.
K. Sruthi and M. Kumar, “Fuzzy reliability estimation within a stress-strength framework incorporating distortion functions,” Journal of Reliability and Statistical Studies, vol. 19, no. 1, pp. 43–64, 2026.
