Neutrosophic Reliability Analysis Using the Kumaraswamy Distribution: A Robust Framework for Uncertain Data

Abstract

In engineering, manufacturing, and defense, reliability analysis is essential, yet conventional approaches frequently overlook ambiguous or inaccurate data. In order to account for constrained uncertainty in parameters, this paper presents a neutrosophic statistical framework for reliability estimation using the Kumaraswamy distribution. By applying conventional maximum likelihood estimation (MLE) to neutrosophic MLE, we are able to derive confidence intervals and stress-strength reliability functions under indeterminacy. Simulation findings show that the suggested strategy outperforms classical approaches in terms of robustness, maintaining about 95% coverage even with 20% parameter uncertainty. More relevant uncertainty quantification is provided by the neutrosophic intervals, which dynamically adjust to sample sizes and parameter constraints. Comparative studies show that while both approaches converge to the true reliability value as sample size grows, the Fisher Matrix method produces tighter confidence intervals than the Direct Interval approach. By providing engineers and decision-makers with a versatile tool for dependability assessment in real-world settings with ambiguous or inadequate data, our study closes the gap between theoretical rigor and actual application.