Neutrosophic Modeling of Lifetime Data Using the Weibull–Exponentiated Exponential Distribution

Abstract

Modeling lifetime data plays an indispensable role in reliability engineering and survival analysis, where the primary goal is to accurately predict time-to-event phenomena. While classical probability distributions, such as the widely applied Weibull-Exponentiated Exponential (W-EE) hybrid model, offer significant flexibility in capturing versatile hazard rates, they possess a fundamental limitation. Specifically, traditional models inherently assume that the observed data and underlying parameters are precise and well-defined. However, this assumption is rarely satisfied in practical scenarios. In real-world applications, data collection is frequently plagued by measurement errors, interval-censored information, environmental noise, and inherent vagueness. Relying strictly on classical statistical methods under such uncertain conditions often yields biased parameter estimates and misleading reliability inferences. To address these critical challenges, this study introduces the Neutrosophic Weibull–Exponentiated Exponential (NW–EE) distribution, a novel extension designed to model lifetime data characterized by indeterminacy. By integrating neutrosophic components into the classical W-EE model, we effectively represent observations and parameters as neutrosophic intervals rather than exact point values. In this paper, we rigorously derive the key statistical functions of the new distribution, including the neutrosophic cumulative distribution function (NCDF), the neutrosophic probability density function (NPDF), and vital reliability measures such as the survival and hazard rate functions. Furthermore, we investigate essential mathematical properties such as neutrosophic moments and variance. Additionally, the model parameters are estimated utilizing the neutrosophic maximum likelihood estimation (NMLE) technique, and the model is validated using real datasets. The results demonstrate that the NW-EE model offers superior flexibility in handling imprecise observations in reliability engineering and survival analysis, providing a highly accurate and realistic alternative to classical distributions. The introduced Neutrosophic Weibull-Exponentiated Exponential (NW-EE) distribution is a sophisticated analytical tool designed to model lifetime data in environments where imprecision and indeterminacy are unavoidable.