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<p>This paper introduces a new statistical distribution called Neutrosophic Generalized Gamma Distribution which is developed to assess the reliability and lifespan of gearbox components in wind turbines under uncertainty and imprecision. The statistical characteristics of the distribution are studied under neutrosophic environment. Neutrosophic descriptive measures including raw moments, mode, mean deviation, quantiles, hazard function, entropy, reliability function and various related statistical functions are derived which is commonly used in real world applications. The neutrosophic parameters <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12597_2025_1054_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="TEX">\({\alpha }_{n},{ \beta }_{n} and {p}_{n}\)</EquationSource> </InlineEquation> of the distribution are estimated using the Maximum Likelihood Estimation (MLE) method. A simulation study is conducted to assess the performance of these estimated parameters. Additionally, some illustrations of the NGGD in areas such as reliability engineering, component failure prediction and maintenance scheduling are examined. The application of NGGD is discussed to estimate the reliability and lifespan of gearbox components of wind turbines in the renewable energy sector. It is also observed that Neutrosophic Weibull, Gamma, Exponential and Rayleigh distributions are the special case of proposed distribution under certain parametric conditions.</p>

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Neutrosophic generalized gamma distribution and its application in lifetime modelling

  • 期刊论文

  • 发表日期：

    2025年11月19日

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  • Rahul Thakur,
  • Masum Raj,
  • S. C. Malik

摘要

This paper introduces a new statistical distribution called Neutrosophic Generalized Gamma Distribution which is developed to assess the reliability and lifespan of gearbox components in wind turbines under uncertainty and imprecision. The statistical characteristics of the distribution are studied under neutrosophic environment. Neutrosophic descriptive measures including raw moments, mode, mean deviation, quantiles, hazard function, entropy, reliability function and various related statistical functions are derived which is commonly used in real world applications. The neutrosophic parameters \({\alpha }_{n},{ \beta }_{n} and {p}_{n}\) of the distribution are estimated using the Maximum Likelihood Estimation (MLE) method. A simulation study is conducted to assess the performance of these estimated parameters. Additionally, some illustrations of the NGGD in areas such as reliability engineering, component failure prediction and maintenance scheduling are examined. The application of NGGD is discussed to estimate the reliability and lifespan of gearbox components of wind turbines in the renewable energy sector. It is also observed that Neutrosophic Weibull, Gamma, Exponential and Rayleigh distributions are the special case of proposed distribution under certain parametric conditions.