Modelling the Reliability of Cement Sheath Data with the Poly-Exponential Weibull Distribution

Abstract

The objective of this study is to assess the applicability of the three-parameter Poly-Exponential Weibull distribution for modelling the reliability of cement sheath data, specifically based on Vickers hardness measurements (MPa). This research explores the theoretical properties of the Poly-Exponential Weibull distribution, including the derivation of its quantile function, incomplete moments, Rényi and q-entropies, mean deviations, and the Bonferroni and Lorenz curves. Parameter estimation is performed using the method of maximum likelihood. The findings suggest that the Poly-Exponential Weibull model offers a promising alternative to existing models in the literature, particularly for handling highly skewed reliability data.