Exploring the Differential Geometry of Reliability Function: Insights from Lifetime Weibull Distributions Under Neutrosophic Environment - Nada Mohammed Abbas; Ghazi Abdullah; Ahmed Hadi Hussain (Neutrosophic Sets and Systems)
This paper characterizes a set N as a two-dimensional surface marked by 𝑅 + × 𝑅 + and demonstrates its properties as a topological 2-reliability manifold and a differential reliability manifold. Utilizing the Weibull lifetime distribution, we derive the formula for the Riemannian manifold (𝑁, 𝑔𝑖𝑗). Finally, we prove that the reliability function represents the critical point of its log-likelihood on the manifold, which also serves as the saddle point. Also, we discuss the same results in a neutrosophic environment, with neutrosophic variables and coefficients from the neutrosophic real ring R(I), where we get similar results of the original approach.