The economic and social studies contain many parametric models for Lorenz curve‎. ‎The Lorenz curve and Gini index were defined by Lorenz (1905) and Gini (1912) respectively are helpful and popular tools for measuring income or wealth‎. ‎After them many extension and inequality measures are achieved in view of them‎. ‎Also‎, ‎Lorenz order and related partial order are applied and modified for comparison of income distributions up to now. ‎The concept of total time on test and aging criteria such as IFR‎, ‎IFRA‎, ‎NBU‎, ‎HNBUE‎, ... ‎have an important role in reliability. ‎The inequality curves and indices and some links with reliability aging and TTT transform curve are concentrated in this talk. ‎Characterizing aging properties via using inequality curves and partial ordering discussed here also‎. ‎Basic notes of TTT order‎, ‎convex (increasing convex) total time on test transform order and total time on test in average (TTTA) are applied in view of inequality measures. ‎Dispersive ordering and inequality ordering and also characterizing right spread order via increasing convex order studied. ‎Application and a sample view and their relations with inequality measures is the last part of this work‎.

Keywords