Some Properties of Total Time on Test and Excess Wealth in Bivariate Cases

‎Most of the introduced transformations have many applications in reliability‎. ‎For example‎, ‎the total time on test (TTT) and excess wealth (EW) ‎transforms are useful concepts in various fields‎. ‎This paper presents bivariate TTT and EW transforms‎. ‎Also‎, ‎the bivariate location independent riskier (LIR) transform has been considered‎. ‎In addition‎, ‎we present the conditions for establishing the TTT transform ordering in the bivariate mode and its relationship with EW order and some stochastic orders‎. ‎Also‎, ‎we establish that the bivariate TTT transform order as well as the presentation of the new better than used in bivariate TTT transform class‎. ‎Finally‎, ‎we describe the relationship between TTT and EW transforms with aging classes in the bivariate mode‎.