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 T T T 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.

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