Recently, Nair and Sunoj (2024) introduced bivariate total time on test transform (TTT) as a scalar measure and studied its properties. We can see that this measure does not determine the corresponding bivariate distribution uniquely. Hence it has limited role in characterizing bivariate distributions, and in reliability applications such as study of ageing concepts. However, in the paper mentioned above, they showed that a vector with two components, in which the components are the TTTs of one marginal and one conditional random variable, determines the bivariate distribution uniquely. Motivated by this, in the present work, we aim to study a vector form of bivariate TTT. Instead of considering the vector of TTTs of marginal and conditional distributions, we use the vector of TTTs of two conditional random variables. The present form of bivariate TTT also determines the distribution uniquely and has several properties useful for analysing bivariate data. The empirical form of the new measure, called the bivariate TTT statistic, is presented. We discuss some of the applications of the bivariate TTT in generating new models and lifetime data analysis. We carry out real data analysis to illustrate the theoretical findings.
