A characterization and sufficient conditions for the total time on test transform order

The total time on test transform has been used in reliability to compare two random lifetimes. Despite that it has been used widely in this context, it is not very clear in which sense the random variables are being compared. In this paper we provide a characterization which reveals the true nature of this comparison. Given that this comparison is of particular interest when the stochastic order does not hold, we also provide sufficient conditions for the comparisons of the total time on test transforms, when the stochastic order does not hold. Applications to the comparison of several parametric families of distributions are provided. Copyright Sociedad de Estadística e Investigación Operativa 2014