Further Results Involving the Mean Time to Failure Order, and the Decreasing Mean Time to Failure Class

The purpose of this paper is to enhance the study of the mean time to failure (MTTF) order in an age replacement model, and the decreasing mean time to failure (DMTTF) class of life distributions. We present new characterizations of the MTTF order in terms of the well-known hazard rate and reversed hazard rate orders. Preservation properties of this order under some reliability operations such as monotonic transformations, mixture, and weighted distributions are investigated. In this context, we provide new results related to the DMTTF class. Finally, the problem of testing exponentiality against such class is discussed, and some numerical results are presented.