Laplace transform ordering of time to failure in age replacement models

The concept of mean time to failure in age replacement models plays an important role in reliability and life testing. In this paper, based on the comparison of Laplace transform of time to failure in an age replacement model, we introduce and study a new stochastic order. This new order is stronger than the Laplace transform and the mean time to failure in the age replacement model orders. Some motivations and descriptions of the proposed stochastic order are provided. In addition, several characterizations and preservation properties of the new order under some well-known reliability operations are discussed. As a consequence, a new class of life distributions is proposed, and some of its reliability properties are investigated. Finally, the problem of testing exponentiality against such class is discussed and some numerical results are presented.