Abstract
The concept of mean inactivity time plays an important role in reliability and life testing. In this investigation, based on the comparison of mean inactivity times of a certain function of two lifetime random variables, we introduce and study a new stochastic order. This new order lies between the reversed hazard rate and the mean inactivity time orders. Several characterizations and preservation properties of the new order under reliability operations of monotone transformation, mixture, and shock models are discussed. In addition, a new class of life distributions called strong increasing mean inactivity time is proposed, and some of its reliability properties are investigated. Finally, to illustrate the concepts, some applications in the context of reliability theory are included.