The purpose of this article is to study several preservation properties of stochastic comparisons based on the mean inactivity time order under the reliability operations of convolution and mixture+ Characterizations and relationships with the other well-known orders are given+ Some examples of interest in reliability theory are also presented+ Finally, testing in the increasing mean inactivity time class is discussed+

The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. Some applications in reliability theory are described. Finally, a new test of such a class is discussed.

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