Some new results about the variance inactivity time ordering with applications

•Further characterizations and preservation properties of the VIT order are introduced and studied.•We present some new interesting implications and characterizations concerning the VIT order.•We develop some preservation properties of this order under some reliability operations such as mixture, and convolution.•Some applications in the context of statistics and reliability theory are included.

The purpose of this paper is to enhance the study of the variance inactivity time order. We first present some new implications and characterizations concerning this order. Then, we develop some preservation properties of this order under some reliability operations such as mixture, and convolution. Finally, we highlight some new applications of this order in the context of statistics and reliability theory.