Characterization and preservations of the variance inactivity time ordering and the increasing variance inactivity time class

If the random variable X   denotes the lifetime of a unit, then the random variable X(t)=[t-X|X⩽t]X(t)=[t-XX⩽t] for a fixed t > 0 is known as the inactivity time. In this paper, based on the random variable X(t), a new class of life distributions, namely increasing variance inactivity time (IVIT) and the concept of inactivity coefficient of variation (ICV), are introduced. The closure properties of the IVIT class under some reliability operations, such as mixing, convolution and formation of coherent systems, are obtained.