Reliability Analysis of the Harmonic Mean Inactivity Time Order

Based on the comparison of a certain function of mean inactivity times of two nonnegative random variables, we introduce and study a new stochastic order. Several elementary and then basic preservation properties of the new stochastic order under reliability operations of convolution, mixture, and shock models are discussed. We also derive characterizations of some well-known stochastic orders by the new order, and point out some results related to the weighted distributions. Some examples are included to illustrate the concepts.