In this article we study the comparison of experiments in system reliability theory when the component lifetimes are independent and identically distributed random variables that have a common two-parameter exponential distribution with a location parameter θ. For this purpose, we define a new stochastic order, which we call the convolution order, and study some basic properties of it. We then focus our attention on the family of distribution functions that are mixtures of distributions of partial sums of independent exponential random variables, and derive results that identify several conditions under which members of this family are ordered in the convolution stochastic order. We apply the results to order lifetimes of coherent systems, and as a consequence we obtain information inequalities among various lifetimes of coherent systems. We find situations wherein high reliability decreases statistical information.