On conditional spacings from heterogeneous exponential random variables

The conditional spacings are investigated here based on a series system with n heterogeneous exponential component lifetimes. First, the survival function and the joint distribution of conditional spacings are obtained. Then, the survival function of the first spacing is shown to be Schur-convex in the hazard rates of component lifetimes. Further, some stochastic comparisons of spacings are carried out. Finally, some results for the conditional sample range are discussed.