A multivariate dispersion ordering is introduced in a weak and strong version. These arise naturally out of the consideration of two-sided versions of a well-known univariate dispersion ordering referred to as 'disp'. Various characterisations of the new orderings are given and some detailed...

There is a duality theory connecting certain stochastic orderings between cumulative distribution functions F1 , F2 and stochastic orderings between their inverses F −1 , F −1. This underlies some theories of utility in the case of the cdf and deprivation indices in the case of the inverse....

Identities and bounds for the reliability of coherent systems are analysed and computed using the techniques of commutative algebra. The techniques are applied to the analysis of some of the most relevant k-out-of-n class systems. The efficiency of the algebraic approach in obtaining exact...