The flexibility of a notion considered by Lindley and Singpurwalla is pointed out. It is shown that their set-up can be generalized by looking at systems whose component life lengths are a priori dependent.

A system of n non-renewable components sharing a common environment is considered. The joint lifetimes of the components are taken distributed as a mixture of n independent exponential laws. It is shown how the mixing distribution can affect the number of components functioning and the reliability of a k-out-of-n system. The analysis is carried out by using different partial orderings for distribution functions.

In assessing the reliability of a system of components, it is usual to suppose the components to fail independently of each other. Often this is inappropriate because the common environment acting on all components induces correlation. For example, a harsh environment will encourage early failure of all components. A simple model that incorporates such dependencies is described, and several properties of this model investigated. Calculations are carried out for a parallel system of two components. Inequalities for multicomponent systems are suggested. The results generalize easily.