Consider two systems with identical components but different structure functions. In this paper we propose a method to compare these two systems when the marginal behaviors of components are specified but when the complete joint behavior of components is unspecified. We also give two useful theorems for applying our method. We apply our techniques to two examples.

The characterization of the exponential distribution as given by Dimitrov and Khalil (1990) is improved by substantially weakening the conditions.

In this short note we derive Sengupta's (1989) invariance relation using elementary arguments and we show that Miyazawa's (1983), (1985) conservation principle, on which Sengupta's proof is based, admits the Palm inversion formula as a consequence. This contrasts with Miyazawa's first proof based on the inversion formula. We also show that Neveu's (1976) cycle formula is a direct consequence of Miyazawa's principle.

The standard uniformization technique for continuous-time Markov chains is generalized to non-exponential stochastic networks.