Coherent Structures of Non-Identical Components

A basic theorem on the covariance of increasing functions of random variables is explored which permits a discussion of the case of coherent structures whose components are independent, but of differing reliabilities. This provides convenient bounds on the reliability of structures, a generalization of some statistical properties (Technometrics, Vol 3, No 1:55-77, 1961) for coherent structures, and finally a generalization of a differential inequality (Jnl of the Franklin Institute, Vol 262:191-208, 281-297, 1956) which relates structural and component reliabilities. One of the consequences of the present approach is a very simple and direct demonstration of the S-shapedness results presented.