This paper deals with the safety analysis and the minimum-weight design of rigid frames based on reliability concepts. A safety analysis of redundant systems has difficult features, which are due to the fact that those systems generally have many various possible failure modes. As a rule, the approximations have been done on the assumptions of statistical independence and complete dependence among failure modes. However, the resulting solutions may be widely different as the number of failure modes increases. Also, usual structures have considerable dependence on their own failure mechanisms. A simple formula presenting a good upper bound is derived herein by using the correlations between every two modes. The discussion is done with respect to the lower bound. Its improvement is attempted by introducing a simple mathematical model, which is used for estimating the probability that any three events occur simultaneously. This paper also outlines the minimum-weight design with reliability constraints. The proposed method is employed in the safety analysis. The results are discussed and compared with those of the deterministic method. For large systems, an approximate design method is proposed, which decomposes the possible failure modes into basic and nonbasic modes
