On the Relation Between the Factor of Safety and Reliability

An approximate relation between the reliability of a design and the classical deterministic factor of safety, used in the design, is presented. An expression of the reliability as function of the mean value and coefficient of variation of the probability density distribution of the factor of safety, is derived. Further, the relation between the deterministic factor of safety and the statistical values of the probabilistic factor of safety, is discussed. Finally an expression for the reliability as a function of the deterministic factor of safety and the parameters determining the stress and strength distributions, is obtained. This function relationship is expressed in a design nomogram relating all the parameters involved.