Method of Developing Optimum Tolerances

Standards should optimize for society. This is approximately accomplished by minimizing the sum of expected present values of initial cost and losses due to failure (entrance into limit states), maintenance, and disutility caused by reduction in users' well-being. On this basis a general theory of standards optimization is developed, applicable to any kind of products, assuming that the least expensive variant satisfying the standards will be purchased (or the contract awarded to the lowest bidder) and recognizing random price fluctuations. A simpler version is applied to rolled steel shapes, especially I-beams. Initial cost is taken as containing a term proportional to cross-sectional area and one due to wear of rollers. Expected failure loss is computed for different safety factors. This leads to computation of optimum tolerances on cross-sectional area. Results indicate that present practice may be too conservative. A more refined analysis is suggested.