Optimum Tolerance Assignment to Yield Minimum Manufacturing Cost

A valid area of investigation for the cutting of manufacturing costs in the mass production process lies in the assignment of tolerances. In this paper we examine a problem in t h a t area. Consider the following fairly typical sequence of events: A piece of equipment is to be designed with a specified nominal response, for example, an amplifier with a specified nominal gain, or a logic gate with a specified nominal time delay. T h e circuit is designed and nominal values are assigned to t h e components of this piece of equipment so t h a t it has the required nominal response. Next, this piece of equipment is to be mass produced, and 461 462 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1958 mass produced economically. One of the manifold problems which arises at this point is the assignment of tolerances to the various components of the piece of equipment. It is at this point in the design for production t h a t the considerations in this paper enter. T h e effect, of component tolerances is to cause the response to deviate from the nominal in a statistical manner. A common approach to component tolerance assignment ignores the statistical behavior of the response deviation and bases the tolerance assignment 011 the "worst case" approach, i.e., the deviations from nominal for all components are assumed to act in concert to maximize the deviation from nominal of t h e response. This criterion corresponds to a very pessimistic viewpoint because, usually, the probability of such a simultaneous occurrence of worst values is extremely small.