Optimal Tolerance Allocation

Abstract

<p>This thesis addresses itself to one of the most general theoretical problems associated with the art of engineering design. Viewed in its entirety the proposed approach integrates the relation between the design and production engineers through the theory of nonlinear optimization. The conventional optimization problem is extended to include the optimal allocation of the upper and lower limits of the random variables of an engineering system. The approach is illustrated by an example using a sequence of increasingly generalized formulations, while the general mathematical theory is also provided. The method appears to offer a practical technique provided a satisfactory cost function can be defined.</p> <p>The thesis presents an analytical approach to full acceptability design conditions as well as less than full acceptability or scrap design conditions. An important distinction between the design and the manufacturing scrap has been introduced and illustrated through examples.</p> <p>The space regionalization technique is utilized to estimate the system design scrap. Optimization strategies are introduced to the mathematically defined upper and lower limits of the regionalization region. This region is then discretized into a number of cells depending upon the probabilistic characteristic of the system random variables.</p> <p>The analytical approach exhibited does not rely explicitly on evaluation of partial derivatives of either the system cost objective or any of its constraints at any point. Moreover, the technique could be applied to engineering systems with either convex or nonconvex feasible regions. It could also be exercised irrespective of the shape of the probabilistic distributions that describe the random variables variation.</p> <p>Industrially oriented design examples are furnished to justify the applicability of the theory in different engineering disciplines.</p>