A paradigm to maximise performance and profitability of engineering products in the presence of manufacturing uncertainty

Abstract

Variation in the manufactured geometry of engineering components is perpetually present in production. Random variation can arise due to slight differences in material properties, machines and tools, processes and even climatic conditions in the factory. To guarantee the functionality or quality of individual components, features are inspected to verify they conform to the tolerance limits imposed. It is undesirable to produce nonconforming features, due to the cost of reworking features or scrapping components. In practice, it is not always feasible to improve manufacturing capability (reduce variation), or design components to be less susceptible to variation; in such a situation the cost of non-conformance should be minimised. Optimal Mean Setting, a methodology to maximise profit from a production system where the manufacturing variation is often greater than a feature's tolerance limits, can be applied in these circumstances. Although the principle of Optimal Mean Setting dates back over 60 years, its application to engineering design is relatively undeveloped. A major part of this thesis was devoted to developing a robust, reliable and generalised framework to practice Optimal Mean Setting in engineering design. Errors were uncovered in previous attempts in the literature relating to Optimal Mean Setting of simple systems. Improvements to the maximum obtainable profit were also realised by implementing a new optimisation strategy to that developed in the literature. Another innovation developed in this thesis was the application of copula function modelling to Optimal Mean Setting. Copulas allowed joint distributions to be created from non-parametric (or non family specific) feature variation distributions. This permitted Optimal Mean Setting to be applied to components with several quality characteristics where different distributions modelled the manufacturing variation. It also allowed the final geometry of a component to be modelled to access the distribution of performance of a batch of components. Numerical examples and the applications to real components are given.

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