Design for quality, a model-based probabilistic approach

Abstract

Detailed within this thesis is a method for determining and improving the quality of a system. An overall 'Design for Quality' method has previously not existed in the field of model-based design. Statistical experimental design has been used in 'off-line' quality control to determine the optimal settings for a system even when the mathematical model is known. Taguchi demonstrated how signal-to-noise ratios could be used to improve performance of a system through variance minimization. However, these statistical methods often don't use the full distribution of information that may be available. Detailed within this thesis is an extension and complement to Taguchi's use of experimental design and signal-to-noise ratios for known system models. The use of a probability transformation method with the mathematical system model will allow designers to perform parameter and tolerance design simultaneously using a method of 'fast integration'. The result is a new method in the field of 'Quality by Design' that can handle both linear and non-linear systems, with components of any distribution type, with or without correlation of the variables, and with single or multiple responses. As an integral part of the method, an interpretation of Taguchi's classification of factors is given in context to this full distribution method. Through the examination of gradients from the probability transformation method, the design variables can be classified into one of three types: neutral, adjustment, or control. In addition, two extensions to the design method are also detailed within the thesis. The first is the use of the probability transformation method to determine an approximate probability density function for the system responses, and the second is the use of the probability transformation method to perform a 'Worst-Case Analysis' on the system response. The former uses the information given about the system to 'profile' the response, while the latter uses uniform distributions for the system variables and an Interval Analysis type approach is performed to determine the upper and lower worst-case values for the response. Both of these extensions are important parts of the over-all 'Design for Quality' method.

All methods within this thesis require a mathematical model and gradient information of the system response. Graph-Theoretic Models (GTM) were used to model many of the systems since GTM provides many advantages. GTM can develop a system model from component models and connectivity equations, and in addition, easily find the required sensitivity information for design analysis and optimization.