each MP can be seen as a dimension) can be even more troublesome when seeking to consider correlated variation patterns and identify useful diagnostic information. \The curse of dimensionality" was term coined by Bellman (1961) referring to the exponen- tial growth of a hypervolume as a function of dimensionality, and is an issue that must be addressed to allow for feasible interpretation of high sample and dimensional optical measurement data of assemblies. Methods that allow for more manageable interpre- tation of such high dimensional data sets would increase the attractiveness of optical measurement technology and enable increasingly detailed levels of process inspection.
Local variation patterns
Optical measurement devices are capable of measuring free form surfaces to unprece- dented levels of detail. Localised variation patterns such as bumps and ripples that can detract from quality perceptions are now readily measurable. It has already been stated that univariate quality measures do not capture the inherent behaviour of geometric covariance in stampings and assemblies, and therefore cannot really describe variation patterns. The ability to measure local variation patterns now presents the additional need to discriminate between variation patterns of different sizes or scales, in order to enhance the ability of manufacturers to measure local assembly variation that can in uence assembly quality. While past research has focused on identifying major (or global) variation patterns in assemblies, new methods that can capture locally occur- ring variation patterns would provide a valuable improvement in quality discrimination and assessment, and make proper use of optical measurement technology.
2.7
Characterising assembly variation
In terms of automotive body assembly, the measurement of deviation and variation forms the backbone of quality assessment: the lower the deviation/variation of an assembly or population of assemblies, the higher the quality of the product. The most common tools used by industry for assessing and monitoring quality are univariate based approaches such as process capability indices and SPC methods, as discussed in the previous section. Through the use of these techniques it is assumed that the quality of an assembly can be measured solely by the mean and standard deviation of a set of (assumedly) statistically independent and normally distributed measurement points. When a customer looks at the dimensional quality of an auto-body panel, it is not a set of SPC charts or process capability indices they see: it is a three dimensional free-form surface with correlated variation patterns such as bows, twists, buckles, and smaller features such as bumps and ripples. Perhaps instead of looking at the standard deviation or process capability of a series of measurement points, manufacturers should
32 CHAPTER 2. BACKGROUND
be looking at whether an assembly has an overall bow or twist, or a buckle on one surface and ripples along another, and most importantly, which correlated variation patterns are more attractive to the end user. If it is correlated variation patterns that a consumer identifies as the determinant of quality, then quality assessment tools must be able to measure and discriminate between such features.
Optical measurement technology has enabled the digital capture of entire surfaces as opposed to a small set of measurement points, therefore allowing the capture of the physical three-dimensional features that customers see on the end product. However, the previous section has identified a number of key limitations of common univariate industry measures of quality that prevent the adequate measure and discrimination of these three-dimensional and highly correlated variation features, which hinders the ability of manufacturers to make decisions that target true quality objectives. For example, the assumptions of statistical independence and normally distributed data make these quality measures incapable of capturing a key characteristic of sheet metal assembly, the correlation between measurement points on a surface, and incapable of representing highly skewed and multi-modal data sets. If model assumptions do not take key behavioural characteristics into account, then judgements based on such models can only be limited. Furthermore, the inability of univariate measures to interpret the additional information provided by optical measurement data, such as dealing with high dimensionality and the characterisation of different scale variation patterns, again limits the ability of manufacturers to assess three-dimensional variation patterns. This inability to adequately measure and assess the physical manifestations of assembly variation that customers see in the end product creates a strong need to develop new quality assessment capabilities. This leads to the key question motivating the work to be presented in this thesis
How can correlated variation patterns in sheet metal assemblies be char- acterised in ways that can enable more advanced levels of dimensional qual- ity assessment and control?
Once dimensional quality can be more adequately assessed, this can then provide improved quality objectives to target with virtual engineering, process diagnosis, and knowledge-based design tools. This thesis progresses through a number of stages in addressing the key research question. Firstly, the sheet metal assembly process and factors that can in uence the quality of assemblies are introduced through an industry case study. Secondly, an aspect of the assembly process that can in uence variation propagation and therefore assembly quality, is investigated and refined according to univariate quality measures. This highlights how sheet metal assembly processes can be refined for a particular quality control target. This leads to the need to define more accurate quality targets and the proposal of two shape characterisation approaches:
2.8. CONCLUSION 33