Conformability Analysis dimensional variability

The measures of dimensional variability from Conformability Analysis (CA) (as described in Chapters 2 and 3), specifically the Component Manufacturing Variability Risk, q, is useful in the allocation of tolerances and subsequent analysis of their distributions in probabilistic design. The value is determined from process capability maps for the manufacturing process and knowledge of the component s material and geometry compatibility with the process. In the specific case to the th component bilateral tolerance, it was shown in Chapter 3 that the standard deviation estimates were ... 

The dimensionality of a data set is the number of variables that are used to describe eac object. For example, a conformation of a cyclohexane ring might be described in terms c the six torsion angles in the ring. However, it is often found that there are significai correlations between these variables. Under such circumstances, a cluster analysis is ofte facilitated by reducing the dimensionality of a data set to eliminate these correlation Principal components analysis (PCA) is a commonly used method for reducing the dimensior ality of a data set. 

Information on those features of the three-dimensional structure of a molecule (small or large) that are important with respect to their chemical or biochemical reactivities can often be obtained by comparisons of analogous molecular geometries in various different crystal structures. Effective techniques for comparing three-dimensional structures are therefore crucial to these types of analyses. If the structure of, for example, the citrate ion is compared as it occurs in several different crystal structures, some measure will be obtained of the possible conformational variability of this ion, as shown in Figure 16.1. Each such conformation determined from a crystal structure analysis represents a low-energy form of the ion. 

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