The Use of Principal Components Analysis in the Assessment of Process Capability Indices

1. Introduction Process capability indices are measures of the capability of a process to produce according to some assigned specifications related to some characteristics of the items produced. In most of the cases it is assumed that the studied process is described through only one characteristic. However, sometimes the need arises for measuring the capability of processes described through two or more characteristics. For such multivariate processes, some indices have been introduced in the literature based on the multivariate joint distribution of the characteristics of the process. Among the suggested approaches for measuring the capability of multivariate processes one may note those by Chan et al. Extensive reviews of the above mentioned and some other proposals for capability indices for multivariate processes are provided by Kotz and Johnson This paper considers the use of principal components analysis in measuring the capability of a multivariate process. The use of this multivariate technique in connection with process capability assessment problems is an issue initially examined by Wang and Chen (1998-1999). The benefit of using this method, is that in some cases, it may simplify substantially the analysis of a very complex multivariate data set, by reducing its dimensionality. The idea is that, if some of the first principal components explain a large percentage of the total variability, the assessment of the capability of the process can be based on them as one does not loose much information by omitting the remaining principal components. In the sequel, some alternative ways of implementing this technique are proposed through the definition