Using principal component analysis in process performance for multivariate data

Quality measures can be used to evaluate a process's performance. Analyzing related quality characteristics such as weight, width and height can be combined using multivariate statistical techniques. Recently, multivariate capability indices have been developed to assess the process capability of a product with multiple quality characteristics. This approach assumes multivariate normal distribution. However, obtaining these distributions can be a complicated task, making it difficult to derive the needed confidence intervals. Therefore, there is a need to develop one robust method to deal with the process performance on non-multivariate normal data. Principal component analysis (PCA) can transform the high-dimensional problems into lower dimensional problems and provide sufficient information. This method is particularly useful in analyzing large sets of correlated data. Also, the application of PCA does not require multivariate normal assumption. In this study, several capability indices are proposed to summarize the process performance using PCA. Also, the corresponding confidence intervals are derived. Real-world case studies will illustrate the value and power of this methodology.