An integrated approach for multivariate statistical process control using Mahalanobis-Taguchi System and Andrews function

The purpose of this paper is to develop a new easy-to-implement distribution-free integrated multivariate statistical process control (MSPC) approach with an ability to recognize out-of-control points, identify the key influential variable for the out-of-control state, and determine necessary changes to achieve the state of statistical control.

The proposed approach integrates the control chart technique, the Mahalanobis-Taguchi System concept, the Andrews function plot, and nonlinear optimization for multivariate process control. Mahalanobis distance, Taguchi’s orthogonal array, and the main effect plot concept are used to identify the key influential variable responsible for the out-of-control situation. The Andrews function plot and nonlinear optimization help to identify direction and necessary correction to regain the state of statistical control. Finally, two different real life case studies illustrate the suitability of the approach.

The case studies illustrate the potential of the proposed integrated multivariate process control approach for easy implementation in varied manufacturing and process industries. In addition, the case studies also reveal that the multivariate out-of-control state is primarily contributed by a single influential variable.

The approach is limited to the situation in which a single influential variable contributes to out-of-control situation. The number and type of cases used are also limited and thus generalization may not be debated. Further research is necessary with varied case situations to refine the approach and prove its extensive applicability.

The proposed approach does not require multivariate normality assumption and thus provides greater flexibility for the industry practitioners. The approach is also easy to implement and requires minimal programming effort. A simple application Microsoft Excel is suitable for online implementation of this approach.

The key steps of the MSPC approach are identifying the out-of-control point, diagnosing the out-of-control point, identifying the “influential” variable responsible for the out-of-control state, and determining the necessary direction and the amount of adjustment required to achieve the state of control. Most of the approaches reported in open literature are focused only until identifying influencing variable, with many restrictive assumptions. This paper addresses all key steps in a single integrated distribution-free approach, which is easy to implement in real time.