Monitoring complex industrial process variability: A necessary and sufficient Shewhart-type control chart
Maman A. Djauhari
Centre for Research in Statistics and Data Analysis
Tjahaja Bina Statistika Indonesia, Ltd. P. (Commanditaire Vennootschap)
In the current practice of complex process variability monitoring, the most adopted control chart is lacking of sufficiency. It is only a necessary control chart (N-chart). Thus, this chart might be misleading. This paper is to overcome this problem. For this purpose, a statistic that leads to a necessary and sufficient control chart (NS-chart) is introduced. To make it practical, its limiting distributional behavior is investigated and to illustrate its advantages, an industrial example is presented.
Keywords: Commutation matrix; Mahalanobis distance; multivariate dispersion; multivariate statistical process control; vec operator.