Risk-based multivariate control chart

• A new Risk-Based control chart is designed that minimizes the number of type II error.
• This chart can handle multivariate case and takes the measurement uncertainty into account.
• The total cost of decision can be decreased applying the RBT2 chart.

Control charts are widely used tools in statistical process control (SPC). Most of the control charts operates on reliability base, so the users assume that the value of the real product characteristic is equal to the value derived from the measurement. It is a frequent case that the conformity of a product is determined by more than one product characteristics. It is recommended to apply multivariate control charts for the control of multiple product characteristics, but the measurement uncertainty can lead to incorrect decisions even in univariate case. In this study, the authors develop a risk-based multi-dimensional T2 chart (RBT2), which takes the consequences of the decisions into account and reduces the risks during the process control. The proposed method can be applied even for non-normally distributed data. Several sensitivity analyses are provided and the performance of the RBT2 chart is demonstrated when Six Sigma regulations are fulfilled.