The color difference (DE) has long been used as a metric for acceptance tolerances. Indeed, much of the impetus for developing better color difference formulas has been this very practical industrial problem. Tolerances objectively quantify the customer's requirements, in this case, for color fidelity. As such, a metric that quantifies our perception of color difference (for example, DE00) is appropriate for customer tolerances.
It should come as no surprise that practitioners of statistical process control (SPC) have generally used color difference as a key metric whereby they benchmark their process. The cornerstone of SPC is to quantify the normal variation of the process to identify when the process starts to behave aberrantly. But, for reasons that are almost universally under-appreciated, the DE color difference is inappropriate for SPC.
The first part of the paper reviews deficiencies of the DE color difference for SPC.
The second part of the paper introduces ellipsification as a means to quantify a cloud of data points in color space. This is described graphically as fitting a three-dimensional ellipsoid to a set of data points. Mathematically, ellipsification is a generalization of the standard deviation to multiple dimensions, in this case, three.
The concept of the Z score is generalized to a three-dimensional metric, which is called Zc ("Z score for color") in the fourth part of this paper. If the original data is "three-dimensionally normal", then the Zc score will be chi distributed with three degrees of freedom.
Finally, these concepts are demonstrated on real world color data. It is seen that data sets from processes that are in good control will closely follow the theoretical distribution, and conversely, data sets from processes that are not in good control will not closely follow the theoretical distribution.
Further related methods are described including a metric to assess whether a process is in control, and metric to compare the variation in color of one process to another, and a way to estimate percentiles of color difference data.