Generally speaking in the Paper Industry we are normally dealing with near-white colors. In that case, we often use the rule of thumb that +/- 0.3 in L*, a* or b* is visually perceptible. However, when we start to look at more saturated colors the question becomes much more difficult.
|L*a*b* color tolerance|
|Color tolerance vs. Visual acceptability|
Obviously, there is a difference here. If we look at the ΔEcmc tolerancing which is based on ellipsoidal tolerances, this does a much better job of matching visual and numerical acceptability. Looking at a particular cross-section of the a* b* space (below), we can see that the visually acceptable ellipses vary in size depending on the position in color space. The ellipses in the orange area of color space are longer and narrower than the broad and rounder in the green area. The shape of the ellipses are larger as the color increases in chroma (away from a*=0, b*=0).
This means that visually acceptable differences in L*, a* and b* differ depending where we are in color space. A Δa*=0.5 would be noticeable on a near-white, but Δa*=5.0 on a red may not be noticeable.
The best advice is to give your customer a series of samples that vary from the target by different amounts. Let them visually analyze the samples and tell you which ones they would accept and which ones they would reject. You can measure all of the samples and help define tolerances based on their feedback. It may also be helpful to keep an archive of samples (over time) that they have rejected. This will help you hone the tolerances based on complaints, returns or rejects.
This same concept can be used for many other measurable quantities as well. Brightness, Gloss, Opacity, Smoothness, Softness, Tensile, Formation, Burst and many more parameters can have tolerances set around them. Giving your customer a say in the matter and then keeping a record of their historical actions can build a strong quality program. Also, it is important to set tolerances that are reasonable. All instrumentation has limits. Setting tolerances is a balance between what the customer sees as objectionable and what the precision and accuracy of the instrumentation.
If you have more questions about this topic, contact me at firstname.lastname@example.org.