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 Acceptance Criteria for Numerical Color and Color-Difference Decisions visitors=

Background
I wrote this in reply to a posting on the ASQ forum. I am a retiree of 3M Company and now have my own company that provides software for developing acceptance sampling plans.

Coordinate System
I have done a lot of work using L,a,b and x,y,z,x' color space. I prefer acceptance criteria that are not only within perception-related requirement like deltaE<=1, but that is additionally based on product/measurement capability.

Acceptance Criterion
I think the acceptance criterion of DeltaE<=1 may be a wider interval than it has to be if you would base it on capability. In my experience, DeltaE has had a within-lot standard deviation close to 0.065 deltaE units. If this is the case with your product/measurement system, then you can measure much more precisely than you can see! (Using DeltaE=1 as a definition of visible difference.)

Acceptable Mean of Delta-E
The acceptance criterion would be the acceptance limit of a sampling plan for the mean of deltaE having an acceptable mean (AQL) of 0.065*3=.195 deltaE units. (Of course you would use a value for the within-lot standard deviation derived from your specific materials and instruments.)

Rejectable Mean and Sampling Risks
Then you would choose a rejectable mean (RQL) a little larger than AQL=.195, maybe 1.5 standard deviations above AQL, chosen such that the sample size is fairly small. I would set the sampling risks to alpha=0.05 and beta=0.05.

Absolute Color
The same method can be applied to L, a, and b individually, which works well if you use the separate within-lot standard deviations of L, a, and b.

Sequential Sampling Plan and Range Test
I have found sequential sampling plans for the mean to be very efficient and practical with color applications, with a minimum n of 2 so that outliers can be detected with a range test.