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Acceptance Criteria for Numerical Color and Color-Difference Decisions

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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.

Additional Information
If you are interested in seeing information on software that have developed for designing this type of plan, and further explanation of the methodology, just send me your fax number by email and I will fax you a 4 page description. Or, send a mailing address.

In summary, I would use acceptance criteria related to process/measurement capability rather than perception-related numbers like 1.0 or 0.5. The suggested methodology is statistically based.

Stan Hilliard

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