Wednesday, January 7, 2015

Whaddya mean 68%? I want 95%!

I opened up an individual serving container of yogurt the other day. You know, the kind of yogurt container that gives yuppies a bad name? Not only was it the fancy "Greek" yogurt, but the kind that uses 5.4 ounces of packaging to give you 5.3 ounces of yogurt? Honestly, I only eat it because my wife buys it at the grocery store.

But I didn't mean for this blog to be about me. The contents of the yogurt container reminded me of a blog post that I have been meaning to write. You see, that yogurt container had only 2.6 ounces of yogurt. Yes, it was half full.

Picture of me, ordering a yuppiegurt

Now, I'm a yogurt-container-half-full kinda guy, but if my wife had opened that container, I am sure she would have immediately been on the phone to the customer service department at Chobani. She would wait on hold for an hour just to give them a piece of her mind. Oh... and she would get a bunch of coupons. What did I do? I smiled, shook my head, and said "sampling and manufacturing tolerances!" Yes, I got the short tail of the Gaussian curve when it came to manufacturing tolerances.

--- Now I'm going to change the subject from the stuff in the package to the package itself ---

This all reminded me of a discussion that I had with my good buddy, Steve Smiley. We were talking about one of our favorite topics - ISO 12647-2. Yes, we can be a couple of wild and crazy guys when you get us wound up. A little beer and a little hot Mexican food, and we're quoting stuff like this: 

The variability of the process colour solids in production is restricted by the following condition. For
at least 68 % of the prints, the colour differences between a production copy and the OK print shall not exceed the pertinent variation tolerances specified in Table 7.

(Table 7, you will recall, has a lot of 4 DE and 5 DE stuff in it.)

Steve has taught me to always check the halftone dot structure before partaking

The last time Steve and I chatted, he told me that the brand owners that he consulted with weren't happy with 68% of the product being within a certain tolerance. They want 90% or even 95% within some tolerance. They know that my wife will be inspecting the labels on the Chobani packages. If just one of them is just a slight bit pale in color, they know that they will be sending yet another packet of free coupons to Milwaukee.

Seriously... while my wife is on a first name basis with the customer support people for almost all the consumer product companies, the real reason that the color of a package is so important is that if a package is a bit off color, then people will pick over it in favor of the brightly colored box. Eventually that off-color package is going back to the factory with its handy fold out pouch between its clam shell blister pack. Just like I found out when I tried stand-up comedy at the Baptist's convention, off-color doesn't sell.

I had a simple answer to Steve's question. I'm sure that I didn't articulate it well, since we were on our third bottle of sriracha sauce by then. It was an application of a blog post I did called "Assessing Color Difference Data". The whole point of this blog is that for distributions of color difference data, there is a simple conversion between the 68th percentile and any of the other percentiles. I copy the table from this remarkably insightful blog post:


It's not obvious from the table, but the conversion is pretty simple. If a color tolerance is stated like this: "68% of production shall be within 5 DE of the target color", then you can convert this to a 95% statement with the following calculation:  (5 DE / 1.224) X 1.840 = 7.52 DE. The first part, dividing by 1.224, converts from a 68th percentile to a 50th percentile. The second part, multiplying by 1.840, converts the 50th percentile DE to a 95th percentile. To put it simply... you multiply by 1.5.

So by my careful and erudite analysis, the following two specifications are equivalent:

"68% of production shall be within 5 DE of the target color"
"95% of production shall be within 7.5 DE of the target color"

If a press run meets the first criteria, then it will pretty well meet the second, and vice-versa. Unless of course, the press has decided to not follow the laws of statistics.

I have intentionally left a topic un-discussed: How do you tell what percentage of the press run was in tolerance? I'm gonna save that thrilling question for my next blog post. 


  1. Joun,

    you assume a normal distribution here. I'm pretty sure that a variation in terms of dE during a print run does not show a normal distribution, don't you agree?

  2. You are correct when you say that DE almost never shows a normal distribution.

    I'm sorry for not being clear, but you are incorrect in saying that I assumed a normal distribution. I assumed that DE is distributed according to the distribution that I empirically derived in a previous blog "Assessing Color Difference" which was linked to in the blog above.