tag:blogger.com,1999:blog-1840985738235902482.post3346114263557066884..comments2018-05-25T02:05:24.013-05:00Comments on John the Math Guy: Statistical process control of color difference data, part 2John Seymourhttps://plus.google.com/107565394741171719003noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-1840985738235902482.post-21161632183864622142016-11-04T13:14:18.993-05:002016-11-04T13:14:18.993-05:00Thank you for the clarification, Steve. You are co...Thank you for the clarification, Steve. You are correct that it is not deltaE which is chi-squared, but rather deltaE squared. A very smart guy once wrote that another very smart guy told him the the equivalent distribution for deltaE would be the Rayleigh distribution. If I recall correctly, the first smart guy is someone you have lunch with every single day that you have lunch. And the second smart guy is Ed Granger.<br /><br />As for the unrealistic assumptions, that is the main topid for the next blog post in this series.John Seymourhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-42405554993731688712016-11-03T17:59:53.358-05:002016-11-03T17:59:53.358-05:00Not chi-squared, but chi. Under several unrealisti...Not chi-squared, but chi. Under several unrealistic assumptions, such as L*, a*, and b* being identically, independently, normally distributed. The assumption of zero mean also is made to obtain the chi distribution with three degrees of freedom, but this is less unrealistic for a process operating close to its aim.Steve Viggianohttp://acolyte-color.comnoreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-29605230961331377102016-11-02T18:14:40.033-05:002016-11-02T18:14:40.033-05:00I am guessing that income distribution has much lo...I am guessing that income distribution has much longer tails that deltaE data. Typically, the 99th percentile of deltaE is a little more than twice the size of the median.<br /><br />Are you using the Dagum distribution for deltaE data, or for income data?John Seymourhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-18529011031209350832016-11-02T10:51:34.120-05:002016-11-02T10:51:34.120-05:00John, I'm using Dagum I. It fits well in most ...John, I'm using Dagum I. It fits well in most cases. Just asking what have an income distribution to do with delta E.<br />Are the high delta E as rare as high income?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-13036741852403131642016-11-02T10:12:27.194-05:002016-11-02T10:12:27.194-05:00You might be interested in this post from the exce...You might be interested in this post from the excellent 'SPC for Excel' site:<br />https://www.spcforexcel.com/knowledge/basic-statistics/deciding-which-distribution-fits-your-data-best<br />Chris Lynnhttp://www.hillamtech.comnoreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-61892597549266897482016-11-01T09:44:45.516-05:002016-11-01T09:44:45.516-05:00Brian, thanks for sharing the article. I had not s...Brian, thanks for sharing the article. I had not seen it before.<br /><br />Anonymous, printing certainly has its idiosyncrasies. Certainly some of this shows up in the data I have above. And I will admit that most of the data sets that I have examined are from print.<br /><br />But, I think the upcoming installments will show that there is an idiosyncrasy with color difference data that is fundamental and based on the underlying math. John Seymourhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-58002449176531663912016-11-01T07:39:50.073-05:002016-11-01T07:39:50.073-05:00There is also a nice 2011 CR&A article from Na...There is also a nice 2011 CR&A article from Nadal, Miller and Fairman discussing "Statistical Methods for Analyzing Color Difference Distributions."Brian Gammhttps://www.blogger.com/profile/06823378511434642178noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-45724837409202768652016-11-01T06:47:57.435-05:002016-11-01T06:47:57.435-05:00Nice articles! I'm wondering if the distributi...Nice articles! I'm wondering if the distributions you are observing are related only to it being color difference data or if it also has something to do with the printing process. What happens if you apply this logic to camera capture process control such as you see with FADGI and Metamorfoze.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-71592786912465876252016-10-29T10:03:13.477-05:002016-10-29T10:03:13.477-05:00Max, here is a teaser from my next part of this se...Max, here is a teaser from my next part of this series:<br />"For a true normal distribution, there is always a chance - perhaps an incredibly tiny chance - that the values could be negative. But color difference data never goes negative."<br /><br />As for your chi-squared conjecture, I can't quote from it, since I haven't written about it yet! But I intend to mention papers from Fred Dolezelak, David MacDowell, and Steve Viggiano about deltaE and chi-squared.John Seymourhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-40011138175935248402016-10-28T15:11:13.826-05:002016-10-28T15:11:13.826-05:00You cannot get normal distrubtion because DeltaE&#...You cannot get normal distrubtion because DeltaE's cannot be negative. Isn't this a Chi-squared distribution?Max Derhakhttps://www.blogger.com/profile/13411859960497744293noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-28864833804038305792016-10-27T08:11:48.843-05:002016-10-27T08:11:48.843-05:00Interesting.Interesting.Dr Narendra Gangakhedkarhttps://www.blogger.com/profile/18063577169444093481noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-50886895055796032322016-10-26T08:39:24.545-05:002016-10-26T08:39:24.545-05:00Stay tuned for the next in the series, Dave! I wil...Stay tuned for the next in the series, Dave! I will, indeed, look at the individual distributions for L*, for a*, and for b*.John Seymourhttps://www.blogger.com/profile/11350487038873935295noreply@blogger.comtag:blogger.com,1999:blog-1840985738235902482.post-56106791481113343832016-10-25T11:54:27.597-05:002016-10-25T11:54:27.597-05:00It would be interesting to see plots of the compon...It would be interesting to see plots of the component differences for this dataset. Conventional wisdom says they will be normally distributed. If that is so, what might you do with this feature? Dealing with multivariate process control specifications is a pain, but folks do it.Dave Wyblehttps://www.blogger.com/profile/09623357167770566661noreply@blogger.com