In the previously attached article by Kotz and Johnson, they stated "Unfortunately, mistrust of PCIs, and especially of their estimators, when based on the meager data often available at factory level, is still not uncommon. Resistance to accompanying a single estimated PCI value by an estimate of its variability (be it confidence interval, standard deviation, or whatever) is still very pronounced, even though accepted statistics, such as sample mean and standard deviation, perform essentially the same function."
Guess what...we still mistrust them for precisely the reason you state: "the meager data often available at factory level". This is especially true when the index is calculated on a 300 pc capability run is expected to represent future variation with other raw materials, operators, etc. - variation not captured by the study. This is the assumption one would make to "approve" such a process based on the Cpk. No number of triple integrals can resolve that problem, gentlemen. The struggle between the academics and the practitioners rages on...
I was amused by the statement: "However, there seems to be, in some quarters, an assumption that the measured characteristic should have a normal distribution (at least, approximately), although it is difficult to see why a good industrial process must result in a normal distribution for every measured characteristic." (My bold emphasis) So true....so true...
Another good point: We finally quote from the Editorial (Nelson (1992)) in the issue of JQT devoted to PCIs: “in fact, it is clear from a statistical perspective that the concept of attempting to characterize a process with a single number is fundamentally flawed.” See
also Herman (1989). This is, of course, equally valid for any summarizing statistical measure used without any qualms. Nevertheless, the statement that “process capability indices are here to stay” (Kotz and Lovelace (1998, page 16)) appears, fortunately or unfortunately, to also be true."
I agree - this fundamentally flawed notion is here to stay...for now. I must admit - this is the first time I have read this article, but I have arrived at the same conclusion as Nelson.
Guess what...we still mistrust them for precisely the reason you state: "the meager data often available at factory level". This is especially true when the index is calculated on a 300 pc capability run is expected to represent future variation with other raw materials, operators, etc. - variation not captured by the study. This is the assumption one would make to "approve" such a process based on the Cpk. No number of triple integrals can resolve that problem, gentlemen. The struggle between the academics and the practitioners rages on...
I was amused by the statement: "However, there seems to be, in some quarters, an assumption that the measured characteristic should have a normal distribution (at least, approximately), although it is difficult to see why a good industrial process must result in a normal distribution for every measured characteristic." (My bold emphasis) So true....so true...
Another good point: We finally quote from the Editorial (Nelson (1992)) in the issue of JQT devoted to PCIs: “in fact, it is clear from a statistical perspective that the concept of attempting to characterize a process with a single number is fundamentally flawed.” See
also Herman (1989). This is, of course, equally valid for any summarizing statistical measure used without any qualms. Nevertheless, the statement that “process capability indices are here to stay” (Kotz and Lovelace (1998, page 16)) appears, fortunately or unfortunately, to also be true."
I agree - this fundamentally flawed notion is here to stay...for now. I must admit - this is the first time I have read this article, but I have arrived at the same conclusion as Nelson.
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