Normal distribution of manifacturing processes
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 This topic has 8 replies, 4 voices, and was last updated 17 years, 7 months ago by Peppe.

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February 17, 2005 at 12:09 pm #38455
Hi All, reading a russian book on probability theory dated 1983 and used in university, I’ve read as follow “… normal distribution was widely considered as universal for manufacturing processes application (SPC I think she refer), but the actual experience (1983) show that for manufacturing and measurement there are different distributions (not reported what) than normal, that describe better the processes ….”
What impressed me have been the use of “..was widely considered..” talking in the 1983 as a past think about normal distribution in Mfg, while still now we know SPC and SS are widely based on normal distribution.
What do you think about ? Have someone already heard about it ?
Rgs, Peppe0February 17, 2005 at 3:12 pm #115019I’ve heard similar accounts and the argumets for & against “assuming” normality. I guess my biggest insight was that of Shewhart/Deming/Wheeler, which was really explained very well in Wheeler’s Understanding Statistical Process Control. In chapter 4, he shows pretty definitively that the use of control charts will work well regardless of the “true” distribution. Consider that Shewhart had formulated these charts back in the 20’s, whether he knew their full potential or not!
0February 17, 2005 at 3:38 pm #115021
HarkanwalParticipant@Harkanwal Include @Harkanwal in your post and this person will
be notified via email.While the control chart constants were created under the assumption of normally distributed data, the control chart technique is essentially insensitive to this assumption. This insensitivity is what makes the control chart robust enough to work in the real world as a procedure for inductive inference. The data don’t have to be normally distributed before you can place them on a control chart. The computations are essentially unaffected by the degree of normality of the data. Just because the data display a reasonable degree of statistical control, doesn’t mean that they will follow a normal distribution. The normality of the data is neither a prerequisite nor a consequence of statistical control.
0February 17, 2005 at 3:47 pm #115022Peppe,
Most of the processes I’ve worked on are multivariate in nature … they could not be described as ‘normal’ – perhaps multinormal – but certainly not normal, and the use of Shewhart Charts for such distributions is inappropriate.
Then there is the question of autocorrelation – a real process without autocorrelation would be a strange process indeed!
Metrology on the other hand satisfies the conditions of random independence – well in theory anyway!
Cheers,
Andy0February 17, 2005 at 4:08 pm #115027Andy,
Do you monitor your multiple streams using a Hotelling’s T^2???
And if you detect an out of control situation, do you have to revert to a traditional Shewhart chart to determine which stream is causing the issue?0February 17, 2005 at 5:27 pm #115033S,
I believe it depends on the process … sometimes streams are independent, sometimes they’re not.
My preference would be to use a Multivari chart to find sources of varation. If there is any evidence of temporal instability, then I would resort to a Shewhart Chart.
Of course these days it is relatively simple to plot all kinds of charts using software – Minitab provides both a Hotelling’s test for the multivariate mean (weight of evidence) and a test of ‘outliers’ (good or bad) using the Mahalanobis distance.
The important question is whether or not it is correct to report a multivarite process as ‘outofcontrol’ on the basis of a Shewhart Chart. Clearly, it isn’t for a multivariate process and the reason is that real processes do not always satisfy the statistical assumptions inherent in a test.
Regards,
Andy
Andy
0February 18, 2005 at 9:32 am #115073Thanks to All for your answers, just last question, maybe due to my ignorance on control charts. The way to evaluate the out of control on “standards” control chart (not multivariate or similar), isn’t related to distribution you have take in account building the charts ?
Rgs, Peppe0February 18, 2005 at 10:22 am #115076Peppe,
I’m not sure I understand your question correctly or not … but my understanding is that ‘standard’ Shewhart Charts are reasonable robust against any nonnormal distribution; except where there is significant covariance between elements of a subgroup, or where there is significant autocorrelation from run to run. (Since the latter is a property of most processes, it does raise important questions about some of the assumptions of SPC.)
It is easy to check if you have a copy of Minitab. I no longer have a copy, but I used to demonstrate this principle using a truncated distribution – a top hat function. Now compare this to a normal distribution having duplicate normal data – a kind of truncated normal distribution that sits on top of a top hat function. If you calculate control limits for these distributions, where there is signifcant covariance or autocorrelation, control limits are too tight, and many ‘false alarms’ are detectable.
This raises general issues about processing … if real processes can have some autocorrelation, ignoring covariance, then is it correct to assume a process should conform to the ‘model’ of a normal distribution. I think not .. and one cannot assert whether or not a process in ‘incontrol’ or outofcontrol, on the basis of SPC. All one can conclude is that a Shewhart chart has detected inhomogeneity, whether it is true or not is a question for process engineering.
Therefore, the assumption that a process should conform to a normal distribution is a ‘theory of forms’ and based in rationalism and not in empiricism.
Cheers,
Andy0February 18, 2005 at 10:52 am #115079Andy, thanks for the answers, your explanation, togheter others, is what I was looking for, maybe asking in incorrect way.
Rgs, Peppe
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