# Industry Std Values Of Sigma for calculating UCL,LCL

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• #28492

Uma MB
Member

I read in some document that the constant sigma values used for calculating UCL, LCL are industry standards. Could the details given below be confirmed please ? And where can I find in print more on these industry std values ?
N=3, MEAN = 4.10,  STDEV=0.14,  UCL=4.51,  LCL=3.69
N is the number of data points considered for a period of 3 months
MEAN is AVERAGE of 3 data points
STDEV has been derived using STDEVP function of MS-Excel
UCL is MEAN + (0.3 * STDEV)
LCL is MEAN – (0.3 * STDEV)
STDEV < 25% of MEAN, then 3 Sigma is used for working out UCL, LCL.
STDEV > 25 % of MEAN but < 50 % of MEAN, 1 sigma is used
STDEV > 50 % of MEAN, then 5 Sigma is used.
Are the above three statements correct (said to be industry standards) ?
Thanks much in advance.
Uma MB

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#71082

James C. Bailey,Jr.
Participant

You are confusing upper(USL) and lower (LSL)specification limits,which are provided by the customer, and process control limits,which are provided by the actual process,i.e., the Voice of the Process. In your example, you specify the number of data points,process mean ,and process standard deviation. If you plot this data in a control chart,you can check if the process is in control by specifying the upper and lower control limits (not customer USL and LSL). Typically,control chart limits are =/- 3 standard deviations,which will include 99.73% of your data if it is normally distributed.The ” Basic Statsistics” book by Kiemele,Schmidt,and Berdine explains this very well in chapter 9,Fourth edition.

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#71086

Mikel
Member

I hope that the advice reflected here did not come from a Six Sigma person. Go read any Shewhart info in any credible SPC book — Wheeler, Grant and Leavenworth, ….

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#71090

Dave Strouse
Participant

Uma –
In answer to your basic question, NO;  these are not correct.
Can you shed some light on where you found such drivel? What industry is supposedly using this information?
Not only are the limits incorrect, but the standard deviation used to compute correct control limits is NOT the standard deviation found in Excel.. An average dispersion statistic as derived from range or standard deviation or moving range AND as modified by Shewhart’s contol factors are the only way to formulate limits.
Please, as another poster suggested, check into correct SPC usage. I would recommend Wheeler over Grant and Leavenworth or just about anyone else for a starting point.
By the way, did you misprint the factor sizes?. You have 3 sigma limits for lowest numeric sd, 1 for middle ranges and 5 for highest. For at least logical consistency should that not be 1,3,5? It’s wrong either way, but would at least be consistent.

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#71097

A. Smith
Participant

I am by no means an expert…. not even close.  But from some training many years ago, and memory is the first to go they say,  the numbers are very close to being correct, may not be stated the correct way, but I believe they are correct.  UCL and LCL that achieves 99.97 % product under the bell cure is the mean  + / – (3*STD).
.14 x 3 = .42
mean 4.10 + .42 = 4.52 UCL
mean 4.10 – .42 = 3.68 LCL
So has the memory gone??
Al

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#71167

Uma MB
Member

Dave,
“By the way, did you misprint the factor sizes?. You have 3 sigma limits for lowest numeric sd, 1 for middle ranges and 5 for highest. For at least logical consistency should that not be 1,3,5? It’s wrong either way, but would at least be consistent. “
That is exactly how it was found in the document from where this example was picked up (and I wanted to print it as it was but forgot to make a remark about this inconsistency) and that is what got me suspicious of this whole calculation and made me post the whole stuff on this forum. I completely agree that at least for logical consistency it should be 1,3,5.
Thank you for the response.

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#71171

Dave Strouse
Participant

Uma –
This ius very interesting to me. Could you share what document you got this out of. Is it an internal one? If so, whoever wrote it should be retrained. If it is from some other source, could it be some esoteric application?
If it is meant to be control chart guidelines, then it is not,nil,nada, negatory correct for Shewhart type charts (or any other I’m aware of). This kind of false information is dangerous to effective control.
Using the SDEVP function out of Excel will give you limits that will almost never be exceeded, even when large shifts and excursions  in the process have occurred.  That is, it will be insensative to the very thing you should be trying to detect. That function gives the standard deviation of the INDIVIDUAL values. This will enclose 99.76%, assuming normality, of the individual readings. But, we are grouping data. So we will contain within limits calculated this way much more than 99.76% of the GROUPS. That is why it is incorrect. Technically we can say we have decreased the ALPHA risk to such a small value and inflated the BETA so greatly that it is not economic to control the process.
Dr. Shewhart derived  the best way to estimate standard deviations for this purpose and settled on +/- 3 sigma (as properly calculated) control limits as the economic way to balance the alpha and beta risks associated with any process. In the almost 75 years since, no better way has been demonstrated.
If you are truely interested I strongly recommend Dr. Don Wheelers book “Understanding Statistical Process Control” as your first step.
Please do let us know where the information came from and I commend you are seeking to find correct methods.

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#71200

pise
Participant

uma,
what you’ve brought up is interesting as people trying to determine the ucl/lcl sometimes end up with seemingly meaningless (read as impossible to implement) results. these so called industry standards you mention would certainly solve the problem i ‘m faced with. i am ceratinly wishing that these industry standards are true.
what exactly was your source of the information? please tell us.

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