The Elsmar Cove Business Systems and Standards Discussion Forums Individual x Chart - Why use the equation is barX+2.66 bar(MR)
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# Individual x Chart - Why use the equation is barX+2.66 bar(MR)

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Post Number #1
14th January 2010, 04:17 AM
 klluk Total Posts: 3
Individual x Chart - Why use the equation is barX+2.66 bar(MR)

we plotted individual x chart but my boss is asking the UCL=barX+3sigma, how comes the equation is barX+2.66 bar(MR) is used? Is it related to the variation, pls help to explain

Post Number #2
14th January 2010, 04:54 AM
 reynald Total Posts: 274
Re: individual x chart

well a simply reply to him would be:
3*sigma is a measure of the population variation, but it is an unknown quantity which can only be estimated by sampling. For this case we used moving range, which needs a correction factor for a more accurate estimate.
Thus, 2.66.
Post Number #3
14th January 2010, 10:30 AM
 Darius Total Posts: 551
Re: Individual x Chart - Why use the equation is barX+2.66 bar(MR)

Quote:
 In Reply to Parent Post by klluk we plotted individual x chart but my boss is asking the UCL=barX+3sigma, how comes the equation is barX+2.66 bar(MR) is used? Is it related to the variation, pls help to explain
sigma = MR/d2
d2(2) = 1.128

UCL=barX+3sigma = barX+3* MR /d2 = barX+3/d2 MR = barX+2.66 MR

d2 table was built to determine the economical control limits by Shewhart in the 20's .. 30's working for Bell labs.
Post Number #4
14th January 2010, 12:00 PM
 pagnonig Total Posts: 79
Re: Individual x Chart - Why use the equation is barX+2.66 bar(MR)

As Dr. Wheeler explained very nicely in his books, sigma is a global measure of dispersion which does not take into account the time behaviour of the data and its "between subgroup" variation, even if we are talking about subgroups of 1 in individual charts.

2.66 * MR consider the data MR and therefore is dependent upon data time distribution.
This is the reason why, if you use limits caluclated with 3sigma, you run the risk to catch the wrong signals (or miss the right ones) coming for your process.

Ciao!

Giuseppe
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 (Article).Wh_Use individual values to compute control limits.pdf (80.9 KB, 504 views)
Post Number #5
14th January 2010, 02:01 PM
 bobdoering Total Posts: 4,031
Re: Individual x Chart - Why use the equation is barX+2.66 bar(MR)

Quote:
I like the conclusion of his article:

"Many articles in technical journals and many software packages in use today
actually use the wrong methods. As to why this is the case, I can only assume it is because novices have been teaching neophytes for so many years that the teaching of SPC is out of control."

Another point on which I agree with Dr. Wheeler. I see it all the time in precision machining.
 Thanks to bobdoering for your informative Post and/or Attachment!
Post Number #6
15th January 2010, 02:00 PM
 Bev D Total Posts: 3,472
Re: Individual x Chart - Why use the equation is barX+2.66 bar(MR)

oooh darn! I wanted to point out that quote!!

It still astonishes me that something as statistically simple as SPC is still not universally correctly taught. No wonder Deming was a cranky cuss in his classes...
Post Number #7
15th January 2010, 02:39 PM
 bobdoering Total Posts: 4,031
Re: Individual x Chart - Why use the equation is barX+2.66 bar(MR)

Quote:
 In Reply to Parent Post by Bev D It still astonishes me that something as statistically simple as SPC is still not universally correctly taught. No wonder Deming was a cranky cuss in his classes...
It's the part about having to "think" and not just rubber stamp charts that makes it so hard for people - especially when they have been trained to rubber stamp.

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