# Multivariable Control Chart - Target, Short Run, Group charts, T2, etc.

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#### mclaubee

i'm newbie in <multivariable control chart> can anyone tell me where can get some articles, journals or anythings that can help me to study on this! TQ
ps: happy to be a new member in this forum!

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#### Darius

Mclaubee, welcome to the forum, I hope you enjoy it as I do.

the book

INNOVATIVE CONTROL CHARTING, Practical SPC Solutions for Today's Manufacturing Environment

writen by Stephen A. Wise and Douglas C. Fair. from ASQ Quality press

I don't know is in the net but the tema are

Group
Group Target
Group Short Run

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#### mclaubee

hi Darius, thanks for your reply! i'll try to search the book that you mentioned...but do you have any idea where can i get "multivariable control chart" in the internet??? like some article...website...tutorial...
ps: sorry for the late reply....last saturday was my sister wedding...was a busy day...

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#### Darius

The most of it is about "short run Spc", you can find info in the net.

https://www.asq.org/pub/qmj/past/vol10_issue4/vermani.html

I included an article about the same variable with different targets.

but as I said, it can be Target, Short Run, Group charts (even a a mixture of them ie. Group Short Run).

Why don't explain it more?, your post looks too general to help.

#### Attachments

• l005.pdf
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#### Dave Strouse

Can you tell us more?

mclaubee -

I think we need more info. Are you trying to control chart multiple characteristics of a single part? e.g. lenght and weight of a part.If so, start off with "Advanced Topics in SPC", Wheeler, Chapter 15.
The internet search most likelky to be fruitfull for this is "Hotelling's t squared."
I found this link which might help.
https://www.itl.nist.gov/div898/handbook/pmc/section5/pmc543.htm

Darius is interpreting your need as being to do short run SPC e.g. lenght of part number 123, equivalent lenght of part 456. The references he cites are excellant for that situation if that is your case.

Juran's (as usual) treats both these in the control chart section ( chapter 45 of the 5th ed) , but is pretty skimpy.

PS I won't be able to give practical advice on either as all my experience has been more prosaic. You must have some "kewl" applications as my kids say, if you are considering these exotic types.
Wonder if common Shewhart techniques might do you just as well.
Only one old dog's opinion.

#### Mike S.

##### Happy to be Alive
Trusted Information Resource
mclaubee,

This might help a little...

Hotelling T**2 Chart. When there are multiple related quality characteristics (recorded in several variables), we can produce a simultaneous plot (see example below) for all means based on Hotelling multivariate T**2 statistic (first proposed by Hotelling, 1947).

There is an example of it (an lotsa other neat stuff) here: https://www.statsoft.com/textbook/stathome.html

Lotsa luck!

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#### ben sortin

An Introduction to Multivariate Statistical Analysis, T.W. Anderson, John Wiley & Sons, 1984.

Introduction to Statistical Quality Control, Douglas C. Montgomery, John Wiley & Sons, 1985.

There are articles of interest in old Technometrics Journals as well.

Got sphericity test?

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#### mclaubee

hai,

i think this is the only word i can say: "thanks!" . when i check on the forums in this morning i felt like i'm not alone....i tried to search in the net and here i got something to share...i think i can get what i want as a beginner...

https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc34.htm

so, check it out!

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#### mclaubee

helo,

i got something again ! try this....

https://www.sys.virginia.edu/mqc/index2.html

i can get some info about the multivariate control chart like...Hotelling's T squared, MEWMA, MCUSUM.....so, checkitout

but i still need to find some journal n thesis on that topic...i'll keep trying...

mclaubee

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#### Darius

from https://www.sematech.org

Increased application of Hotelling T sq and its use within manufacturing warrant examination of violations of basic statistics assumptions. Over 80 percent of industrial processes violate these assumptions. Hotelling T sq assumes normally distributed and independently sampled data. Process control decisions on defect detection, adjustment of manufacturing processes, or on modifications to manufacturing equipment, are all subject to expensive mistakes if supporting statistical methods are applied invalidly. This paper discusses assumptions violations and techniques to prepare manufacturing data for valid application of Hotelling T sq, and additionally for principal components analysis, which is often used in conjunction with Hotelling T sq. Violation conditions, effects and remedies are tested and illustrated.

And Wheeler on Advanced Topics in Statistical Process Control said
while the T2 Chart is more complete and more mathematically rigouros than Dp Chart, it only works for a narrow set of conditions, and it is virtually impossible to ever verify if there conditions are completely satisfied.

So don't just use the math, be carefull.