Control Chart Rules - Trend and Statistics Explainations

[YKT]

This may sound sily to some, but probably some of the statistic gurus might be able to help me out in explaining the control chart rules....

What is the statistic explaination for the following ?

1. Why must be 7 consecutive points that continue to increase is consider a trend ? Why not less than it ?

2. Same goes for runs...why 7 points on one side is consider a run ? or 10 out of 11 points on one side of the center line consider a run ?

Anyone care to explain on the statistical explaination ?


Many thanks

 

[M Greenaway]

All to do with probability.

A process running in control should be randomly distibuted around the mean value. It is highly improbable that a run that shows seven points above or below the mean is a random distribution around that mean.

So in a nutshell - probability.

 

[Atul Khandekar]

It is probability. Check NIST handbook http://www.itl.nist.gov/div898/handbook/pmc/section3/pmc32.htm
for Western Electric rules.

 

[D.Scott]

Hi YKT - welcome

Think of flipping a coin. it has a chance of landing either heads or tails. For every flip the posibility is 1 in 2 (1/2) that it will land heads. If you flip it once and it is heads, the chance of it happening on the next flip is still 1 in 2 (1/2).
Here's the catch - what is the chance it will be heads 2 times in a row? to find out you multiply the chance of the first time by the chance of the second time or 1/2 X 1/2 = 1/4. Therefore you can see the chance of 2 in a row is 1 out of 4 times. For 3 times in a row you do the same thing 1/2 X 1/2 X 1/2 = 1/8. So 3 in a row is likely to happen only 1 in 8 attempts. The higher the number of recurrances, the less likely it becomes statistically.
Now think of your control chart - above the center line is "heads" and below the center line is "tails". To get 7 in a row above the line would be 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 X 1/2 = 1/128. You can see it is highly unlikely for this to happen UNLESS SOMETHING HAS CHANGED. When you see the condition it should signal to you that "Something doesn't look right" and you can investigate the process to find what has changed.
The same principle applies to trends of up and down. Think of up as heads and down as tails. Trends can be indicated with fewer than 7 points and depending on how robust your process were and how dependable the data you may look for indicators as low as 5 in a row.

Hope this helps a little

Dave

 

[Atul Khandekar]

. Trends can be indicated with fewer than 7 points and depending on how robust your process were and how dependable the data you may look for indicators as low as 5 in a row.

I have read somewhere (I'll have to dig up that reference-don't have it at hand right now) that the rule of 7 points ascending/descending should be discontinued as it tends to increase the rate of false alarm.

 

[Darius]

Atul you posted the article in Precontrol ( 22nd December 2002)
http://Elsmar.com/Forums/showthread.php?s=&threadid=5156&pagenumber=2

http://www.asq.org/pub/jqt/past/vol32_issue4/qtec-341.pdf

I am agree that 7 points going up or down are almost imposible to happen, because of the natural noise of the variable, the measurement error, etc, the case that is likely to happen is in a continuos process (like taking samples in a chemical batch, where a chemical reaction is happening), but in this case is what is expected to happen (no special events), so I am agree with you, 7 points should be discontinued as it tends to increase the rate of false alarm.

Darius

:thedeal:

 

[Atul Khandekar]

Yes, that's the one Darius, thank you!

 

[KidPaddy]

Paddy,

What are the calculations ( formulas, constants ) for a single sample size of X bar & R? Help anyone?

 

[roland_lu]

Atul you posted the article in Precontrol ( 22nd December 2002)
http://Elsmar.com/Forums/showthread.php?s=&threadid=5156&pagenumber=2

http://www.asq.org/pub/jqt/past/vol32_issue4/qtec-341.pdf

I am agree that 7 points going up or down are almost imposible to happen, because of the natural noise of the variable, the measurement error, etc, the case that is likely to happen is in a continuos process (like taking samples in a chemical batch, where a chemical reaction is happening), but in this case is what is expected to happen (no special events), so I am agree with you, 7 points should be discontinued as it tends to increase the rate of false alarm.

Darius

:thedeal:

AIAG SPC 2nd Edition indicates 6 in a row, all increasing or all decreasing, shall be identified as out-of-control condition, which makes you wonder the more alarms, the better for the big 3.

 

[Jim Wynne]

Paddy,

What are the calculations ( formulas, constants ) for a single sample size of X bar & R? Help anyone?

Xbar/R charting is intended for use with rational subgroups, not individuals. The "R" part of it deals with subgroup ranges, and if there are no subgroups, there are no ranges. You need to chart individuals (X and moving range, for example, or use some other sort of analysis. In this thread I referred you to the online NIST engineering statistics handbook; you might want to refer to it for information on Individuals Control Charts.