How to justify Widened Control Limits - No Assignable Cause scenario

W

wchuey

Hi fellow quality practitioners,
I am not sure if any one of you has encountered this problem before.

Based on the AIAG manual, control limits for SPC charts are set at +/- 3 sigma. However, as the process improves, the sigma decreases and the control limits start to get closer and closer to the centre line with each review.

I am currently in a situation where points fall out of the control limits with no assignable cause (the only logical explanation is that the control limits are too tight). :bonk: The Cpk of the process is greater than 4.

Is there a way in which I can justify for an widened control limit?

My colleague suggested increasing the control limits to +/-6 sigma, since the Cpk obtained at 6 sigma is greater than 2. I have always know the formula for Cpk as (USL-mean)/3sigma and was surprised to hear that when the control limits are set at +/- 6sigma, the Cpk for the process changes to USL-mean)/6sigma. Is this a statistically sound method?
 
D

Darius

Re: Widen control limits - how to justify?

My colleague suggested increasing the control limits to +/-6 sigma, since the Cpk obtained at 6 sigma is greater than 2. I have always know the formula for Cpk as (USL-mean)/3sigma and was surprised to hear that when the control limits are set at +/- 6sigma, the Cpk for the process changes to USL-mean)/6sigma. Is this a statistically sound method?

IMHO A big NO about control limits at +/- 6 sigma, but agree with the /6sigma change if you are going to use it. The reason about it is that the Cpk divides how far you are from the specs by the half of the process spread (3sigma in the original equation, and if you dear to change the process spead to 6sigma it must be it)

Your problem seems that your process is a chemical batch or something like that, so the autocorrelation is too high, making the control limits to tight. I saw once a chemical batch with a chemical concentration taken every 15 minutes, the variation between points where to small but because the specs where big, no control was needed until some point (the LSL), so something like a chainsaw chart happen and the control limits where almost the same value as the mean leaving to many points outside of control limits (almost all). There are 3 ways (4 if you like your first approach) to skin the fish.

1-to take take more time between measures
2-to add autocorrelation to your chart.
3-to take the trend into acount.

The numbers 1,2,3 is in order of complexity. My favorite ones is number 2. Altho some guys may say that with a bigger sample size (option number 1.5), IMHO it just hiddes the behabiur.

Check on autocorrelation factor, Donlad Wheeler wrote about it in his SPC books.

The autocorrelation factor affect the estimate for variation in a IXMR chart (individuals with moving range).

x y
__ __
s1 s2
s2 s3
s3 s4

r^2 = ((n Sxy - Sx Sy )^2/((n Sx^2 – (Sx)^2 )* (n Sy^2 – (Sy)^2))

the factor is

Factor =(1-r2)^-0.5

SD within sample with autocorrelation =SD within sample without autocorrelation * Factor:magic:
 
W

wchuey

Re: Widen control limits - how to justify?

Hi Darius,

We are using the Xbar-s chart with a subgroup size of 15 with wirepull strength data as inputs.
 

Steve Prevette

Deming Disciple
Leader
Super Moderator
Re: Widen control limits - How to justify? No assignable cause scenario

Is there a way in which I can justify for an widened control limit?

NO.

Are you sure you have calculated the current limits properly?

Now, there is always a chance for a false alarm when control charting. It shouldn't happen very often, but it can and will eventually happen.
 

Miner

Forum Moderator
Leader
Admin
Re: Widen control limits - how to justify?

Hi Darius,

We are using the Xbar-s chart with a subgroup size of 15 with wirepull strength data as inputs.

Have you tried reducing the subgroup size? You could take an existing chart and model new limits using a subgroup size of 10 and 5 until you get the level of responsiveness that you want.
 
W

wchuey

Re: Widen control limits - how to justify?

Hi,

There are 15 wires in a unit which is why the subgroup size is set as 15. I am looking into the autocorrelation factor as suggested by Darius. This is something new to me and would appreciate if you guys could direct me to any relevant websites. Thanks!
 

Tim Folkerts

Trusted Information Resource
Re: Widen control limits - How to justify? No assignable cause scenario

You might want to look at this recent thread. It discusses a situation that was quite similar... http://elsmar.com/Forums/showthread.php?t=20694

You might consider a couple different control charts that focus on the variations of most interest to you.
* To check that the wires within each assembly are similar to each other, the S chart for the 15 values would be valuable. (The X-bar chart would have less meaning, since you might well expect it to be out of control due to the variations you see between subgroups.)
* To check that entire assemblies are similar to each other, an I-MR chart of the average value for the 15 wires might be appropriate.


As far a capability calculation, Ppk might be more appropriate than Cpk. In this case, it is pretty clear that there is variation between assemblies beyond the variations seen within each assembly. Since Cpk is based only on the tighter variations within each assembly, it will gave an inflated value for the overall capability of the process. Ppk is based on the overall standard deviation, so it gives a better estimate of the overall capability.

Tim F
 
Last edited by a moderator:

Statistical Steven

Statistician
Leader
Super Moderator
Re: Widen control limits - How to justify? No assignable cause scenario

A simple solution. Use an X/mR chart by plotting the means of the 15 units. The problem seems to be very tight within batch variability. By switching to a X/mR chart you can evaluate batch to batch variability.
 
J

jeffrey_Chang

Re: Widen control limits - How to justify? No assignable cause scenario

I am currently in a situation where points fall out of the control limits with no assignable cause (the only logical explanation is that the control limits are too tight). :bonk: The Cpk of the process is greater than 4.

Hi wcheuy,
IMO, with a CPK of > 4, if it is correct, why do you still want to continue to monitor the wire pull. With such a good process capability, I would suggest you stop monitoring the product output; in this case, the wire pull, but to consider monitoring the process parameter; i.e. the input, that affect the wire pull instead. That would provide you with a more meaningful insight into your proces and should still continue to maintain your wire pull capability.
thks.
jeffrey.
 
D

Darius

Re: Widen control limits - How to justify? No assignable cause scenario

Agree with Statistical Steven :agree1:
A simple solution. Use an X/mR chart by plotting the means of the 15 units. The problem seems to be very tight within batch variability. By switching to a X/mR chart you can evaluate batch to batch variability.

Agree with Jeffrey, that you need to know if is needed to do such charts, altho is needed for the right capability index determination.:cool: I must say that your friend comment about the capability index has some good points, most of practitioners just use the formulas without any thinking.:applause:

There is not much on the net about autocorrelation and control limits, I found this free article (thanks to asq).

http://www.asq.org/pub/jqt/past/vol32_issue4/qtec-395.pdf

But I tried to write down, how to do it in my last post.
being sample1 = s1, sample2=s2, etc.
x y
__ __
s1 s2
s2 s3
...

obtain the r2 (fisher correlation factor) and apply as I said before. For me worked as a clock-work. And altho Wheeler didn't went as far as control limits, IMHO it applies to capability index too.

or post some of your info, so it gives to us something to play.
 
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