p-chart for large subgroups

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• #36517

Sorour
Participant

Hi all,
Most likely a stupid question :-). I got stucked in the p-chart data interpretation. I was happy with the weekly charts we started to use – they seem to indicate when our production yield is under control and when not.
However, when I tried to use the same p-chart for the monthly data, all the points fell out of the control limits. This seems to be quite logical since the control limits for p-chart get narrower with the increasing size of the subgroup.
So if we produce say 50000 products per month, then there seems to be a little chance of having the yield under control. So I am a bit puzzled now – if I choose a small subgroup size, the chart will most likely be under control and vice versa.
Can anybody help me with the p-chart out-of-control points interpretation?
Thank you,
Paul

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#105556

Gabriel
Participant

LArger subgroups are more powerfull to detect out-of-control situatuins than smaller subgroups, and that holds true for any type of chart.
So if we produce say 50000 products per month, then there seems to be a little chance of having the yield under control. So I am a bit puzzled now – if I choose a small subgroup size, the chart will most likely be under control and vice versa.
I would say that if your process was stable, chances are that the control charts will look under control, both the monthly and the weekly chart.
You already said I was happy with the weekly charts we started to use – they seem to indicate when our production yield is under control and when not. That gives the idea that some weeks are not under control. When you put this week’s data into the monthly chart, you are including variation due to special cuases there too. So it is not surprising that the monthly chart looks out of control – it is.

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#105572

Sorour
Participant

Hi Gabriel,
thanks, your explanation sounds more than reasonable. For some reason I had a feeling (looking at the formula for p-chart control limits calculation) that the large subgroups were somehow disadvantaged :-)
Paul

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#105590

Gabriel
Participant

That’s because the control limits become narrower as the subgroup size increase. But the variation in the subgroup p value also becomes smaller when sampling variation reduces as sample size increases.

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#105597

Loehr
Member

Hi Paul,
Instead of a p chart, try using an IX & MR chart, with each monthly p value plotted as an IX value.
According to Don Wheeler (Making Sense of Data, p. 223), the IX control limits will sometimes be more appropriate than the p-chart limits for describing the distribution of p values, especially for large subgroup sizes. Plus, you do not need to calculate different control limits each time the subgroup size changes.
Hope this helps.

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#105617

Sorour
Participant

Ross,
I tried using Individuals/Moving Range chart and thought that if the subgroups sizes were relatively constant the I/MR chart could be appropriate.
However, the I/MR chart indicates that the process is under control (the control limits are pretty wide though) whereas the p-chart shows all the poits outside the control limits. So the results are totally different.
Unfortunately I do not have the book you are refering to so I cannot read more about it.
Paul

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#105640

Savage
Participant

Wheeler’s book is available from SPC Press, http://www.spcpress.com
Matt

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#105666

Ken Feldman
Participant

Hey John, how about wading in here and helping poor Paul out?  Explain to him why the I/MR might show the process to be in control and the P chart might not.  I am at a loss and am hoping you can help us out here.

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#105752

Markert
Participant

The p chart makes a hard assumption that the data follow a binomial distribution with a single proportion defective “p”.  The control limits are based upon a normal approximation to the binomial which typically works well for large subgroups.  If the assumptions for the binomial are violated the p chart does not work well if at all.  The case you describe for monthly data is sometimes referred to as the over dispersion problem and its most likely due to the fact that over a month’s time you are aggregating data from multiple binomial processes — this is quite common.  A suggestion is to simply track monthly yields on an Individuals chart based upon a calculated monthly yield value p. The Individuals chart may seem a bit ad hoc but it works quite well in terms of observing the month to month variation in yield where the standard p chart does not work.

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#105763

Graeme Wilson
Participant

Paul,
Do you have access to the Blackbelt Memory Jogger? Check out page 147
If np>5 & n(1-p)>5, then use IM-R chart instead of the P-chart because under these conditions the binominal distribution can be approximated by the normal distribution.
Best Regards, Graeme

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#105766

Gourishankar
Participant

Hi
Please refer to Don Wheeler’s “Understanding Variation” – SPC Press for an excellent treatment on the this subject.
Gourishankar , ASQ Certified Quality Manager
Chennai, India

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#105788

Participant

Dear Mr. Paul,
The “P- Chart” used preferably for batch production with individual limits. Hence you decide whether the 50,000 products are batch production or continuous production with minimum variables.

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#134813

Savage
Participant

Agree with Graeme.  We use I/MR for our customer satisfaction data (percent satisfied – so technically a proportion) for the following reasons:
np > 5, so binomial distribution can be approximated by normal distribution
You don’t have fluctuating control limits with I/MR, which is easier for management to “digest”
You get both the long-term (I) and point-to-point (MR) charts, so more ability to understand variation
Minitab offers 8 tests for special cause for the I/MR vs. 4 for P-chart.

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