pchart for large subgroups
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 This topic has 12 replies, 9 voices, and was last updated 16 years, 2 months ago by Savage.

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August 12, 2004 at 12:17 pm #36517
Hi all,
Most likely a stupid question :). I got stucked in the pchart 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 pchart for the monthly data, all the points fell out of the control limits. This seems to be quite logical since the control limits for pchart 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 pchart outofcontrol points interpretation?
Thank you,
Paul
0August 12, 2004 at 1:59 pm #105556
GabrielParticipant@Gabriel Include @Gabriel in your post and this person will
be notified via email.LArger subgroups are more powerfull to detect outofcontrol 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.0August 12, 2004 at 3:26 pm #105572Hi Gabriel,
thanks, your explanation sounds more than reasonable. For some reason I had a feeling (looking at the formula for pchart control limits calculation) that the large subgroups were somehow disadvantaged :)
Paul
0August 12, 2004 at 6:59 pm #105590
GabrielParticipant@Gabriel Include @Gabriel in your post and this person will
be notified via email.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.
0August 12, 2004 at 8:32 pm #105597Hi 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 pchart 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.0August 13, 2004 at 7:22 am #105617Ross,
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 pchart 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.
Paul0August 13, 2004 at 4:01 pm #105640Wheeler’s book is available from SPC Press, http://www.spcpress.com
Matt0August 13, 2004 at 9:03 pm #105666
Ken FeldmanParticipant@Darth Include @Darth in your post and this person will
be notified via email.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.
0August 16, 2004 at 4:54 am #105752The 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.
0August 16, 2004 at 9:40 am #105763
Graeme WilsonParticipant@GraemeWilson Include @GraemeWilson in your post and this person will
be notified via email.Paul,
Do you have access to the Blackbelt Memory Jogger? Check out page 147
If np>5 & n(1p)>5, then use IMR chart instead of the Pchart because under these conditions the binominal distribution can be approximated by the normal distribution.
Best Regards, Graeme0August 16, 2004 at 9:52 am #105766
GourishankarParticipant@Gourishankar Include @Gourishankar in your post and this person will
be notified via email.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
0August 16, 2004 at 4:12 pm #105788
R. SivaprasadParticipant@R.Sivaprasad Include @R.Sivaprasad in your post and this person will
be notified via email.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.0March 9, 2006 at 2:12 am #134813Agree 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 longterm (I) and pointtopoint (MR) charts, so more ability to understand variation
Minitab offers 8 tests for special cause for the I/MR vs. 4 for Pchart.0 
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