# Control Chart Question

Six Sigma – iSixSigma Forums Old Forums General Control Chart Question

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• #37634

Bentley
Participant

I am using an I-chart to track monthly quality performance (ex: May = 98%, June = 98.3%, etc.).
How many data points do I need to track in order for my control chart to be statistical valid and why that number of control points?
Thanks for the help!!

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#111143

Darth
Participant

The I-MR chart is usually reserved for continuous data with rare use for discrete under certain conditions.  Since you are plotting %s, I first wonder if it is even the most appropriate control chart to use.  What is the performance characteristic that you are control charting?  In any case, you need enough points to set up the chart such that the underlying common cause variation has a chance to show up.  This may be as much as 100-125 individual data points for an I-MR chart.

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#111144

Bentley
Participant

We have a process that we gauge monthly against an SLA.  The monthly data point is a yield (accuracy).  I have been asked to plot these monthly yields on a control chart.  Keep in mind that I will never have a data point in excess of 100% and my SLA is not to have any monthly data points below 90%.
My thought is to use an Individual chart and set the UCL at 100 and the LCL at 90.  Is this not correct?  If not, what would be the best control chart to use?  Also, you are recommending 100+ data points, but I do not have 8+ years to collect data points!  :-)
Thanks for the help!

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#111145

Darth
Participant

Point number one!!!  You do not set the control limits, they are calculated from the data!!!!!  They represent the Voice of the Process.  Your SLA is the Voice of the Customer and you can do process capability analysis as a separate study.
Certainly you can use less than the 100 numbers but keep in mind that the control limits are supposed to represent the steady state, common cause variation of the process.  With limited data, you can’t be sure that what you are seeing truly represents the process.  For example, you know that the average of 2 dice is 7 and that the range of the two dice would be 2 to 12 or 10.  The shape is known since you have 1 way to throw a 2, 2 ways to throw a three etc.  Now throw the dice 12 times and see if the average is indeed 7, the range 10 and the shape of the distribution matches the known distribution.  You will have a similar challenge.
What is the monthly data point that you are using against the SLA?  That may help determine whether another chart is more appropriate.

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#111146

Bentley
Participant

Okay, I have a process wherein the SLA is 90%, meaning that for any given month, my process yield cannot go below 90% or I am in violation of my SLA.
So, I need to chart the following:
May: 95%; June 95.3%, July 96.8%; Aug 98%; Sept. 98%, Oct. 100%
So, if I understand what you are saying, I should never set the UCL or LCL limit to be in line with an SLA, correct?
1) Which control chart should I use?
2) How do I represent the SLA on the control chart?

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#111147

Darth
Participant

Bentley, you definitely have some sparse knowledge of control charts.  I wonder why your manager dumped that project on you.  Again,
NO, you do not set the upper and lower control limits, they are computed from the data.
NO, you do not put specs (read SLA) on the control chart.  You use a control chart to monitor the process over time against what would be common cause variation.  Specs are handled separate from the Control Limits.  I suggest that you do a Google or pick up a basic SPC or Control Chart book and familiarize yourself with some of the basics.
You still haven’t answered my question.  You are caculating a ratio and coming up with a percentage.  What is the numerator and what is the denominator?  Frankly, if you only have 6 data points, I would strongly suggest that you start with a simple run chart and once you have more data you can shift to a control chart.  Six points on a chart is hardly enough to determine what the process is doing.  Throw the pair of dice six times and tell me something about the hypothetical distribution.  You won’t even be close.

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#111149

Bentley
Participant

The yield is calculated as follows: # of defects/number of opportunities.  Then 100 – result of the above.
Am I to infer then that perhaps a control chart is not really appropriate to track this sort of data at this point and time?  Would a Process Capability be a better graphical representation of the data.
See, here’s the thing: the control chart was at the request of our client who wants to see how we are performing against their SLA over time.  The client SVP — who states that he has a great deal of Six Sigma knowledge — was very specific that a control chart is what he wanted.  My initial pushback was that a control chart didn’t appear to be appropriate.  Am I wrong?

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#111151

Darth
Participant

Ah, now it all becomes clear.  I would suggest that you check out the use of a C or U chart.  If the client SVP has a great deal of SS knowledge then he/she wouldn’t have asked you to use the control chart to see how you are doing against the SLA.  You would use the control chart to demonstrate process stability and then Sigma Level or some other capability measure to see how you are doing against the SLA.  Bentley, if you wish to take this offline and dive a little deeper I would be happy to chat.  Email me at [email protected] and we can explore this further if you wish.

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#111155

Bentley
Participant

Darth:
You’re the best!  I will contact you directly.  Funny thing is: this client already gets a monthly sigma level from us as well as notification about whether the SLA was met or not.  As long as our SLA is being met, I don’t see where it matters what the control data looks like.

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#111409

Markert
Participant

Hi
1) It is perfectly possible to use an I-mR chart for percentage (or any other attribute) data. All attribute data is ultimately individuals data. The difference between traditional attributes charts (e.g. c, u) and I-mR charts is that c, and u charts rely on the theoretical link between the mean and standard deviation of the Poisson distribution (or binomial in the case of p and np charts) to determine the standard deviation for calculating the control limits. I-mR charts determine the standard deviation empirically from the data (via the moving range). IF the assumptions of the Poisson model are justified then c or u charts will have slightly more degrees of freedom. However, the assumptions of the Poisson distribution are often NOT satisfied – in that case the I-mR chart (which is independent of any distribution – including the normal!) will still give you correct control limits, but the c and u chart limits will be wrong!
2) Darth is absolutely correct. Control charts must use (3sigma) limits determined from the process (with a “within” estimate of sigma). They represent the “voice of the process.” Specification limits represent what we want the process to achieve (wishes and hopes) and represent the “voice of the customer.” The process neither knows nor cares about the voice of the customer. The issue here is to use the control chart as a guide to correct action – i.e find and eliminate special causes (points outside 3sigma) which represent process unpredictability, or work to improve the whole system if only common cause is present (no points outside 3sigma). Working to find arbitrary and spurious “causes” for points outside specification limits will increase costs, scrap, rework, variation etc in any process. (Take a look at Deming’s funnel experiment)
3) It is perfectly possible to start a control chart with only a few data points (even as few as 5 or 6). The calculated limits will be “soft” and will have only a few degrees of freedom, but they are still usable. If anything – because any special cause signals will not be diluted – they will be slightly wider than limits with more data, so while points outside the 3sigma limits will be definitely out, points just inside might be missed signals. Don Wheeler (Advanced Topics in Statistical Process Control – SPC Press) plots a graph of degrees of freedom against number of data, which has an elbow at around 15 to 18. Once you have that amount of data you can always recalculate your limits. Beyond 15 to 18 points, additional data will only have a marginal effect on refining the limits.
Darth is right when he talks about sampling variation giving you a different result to the hypothetical when you throw a die, but that misses the point of what control charts are for.
REMEMBER – the point is not to have “correct” limits, but limits which work to identify opportunities for improvement! That is the purpose of a control chart.
Phil

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#111430

Darth
Participant

Phil, isn’t there some little guideline about np>5 before you start using the I-MR for percentages?

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#111436

Jonathon Andell
Participant

I don’t recall seeing such a guideline, but it could be out there.Here are some additional thoughts on how to chart the data:1. For more data points, see if you have enough process volume to sustain weekly charting instead of monthly.2. Consider coming up to speed on binomial probability plots. While they are not control charts in the strictest sense, they actually can covey a lot of information – and they will support weekly charting as easily as monthly. I don’t know how well that will sit with your client, but they are handy.

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#111443

Darth
Participant

Hey Johathon, how are you.  Of course you can’t recognize me due to my posting name but we did some work together, I believe, at TRW Space & Electronics in CA.
The np>5 relationship deals with the normal approx. to the binomial.  I know that we say the control chart is rather robust to normality but if the np relationship is too small we do get a bias that might give us some false signals.  So, to be on the safe side, I like to use the np>5 to determine whether the I-MR will be suitable for percentages.

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#111451

Jonathon Andell
Participant

Sounds reasonable. I will incorporate that “rule” if I happen to use I-MR charts on percentage data.For what it’s worth, binomial probability plots don’t require any approximations.Here’s one more thought, inspired by Donald Wheeler: consider plotting “opportunities per defect” on an I-MR chart. There are two options: 1) literally count how many opportunities happen between each and every defect, or if that’s impractical, 2) plot the ratio on periodic intervals. This chart also lends itself to weekly intervals, so you can get more data points at the outset. With this kind of chart, you hope to see the intervals between defects continually increase.

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#111455

Darth
Participant

Jonathon, first of all you have to be a Geek to invoke the rule and secondly, it more like a guideline than a strict rule, Eh Matey.  Sorry just saw Pirates of the Caribbean for the 10,000th time.
One of the Stans said we need to ignore Wheeler because he isn’t as good looking or charming as Stan.  Probably doesn’t hold for the Old Stan and is more appropriate to Helga Stan.

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#111458

Mikel
Member

Hey, I didn’t say to ignore Wheeler, anymore than I have ever said to ignore Shainin (Dorian that is, you can ignore Peter and Dick). Just be careful when any of these guys start telling you about their “superior” methods.
Wheeler is a very smart man.
I once derived Wheeler’s MSA measures from the P/TV that the rest of the world uses in fromt of a bunch of Wheeler zoombies – talk about disillusionment! If I know Wheeler’s measures I also know P/TV and Distinct Categories. Hard to be superior when you are the same!

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#111468

Markert
Participant

The rule that np>5 AND n(1-p)>5 is a requirement for the normal approximation to the binomial.
I am interested in your comment that “the control chart is rather robust to normality”. In fact, the control chart is totally independent of normality. The 3 sigma limits on a control chart are empirical. They are not probability limits and they do not rely on any assumption of a hypothetical probability model (except in the case of p, np, c, and u charts which rely on the assumption of either the binomial or Poisson distributions to determine the standard deviation as a function of the mean) Control charts are non-parametric, therefore the normal approximation to the binomial (or the Poisson in the case of c or u data) has no relevence to the ability to place data on an XmR chart, or a traditional attributes chart.
The only thing you might want to check is whether the average count per sample is less than 1, in which case you might need to chart the area of opportunity between events, rather than the count of events per sample.

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#136693

sepet
Member

I am using an I-chart to track monthly quality performance (ex: May = 98%, June = 98.3%, etc.).
How many data points do I need to track in order for my control chart to be statistical valid and why that number of control points?

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#136696

Andhale
Participant

Since control charts are developed with assumptions of normality and indepence of the data, atleast 30 points are necessary to develop control charts (this is what theory says). But, in reality it might not be reasonable to wait until 30 products are manufactured, for example if you are manufacturing microprocessors, you cannot wait until 30 are manufactured and find out how many are out of control. So, my answer is IT DEPENDS ON THE PROCESS. Central limit theorem is used to support the argument for normality when used for constructing X-bar chart.

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