# Accurate Chart Interpretation

Six Sigma – iSixSigma Forums Old Forums General Accurate Chart Interpretation

Viewing 8 posts - 1 through 8 (of 8 total)
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• #46941

Emilio Caliandro
Participant

Dear all,
When a control chart reports all points of  Xbar  between the 2 limits ( -/+ 6 s ) and some, also very few,  point of Range Chart (or S Chart) are over the UCL, how interpret this result?

Is it still possible to affirm that the process is in control?

Which further analysis are appropriate in this situation?

Regards,

Emilio C.

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#155874

TC
Member

Emilio,
If either your Xbar or range chart exceeds the control limits, your process is out of control.  Your range is an indicator of process spread (better one is standard deviation).  You can have Xbar in control and range out of control as follows:
Data points:  1, 3, 5, 7, 9

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#155876

TC
Member

Emilio,
Your process is still out of control.  If either your Xbar OR range chart exceeds control limits, your are out of control.  Your range is telling you that you have excessive variation, although the mean is OK.  Here is one possibile way to get this result:
Sample 1 points:   3, 4, 5, 6, 7     Xbar 5, Range 4
Sample 2 points:  1, 3, 5, 7, 9      Xbar 5, Range 8
Your mean (Xbar) did not change from sample 1 to sample 2, but your range doubled from 4 to 8.
In this case, your want to understand what is causing the range to increase.  There are a number of analyses you could perform to determine the source of your variation.  Depending on how well your process input variables are understood, you may need to perform DOE on your process to isolate and optimize key variables.

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#155880

DaveS
Participant

Emilio,
If your post is absolutely accurate and you truely have your limits set at +/- 6 sigma, than any out of control point would be a strong signal of out of control process. However, why are you using plus/minus 6 sigma limits?
If youi really mean plus minus 3 sigma limits and a 6 sigma spread between which is standard Shewhart methodology, than you may or may not have a problem. You need to quantify what is “some, also very few”. Any standard control chart will have a false out of control signal of approximately 3 in 1000 points. If the underlying distribution is exceedingly skewed, it might be higher.
The meaning of a point out of 3 sigma limits is “There is sufficient evidence of a possibly assignable cause (out of control condition) to economically justify an investigation into the process perfrmance at that point in time. It does not mean the process is out of control, only that it may be.

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#155881

Emilio Caliandro
Participant

Sorry,
I meant  -/+ 3 Sigma .
Thank you , Emilio

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#155890

Erik L
Participant

Emilio,

The control charts use estimates of variation derived from within sources of variation.  Once this has been established from stable VOP, then we can proceed to a meaningful contrast of the between sources of variation.  Of the two charts, the range (or standard deviation) element of the SPC is the most critical to demonstrate control (this importance is further highlighted if we have not captured enough data at present to fix the control limits and/or are using SPC methodology to calculate a meaningful estimate of variation for sample size calculations and capability estimates (short-term).  If the control limits for your data are still dynamically adjusted with new data, then we should be concerned that the OOC condition seen in the range control chart is inflating the subsequent estimate of the within source of variation and that this is subsequently artificially pushing the UCL and LCL of the Xbar chart further out.  So, we could be in a situation where the data points on the Xbar chart should really be flagged as OOC but they are not at present due to the inflated estimates pushing the CLs wider.  Try censoring those data points triggering the OOC condition from the Range and Xbar charts and take a look at the new limits that are created.  You may see signals that were never there before.  If we continue to see OOC conditions in the Range section of the chart, this could be telling us that we need to re-address the concept of the rational subgroup.  Something is occurring within the subgroup that is causing more variation than what we are observing between our subgroups and this is the exact opposite of what were trying to achieve with the concept of rational subgrouping.  Multi-vari/Components of Variation Study/General Linear Models (GLMs) could help provide graphical and analytical clues to what the rational subgroup should be for your data.  Good luck with your process improvements!

Regards,
Erik

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#155902

youtwo
Member

Wow….listen to dave s…good advice to a simple question.

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#156151

mcintosh
Participant

The process is out of control, unless there is a special cause assigned to the points above the UCL

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