# Statistical Significance and SPC Control Chart Reports

J

#### JAG2013

Hi all,

I've been working for a while with SPC and have a few questions. First of all, I monitor an X-bar - R chart for a process. The subgroup size is 6. I have setup alarms for out of control points and significant shift (8 points above or below the center line per WECO rules). First question, I've been told that when a shift is noticed a statistical analysis must be performed to determine if there is statistical significance. How should I calculate the statistical significance? Do I have to use an Anova to compare the 8 subgroups that cause the shift with the center line/average and determine statistical significance?

Another thing is that I prepare reports of the results of the control charts. For every alert/alarm triggered I have to generate a report. Also, on a weekly basis, I have to analyze the results and assign actions to improve the deficiencies. In addition, I have to prepare quarterly reports that should provide a summary of the alerts and alarms that occur during the quarter. Any recommendations in regards to how reporting should be done? Any templates for SPC control chart reporting I can look to have a reference? Seems I can report biweekly the SPC data and not quarterly, but how can I justify this?

#### Jim Wynne

Staff member
I've been working for a while with SPC and have a few questions. First of all, I monitor an X-bar - R chart for a process. The subgroup size is 6. I have setup alarms for out of control points and significant shift (8 points above or below the center line per WECO rules).
What kinds of things are being measured, and how?

First question, I've been told that when a shift is noticed a statistical analysis must be performed to determine if there is statistical significance. How should I calculate the statistical significance?
Who told you that, and what was the basis? To be honest, this sounds a little like Six Sigma Overkill?, but perhaps it's not. In general WECO and other "rules" are more like guidelines to tell you that something improbable is happening (or has happened) in the process. Improbable ≠ impossible, though. I'm not sure what statistical analysis is going to do for you. You need to see if you can identify the cause of what happened, if you can.

Tell us more about the process and the measurement.

J

#### JAG2013

1.What kinds of things are being measured, and how?

I'm measuring the length of a device. It is measured with the aid of an Inspection Vision System.

I'm trying to establish a way to calculate the statistical significance if 8 points continously are above or below the center line. I know the 8 subgroups above or below the center line are address as a non-random pattern but how can I calculate whether that non-random pattern is significant? I have attached a control chart for reference.

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#### Steve Prevette

##### Deming Disciple
Staff member
Super Moderator
1. There is no need nor desire in SPC to calculate statistical significance of a shift. I would agree that sounds like sick sigma hogwash. Dr Deming and Wheeler definitely point out that SPC is not an exercise in probability and it does not further learning to try to calculate levels of significance.

2. On display formats, take a look at http://www.efcog.org/wg/esh_es/Statistical_Process_Control/. One thing I do propose in that set of materials is a color coded scorecard based upon the SPC results.

#### Miner

##### Forum Moderator
Staff member
To be honest, this sounds a little like Six Sigma Overkill?, but perhaps it's not.
I would agree that sounds like sick sigma hogwash.
This is nothing taught in Six Sigma (at least not by mainstream companies). We typically teach Nelson's Rules for Minitab users. WECO or AIAG rules are also common. It sounds like something said by someone that knows just enough to be dangerous.

#### Bill McNeese

##### Involved In Discussions
There is no need to check the significant of the Western Electric patterns. The patterns do represent significant changes in the process. Someone does not understand what they are asking for.

But since you asked, the Western Electric Statistical Quality Control handbook does the give the probabilities for the various patterns. The eight above the average is easy to determine. It is simply .5^8 or 0.0039.

As far tracking signals, I would use a control strategy approach that provides a record for what was found for each out of control point as well as what was done. It is easy to set up on a computer. Here is a link on my web site of one such approach: http://www.spcforexcel.com/my-process-out-control-now-what-do-i-do

You need to include those closest to the process in this approach.

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#### Jim Wynne

Staff member
There is no need to check the significant of the Western Electric patterns. The patterns do represent significant changes in the process. Someone does not understand what they are asking for.

But since you asked, the Western Electric Statistical Quality Control handbook does the give the probabilities for the various patterns. The eight above the average is easy to determine. It is simply .5^8 or 0.0039.
Just as a qualifier, it should be noted that the WECO "rules" are based on the underlying statistical assumptions being true, and the further away from those assumptions being true the process gets, the less reliable the rules become. In the OP's case, there is a chart posted that shows 19 of 25 points either at or below the mean, which means that there's something going on with the charting that renders the 8 points in a row mostly meaningless. It appears that there might have been a significant shift in the mean at some point and process wasn't adjusted or the mean and control limits weren't recalculated.

D

#### Darius

rules..., Wheeler put it into the article, I added in this post

Which rules must I apply for SPC

As I see in your chart, this trend "problem", is common when the specs limits are to wide in compare to the variation of the process, a way to disminish this behabiur is to sample with less frequency, or don't take that as a problem.

#### bobdoering

Trusted Information Resource
Here is the point of the "rules" with Shewhart charts. The assumption is that all special causes have been removed. That leaves a truly random "noise" (random variation of common causes) centered about a central value. If out of this noise arises anything that has "pattern", then it can no longer be deemed noise, and is evidence of a special cause. Common patterns observed are found in Western Electric rules, et. al. The cause must be identified and removed to get back to the common cause noise level.

The fundamental assumption is the process you are evaluating has a steady state of random noise with its particular common causes. Not all common causes behave in that manner, and if not Shewhart charts may not be appropriate.

#### Bev D

##### Heretical Statistician
Staff member
Super Moderator
those who have said that the person asking you to determine statistical significance doesn't understand SPC are correct. the limits - if properly calculated - and rules provide the statistical significance of the change. It will be around .3% to 5%. Donald Wheeler has many easy to read and informative articles at Quality Digest.

the 8 points you see are not a repeating pattern - at this point. however, it looks like it may be an anomaly of how the limits were calculated. it looks like the limits were calculated using all of the data present in the chart. limits should be calculated from a stable period and SET. points ar plotted against these limits in the future. limits are not supposed to be recalculated each time a new data point is entered.

Can you tell us how the limits are calculated and how you chose to subgroup the data?

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