Example Capability Study #1
Six Sigma SPC - 2070 W. Washington St. #5 Springfield IL 62702  Ph: 217.698.0063
6 Sigma Statistical Process Control (SPC) Software for Windows 95/98/NT/2000/XP/ME

This study involved a process that used Pre-Control limits on the X-Bar and Range control charts and what happens to the results when you apply WECO, (Western Electric Company) rules. This company is a precision metal stamping company. It is assumed that the Pre-Control limits are used to keep from changing the stamping tool so often. This may be the only way for such a company to be competitive.

Note: the notes that appear in a RED BOX on the chart ARE NOT generated by the software.

You can not just use one statistical tool to evaluate a process, but if you use just a distribution, X-Bar, and Range charts you can obtain a lot of information.

We took the first 75 pieces of data submitted to establish the upper and lower control limits. Remember that for Six Sigma to work, THE PROCESS MUST BE IN STATISTICAL CONTROL, or everything else is N/A. For this example, I based design margin on 4.5 sigma. i.e. 1.5 Cpk, (process capability). I increased the accuracy of the calculation to .0000000 number of decimal points using double precision math.

Here are the part's characteristics and the evaluation of Data to Specification ...

The above information actually looks like the picture below on the ZeroRejects screen. The Part Description, which had the actual company name in it has been censured.

Ok, so the Evaluation looks OK, but it is based on averages and is reliant on the X-Bar and Range charts being in control. The next thing we do is look at the control chart to see if the process is in control.

Here in the X-Bar chart we start to see a problem. About every 6th to 10th sample the process goes out of control when you apply WECO, (Western Electric Company) rules. As a matter of fact, every 6th to 10th sample, the process mean, (average), jumps by more than 3 Sigma, but not more than 4.5 Sigma. (Remember Six Sigma allows for a process to jump this much and still meet the design margin, and believe me, this is real data and this happens more often than you think in the real world) Now with the 'Pre-Control' limits the company has set for this process, I'm sure it stays in control, but, just the fact that the product can jump this far indicates several things. First note that the best fit line is in a downward trend this will be important later. This process needs to be monitored twice as often as it currently is. This would damper these large shifts in the mean.

Next we want to look at the Range chart.

The Range chart also looks pretty good, at least it is in control.

Next we need to look at the Distribution Chart.

This Distribution chart indicates several things.

A bell shaped curve is centered around the mean, or average, of the data. The tails of the curve have a spread of 3 Sigma on both sides of the mean or X-Bar Actual, in this case .2486420.

Notice that with the Distribution above, - 3 Sigma from the Nominal Specification, indicated with the RED circle, is greater than 6 Sigma from the actual mean, or X-Bar Actual, of the data samples measured. This is a large shift, but, because the part specification is very wide, it still meets the +/- 4.5 Sigma design margin. We know this because of the lines on the left side of the chart. The Lower Specification Limit, (LSL), of .248 is less than - 4.5 Sigma which is .2480277.

Last we want to look at the Cp and Cpk values. I have seen some people do a distribution of the Cp and Cpk values, but we feel that a line chart gives more information. Using a line chart, we can correlate or compare the corresponding point on the X-Bar and Range charts. This can sometimes demonstrate patterns that may be missed otherwise.

Here is the Cpk line chart.

We can see that this process can fall close to a Cpk of 1.0 and below a Cpk of 1.5. While the average Cpk of 2.555 is a Six Sigma design and the Best Fit Line's trend, (dashed line around the average line), is flat, this process can shift almost 4 Cpk between samples.

Next we look at the Cp chart.

The Cp chart is good and has an average Cp of 7.8 with the lowest value being about 3.2. I know this because of the Data Sheet Below.

If this part meets their customers requirements or not, I do not know. However, I feel this process could be improved with closer monitoring by taking samples more often. (see the X-Bar chart) This may cause the Cpk and X-Bar values to fluctuate less and thus have a better and more stable process.

Because of this, If I were their customer, I would require data and charts from ZeroRejects to be submitted with each lot and I would take a random sample from the lot, at incoming inspection to insure the trends are the same and that the shift is not more than .25 Sigma from where it currently is.