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Process Capability chapter from Sigma Statistics using Minitab 17, Green Belt Edition.

It does not include 10.11 Process Capability for Attribute data.

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Example 10.10.2 More Squash Balls

Brauer Squash Balls Ltd want to qualify a secondary supplier , Parky Squash Balls limited. Parky Squash Balls claim that none of their squash balls will be out-of-spec on weight. The weight specification on squash balls for the WSF is 23g to 25g. Parky Squash balls send data from their production line on ball weights using a subgroup size of 3. Use their data on ball weight to conduct a capability assessment of their manufacturing process.

All data for this chapter is in ‘10 Process Capability.xlsx’ and the data for this example is in the worksheet called ‘Ball Weight’.

  1. Transfer the  data from the spreadsheet into Minitab. There are two columns of data. The ‘Weight’ column contains the continuous data of ball weight and the ‘Group’ column is an index of the subgroup number.
  2. Click Assistant<<Capability  Analysis
  3. Click on the Capability Analysis box which is used for continuous data.
  4. The test menu opens. As we have data in subgroups we can use the Complete Analysis. Select the radio button for the ‘Complete’ analysis.
  5. Under Process Data, use the drop-down selector to tell Minitab that ‘Data are in one column’. Select Weight as the single column of data. We could use the radio button for a subgroup with a constant size or we can tell Minitab which column the subgroup IDs are in. I have opted for the latter.
  6. Enter the specification limits of ’23’ and ’25’. As it is sensible to have the process in the centre of the specification limits we can check whether our process has a mean of ’24’.
  7. Click OK to execute the procedure.

Let’s start with the Summary Report which is mainly based on the overall capability. The only exception is the bar display which tells us how capable the process is in terms of Z Bench score. Here we get the Z actual (overall score) and the Z potential score. Although, there should be no out-of-spec ball weights the score is less than 3. We are also told that the process mean is different to 24.

On the bottom left of the Summary Report we have the Overall Capability Plot. We see the sample data as a histogram together with the fitted Normal curve using the Overall StDev. It is clear that the mean is to the right of the target and is closer to the USL than the LSL.

On the right, underneath the Customer Requirements section we have the Process Characterization which delivers our capability data.
We have a simple capability , PP, of 0.99. This value is very close to  1 which means that the process width is just shy of fitting within the specification limits. As the overall capability, Ppk, is 0.68 we can establish that the process is not centered and should be making defective parts.

When we are given data on %defects we are told that there should be 2.01% defective parts. This should be setting off alarm bells. The capability study states that there should be 2.01% defects but Parky Squash balls state that none of their balls will be out-of-spec. Let’s look at the rest of the data before we make any conclusions.

Let’s have a look at the SPC charts on the Diagnostic Report. We are presented with an Xbar R chart. From the chapter on control charts we already know that that is the appropriate chart when you have a subgroup size of 3. We see that two points are out of control on the Xbar half of the chart. It does not tell me anywhere why these points are out of control but I deduce that it is because of Test 2 (9 points all in a row on either side of the centre line).  

Below the Xbar R chart we have the Normality plot for our process data. With a P-Value of 0.011 we can say that our data probably did not come from a normally distributed population. However, the fitted curve fits our sample data rather well, it’s only the right hand side of our sample data that is missing. We discussed Normality of our data in section 10.8. This is the occasion that we have to think about whether the underlying distribution is normal and is being affected by special cause variation or whether the underlying distribution is of a different type. We can only use the metrics in this study if we can conclude that the low P-Value for normality is due to special cause variation.

Again just keep this in mind until we review all the data.

We then get to the Process Performance Report. This adds Within (or Potential) capability data to the information we have seen in the Summary Report already. Rather than go over the differences between the Actual and the Potential data let’s have a look at the Observed and Expected data. The Observed % Out of  spec is 0%. As stated by the manufacturer you won’t get a ball that is out-of-spec on weight.  But the Expected % Out of  spec is 2.01%.  What this probably means is that the manufacturer is checking all the weights and removing those that are out-of-spec. Hence, the really nice distribution with the right hand side chopped off.  This is also why the P -value for the Anderson Darling test was so low.  This removal of the out-of-spec balls is a form of special cause variation.

The conclusion is that if you are buying from this manufacturer you want them to continue with the 100% inspection. On the downside it is probably their customers that are paying for the 2% of  defects and the 100% inspection. I would steer well clear of this company.

What this example does show is a really positive facet of capability studies. And that is you don’t have to have all the analysis of a parameter to make an assessment of a process. You only have to have enough samples to be able to fit a distribution and check SPC charts.