10.10 Process Capability for Continuous Data

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Example 10.10.1 Yellow Dot Squash Ball

The World Squash Federation has strict specifications for the equipment used in the game of squash. The single yellow dot ball must have a diameter between 39.5mm and 40.5mm. Brauer Squash Balls Ltd empties one of its boxes and checks the diameter of 100 squash balls. Use their data on diameter 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 Diameter’.

As a box of squash balls has been emptied and then measured we have no way of knowing if they were made in time order. Additionally, because we don’t know anything about the time they were made we cannot produce sub-groups. It is for these reasons that we must use the Snapshot Analysis for Process Capability.

  1. Transfer the  data from the spreadsheet into Minitab.
  2. Click Assistant<<Capability  Analysis
  3. Click on the Capability Analysis box which is used for continuous data.
  4. The test menu opens. To start with we need to select whether we want to do the Complete or Snapshot analysis using the radio buttons. Select ‘Snapshot’. When Snapshot is selected any menu options used for the input of subgroups disappear.
  5. Under Process Data, use the drop-down selector to tell Minitab that  ‘Data are in one column’. Select Diameter as the single column of data.
  6. Enter the specification limits of ‘39.5’ and ‘40.5’. 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 40. Enter the target for the mean as ‘40’.
  7. Click OK to execute the procedure and generate the Report Card and Summary Report.

In the top left corner of the Summary Report we are shown the histogram of our process data with fitted Normal curve, the specification limits and target for the process mean. We can see that our squash ball distribution is closer to the USL than the LSL. None of the balls that were checked are out of specification.

Below the Capability Plot we have the Normality plot for our process data. With a P-Value of 0.856 we can say that our sample data probably did come from a normally distributed population. This is a very important step in the analysis as it is the fitted curve that lets us predict the shape of the population.

On the right, underneath the Customer Requirements section we have the Process Characterization which delivers our capability data. As we used the Snapshot analysis, with no option for subgrouping, all the capability metrics are for Overall Capability.

We are told that the sample mean is 40.199 and that the mean is off-target. If you think back to the 1 sample t Test this means that the population of ball diameters is not likely to have a mean diameter of 40.

Our process has a simple capability , PP, of 2.41. As this value is above 1 we know that the process width fits within the spec limits. As the overall capability, Ppk, is significantly less than Pp we can establish that the process is not centered. Also, as Ppk is greater than 1 we know that the process is not breaching the closest spec limit.

We are then given data on %defects and PPM (parts-per-million) or DPMO defects. Expected and observed relates to the fitted curve and the actual sample, respectively.

The conclusions from this analysis would be that the process is performing well against the spec limits. However, if it were centered it would be quoted as being a Six Sigma process.

The report card tells us that our data was normally distributed, therefore, this analysis was appropriate. The amount of data we had was sufficient for establishing normality and giving accurate results. Finally we are given information on the selection of the Snapshot analysis.

Free Sample

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

It does not include 10.11 Process Capability for Attribute data.