The lower spec limit for the cable diameter is 0.5 and the upper spec limit is 0.6.Ĭalculating the Mean and Overall Standard Deviation This sample data set is from a manufacturer of cable wire the data was collected in subgroups of 5, then the diameters of the cables were recorded and entered in the Minitab worksheet. Go to File> Open Worksheet, click the Look in Minitab Sample Data folder button at the bottom, and open the dataset named CABLE.MTW. To illustrate the calculation of Ppk and Cpk, we’ll use a sample data set available in Minitab. Under the Potential capability heading we find the formulas for Cpk, and under Overall capability we find the formulas for Ppk. If we click Estimating standard deviation, we can find the formulas for the pooled standard deviation. The Methods and Formulas section shows the formulas Minitab uses. Then, from the Help window shown below, click the see also link, and then choose Methods and formulas: To see details of the formulas used, we can click the Help button in the lower-left corner. If we click the Estimate button in the dialog box that comes up, we can see the default methods used in Minitab:įrom the dialog box above, we can see that Minitab 17 uses the Pooled standard deviation when subgroup sizes are greater than 1. Then, in my next post, I’ll show you how to calculate Cpk.įor data that follow the normal distribution, we use a Normal Capability Analysis ( Stat> Quality Tools> Capability Analysis> Normal). So in this post I will show you how to calculate Ppk using Minitab’s default settings when the subgroup size is greater than 1. Michelle Paret already wrote a great post about the differences between Cpk and Ppk, but it also helps to have a better understanding of the math behind these numbers. In technical support, we frequently receive calls from Minitab users who have questions about the differences between Cpk and Ppk. We also are developing a 1-day training course called Detecting and Analyzing Non-Normal data to be released in 2015. Minitab will deliver a presentation on Detecting and Analyzing Non-Normal Data at the IHI conference in Orlando FL on Monday, December 8th 2014. It suggests that the Normal distribution is a good model for the difference in weights for this surgery. The resulting graph from one iteration of these steps is shown below. Repeat steps 1-3 several times if you want to see how the results are affected by the simulated values.Create a normal probability plot using Stat > Basic Statistics > Normality Test.Use Calc > Calulator to add the noise column to the original column of data.Store simulated noise values from -0.5 to +0.5 in a column using Calc > Random Data > Uniform.In effect, we want to add a random value from -0.5 to +0.5 to each value to get a simulated measurement. The difference in weight values were rounded to the nearest pound. How can we see a probability plot of the true weight differences? Simulation can used to show how the true weight differences might look on a probability plot. A probability plot that supports using a Normal distribution would be helpful to confirm the Ryan-Joiner test results. In this example, the Ryan-Joiner p-value is above 0.10. The Ryan-Joiner test generally does not reject normality due to poor measurement resolution. In a previous blog post ( Normality Tests and Rounding) I recommended using the Ryan-Joiner test in this scenario. The Anderson-Darling Normality test typically rejects normality when there is poor measurement resolution. If the true measurement can take on any value (in other words, if the variable is continuous), then the cause of the clusters on the probability plot is poor measurement resolution. This occurs on a probability plot when there are many ties in the data. The red line appears to go through the data, indicating a good fit to the Normal, but there are clusters of plotting points at the same measured value. The probability plot above is based on patient weight (in pounds) after surgery minus patient weight (again, in pounds) before surgery. Have you ever had a probability plot that looks like this?
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