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PPM Charts

Abstract: Simple Calculations to create PPM charts

PPM is short for Parts Per Million. A PPM Chart reports data in units of parts per million. The most direct way to get a chart like this is to convert your data to the proper units, and then display the chart.

For example, take a look at the data we include with Statit in the workspace file, pvarn.wrk. Read this data into Statit using the Open Workspace dialog or the GETFILE command and you will find three variables. The Date variable identifies the day on the which the data was collected. On the given day, a number of pieces were tested and this number was put in the Inspected variable. Of those pieces, a certain number failed the test and this number was put in the Rejected variable. The data looks like this:

 Inspected Rejected Date 3350 31 01-Nov-1991 3354 113 01-Nov-1991 1509 28 01-Nov-1991 2190 20 01-Nov-1991

A p Chart is appropriate for looking at this data. The data variable is the number rejected and the subgroup size is the number inspected. You can have the p Chart display either the fraction or the percent rejected. Try these commands:

gpchart Rejected by Inspected /axis=Date
gpchart Rejected by Inspected /axis=Date /percent

As this shows, the data we have gives us the fraction of the total inspected that were rejected. To display this as the number rejected in units of PPM, we first convert the data to these units. This is done by the following expression:

let PPM = (Rejected / Inspected) * 1e6

This creates the variable PPM, which contains the fraction of 1,000,000 pieces (PPM) which would have been rejected if there were 1,000,000 pieces inspected every day. (1e6 is a short way of expressing 1,000,000.) Since we now have this calculated value, we use an X chart (also called I or Individual or Run chart) to display this:

gichart ppm by 2 /axis=Date /ymin=0

Note that we specify a minimum Y value, since this attribute data will not go below 0. Notice that the control line, which is calculated, is now straight because the subgroup size is constant. We are not concerned with specifying the 2 for the subgroup size on this command because the subgroup size is already included in the calculation of the PPM values and is used here for the control limit calculation.