P Chart

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:05 Well, now let's look at the attribute data control chart known as the P chart.
• 00:12 The P chart gets its name because it's a chart of a proportion, or percentage.
• 00:17 This chart is used with pass/fail data.
• 00:20 It tracks the percentage of passes or fails.
• 00:23 It determines the percentage of each subgroup and
• 00:26 it is that percentage which is plotted on the P chart.
• 00:30 The P chart is tracking defectives, not defects.
• 00:34 That means that the percentage is a percentage of units that have no defects.
• 00:38 Whether a unit has one defect or
• 00:40 it doesn't, it counts the same as one defective unit.
• 00:44 The control chart is unique, it is the only one that plots percentages or
• 00:49 proportions.
• 00:50 That means that the y-axis will always be a value between 0 and 1.
• 00:55 I often see this type of chart used to track error rates for processes,
• 00:59 such as error rates while processing an order or error rates on forms submitted.
• 01:05 Let's look at an example of a P chart.
• 01:07 Of course, it also has all the standard control chart elements of a mean and
• 01:11 control limits.
• 01:13 You see on this one we have an out of control condition out at 0.28.
• 01:17 The rule that was violated was 14 consecutive points in an up-down pattern.
• 01:23 That normally means there's some extra control function acting on the process and
• 01:27 trying to compensate for the previous value.
• 01:30 It's not just random variation.
• 01:32 And you can see that the y-axis is the percentage or proportion of defects.
• 01:38 You can also turn this around and measure the proportion of successes.
• 01:43 As with another chart that we've discussed,
• 01:45 the control limits are recalculated with every new data point.
• 01:49 You will see that the control limit calculation is based in part
• 01:52 upon the subgroup size, and as that changes, the control limits will change.
• 01:58 Now, this is a pain if you're doing this calculation by hand, but
• 02:01 it's easy to do if the process is automated.
• 02:04 An alternative form of calculating the control limits is to use the mean
• 02:08 of the subgroup size, and then the control limit line is a straight line.
• 02:13 As we saw with other attribute data control charts, the lower control limit
• 02:17 cannot be less than 0, you can't have a negative count of defects.
• 02:22 But something else a little special about this chart is that the upper control limit
• 02:26 cannot be greater than 1.
• 02:27 The maximum number of defective units in a subgroup is all,
• 02:33 and that would be 100% of the value, or 1.
• 02:37 Well, we went through the steps of creating a control chart in the previous
• 02:40 module, now let's look at some specifics about the P chart.
• 02:44 We need a count of the number of units in each subgroup.
• 02:47 The P chart is used when the subgroup per sample size varies.
• 02:51 I normally put these values in one column of my spreadsheet.
• 02:54 Next, in each subgroup you determine the number of defectives,
• 02:58 that means a unit with at least one defect.
• 03:01 It could have more than one, but that does not increase its score as a defective.
• 03:05 Incidentally, we want to be using subgroup sizes so
• 03:08 that the number of units times the proportional mean is greater than 5.
• 03:13 Or, if the proportional mean is above 50%,
• 03:16 use the number of units times 1 minus the proportional mean.
• 03:20 Next, calculate the proportional mean and the control limits.
• 03:23 These must be calculated after each new subgroup, since the number of units
• 03:27 affects these limits and they change with every subgroup.
• 03:30 Now plot your proportion, the mean, and the control limits.
• 03:34 And of course,
• 03:35 if the chart shows that the process is not in control, take action to stabilize it.
• 03:39 Let's look at how we do the calculations manually or in Excel.
• 03:43 As with the other modules, the formulas are shown on the right side of the screen
• 03:47 and the calculation steps are discussed on the left side.
• 03:51 The first step is straightforward, count the number of units in the subgroup and
• 03:55 the number of defective units.
• 03:57 With those two values, you can calculate the proportion or
• 04:00 percentage of the subgroup units that are defective.
• 04:04 Now calculate the mean of the proportion and a mean for the subgroup size.
• 04:09 We will calculate the mean of the proportion by adding up
• 04:12 the total number of defectives and dividing by the total number of units.
• 04:17 So the mean will change with each new data point.
• 04:20 The mean for the subgroup size is the total number of units of all subgroups
• 04:25 divided by the number of subgroups, and
• 04:28 with that you're ready to calculate the control limits.
• 04:30 This is done by multiplying 3 times the square root of the proportional mean,
• 04:35 times 1 minus the proportional mean,
• 04:38 divided by the subgroup size for each point.
• 04:43 Add this product to the proportional mean to get the upper control limit, and
• 04:47 subtract it to get the lower control limit.
• 04:49 An alternative method to calculating the control limit, that is easier but
• 04:54 not as precise, is to use the mean of the subgroup size and
• 04:58 calculate the limits once.
• 05:00 The upper control limit and the lower control limit are then straight lines and
• 05:04 don't vary with each new data point.
• 05:07 Keep in mind, upper control limit cannot be greater than 1 and
• 05:10 lower control limit cannot be less than 0.
• 05:13 If using Excel you can plot your data, the mean value, and
• 05:17 the upper and lower control limits using the Line Chart graph option.
• 05:22 Now let's look at creating this chart in Minitab.
• 05:25 Go to the Stat menu, select Control Charts, then select Attribute Charts, and
• 05:29 finally select the P chart.
• 05:31 When you do that, you should get a panel that looks like this.
• 05:33 Place your cursor in the Variables window to activate the column display.
• 05:38 Highlight the columns where your defective units are located,
• 05:41 then click the Select button.
• 05:43 Your data column should now be in the Variable window.
• 05:47 Do not use the column with the P ratio,
• 05:50 Minitab will calculate that from your defectives and unit columns.
• 05:54 Next you have to identify where the unit size is for each subgroup.
• 05:58 Put your cursor in the Subgroup size window,
• 06:01 then highlight the column with that subgroup and click the Select button.
• 06:05 That column should now be in the Subgroup size window.
• 06:09 Now you can click on the OK button in the bottom of the panel and
• 06:12 Minitab will generate your control chart.
• 06:15 So that's the P chart, the attribute data control chart that shows
• 06:19 us the percentage of errors or defects in variable size subgroups.

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