U Chart

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:05 Now let's look closely at the attribute data control chart known as the U chart.
• 00:11 >> The U chart gets its name because it's a chart of counts per unit.
• 00:16 With this chart, you must count two things in each subgroup.
• 00:19 A count of all the defects that occurred in that subgroup, which will
• 00:23 also be a whole number, and a count of the number of units in the subgroup.
• 00:28 Depending upon how you've defined a unit, that can be a fraction or
• 00:32 a decimal number.
• 00:34 The U chart is very useful for
• 00:35 tracking defects in the process with a volume can vary greatly.
• 00:40 By normalizing over the number of units, we can see whether the change in
• 00:44 the number of defects is really a change in the process or
• 00:47 just due to a volume change.
• 00:49 If there's a change in the process, the defects per unit will change.
• 00:53 If there's only a change in process volume, the units and defects change, but
• 00:58 the defects per unit will be within the bounds of statistical control.
• 01:02 This is why the U chart is such a good chart for
• 01:05 tracking processes with erratic flow.
• 01:07 >> Let's look at an example of a you U chart.
• 01:10 Of course it also has all the standard control chart elements of a mean and
• 01:14 control limits.
• 01:16 And you can see that the y-axis is the ratio of counts per unit.
• 01:21 A difference with this chart from the other control charts that we have seen so
• 01:26 far is that the control limits are normally recalculated with every new data
• 01:30 point.
• 01:31 You'll see that the control limit calculation is based in part upon
• 01:34 the subgroup size, and as that changes, the control limits will change.
• 01:39 This is a pain to recalculate if you're doing this chart by hand, but
• 01:42 if you automate things, it's not so bad.
• 01:45 An alternative approach to doing this by hand is to calculate the control limits
• 01:49 with the average of the subgroup size.
• 01:51 In this case, the control limits will be a straight line.
• 01:55 And as we saw with other attribute data control charts, the lower limit cannot be
• 02:00 less than zero, you can't have a negative count of defects.
• 02:04 Well, we went through the steps of creating a control chart in previous
• 02:07 modules, but let's look at some specific items about the U chart.
• 02:11 The unit sizing is a little funky on this one and that's where we want to start.
• 02:16 We must determine the definition of a unit size.
• 02:19 Now in many cases, it's an obvious physical unit such as a truckload
• 02:23 shipment, but often it is somewhat arbitrary.
• 02:26 For instance, in manufacturing environments, I have said a unit size to
• 02:29 be a specific quantity of items manufactured such as 50 or 100.
• 02:34 Now within each subgroup, count the number of units, this may be a whole number or
• 02:39 it may be a fraction.
• 02:40 Subgroup should be calendar based, such as a day or a week.
• 02:44 Remember the horizontal axis of the control chart is usually time.
• 02:48 Now normally we want to have a subgroup where the average number of
• 02:51 defects is at least 5, but this is a process with erratic flow.
• 02:56 So you may have some subgroups with very low unit volumes and
• 03:00 therefore low defect count.
• 03:03 Now count the number of attributes or defects for your subgroup, and
• 03:06 you can calculate the U ratio of defects per unit for that subgroup.
• 03:11 When you have enough data points, calculate your mean and
• 03:14 initial control limits.
• 03:15 But this chart,
• 03:16 you will need to recalculate control limits after each new data point.
• 03:21 Now, plot your data points, mean, and control limits.
• 03:24 And of course,
• 03:25 if the chart shows that the process is not at control, take action to stabilize it.
• 03:30 >> Let's look at how we do the calculations manually or in Excel.
• 03:34 As with the other modules, the formulas are shown on the right side of the screen
• 03:38 and the calculation steps are discussed on the left side.
• 03:42 The first step is easy, count the number of attributes in each subgroup, and
• 03:46 then the number of units and put it in your spreadsheet.
• 03:49 I normally put those data points and adjacent columns, then calculate the U
• 03:53 ratio, which is the defects divided by the units for each subgroup.
• 03:59 The U ratio mean is calculated by taking all the defects and all the units for
• 04:04 your initial subgroups and dividing them.
• 04:07 Do not average the daily or weekly U ratios.
• 04:10 That would give too much weight to those ratios from days with little volume and
• 04:15 not enough weight to those with high volume.
• 04:18 Also, if you're going to use straight-line control limits,
• 04:21 you'll need to determine the average number of units in a subgroup.
• 04:26 Next, calculate the control limits.
• 04:28 This is done by multiplying 3 times the square root of the main value for
• 04:33 the data set divided by the sample size or that specific subgroup.
• 04:38 Then add that product to the mean for the upper control limit and
• 04:42 subtract that product from the mean for the lower control limit.
• 04:46 But remember, the lower control limit can never be less than 0.
• 04:50 Again, a less precise control limit would divide the mean value for
• 04:54 the data set by the mean value for the number of units in a subgroup,
• 04:59 essentially, using n bar instead of n.
• 05:03 If using Excel, you can plot your data than mean value and the upper and
• 05:08 lower control limits using the Line Chart graphing option.
• 05:12 >> Now let's look at creating this chart in Minitab.
• 05:16 Go to the start menu, select Control Charts, then select Attribute Charts and
• 05:20 finally, select the U Chart.
• 05:22 When you do that, you should get a panel that looks like this.
• 05:25 Place your cursor in the variables window to activate the column display.
• 05:29 Highlight the column where your defect is located, then click the Select button.
• 05:33 And your data column should now be in the Variables window.
• 05:37 Do not use the column with the U ratio,
• 05:40 minitab will calculate that from your Defect and Units column.
• 05:44 You now have to identify where the unit size is for each subgroup.
• 05:48 Put your cursor in the subgroup size window,
• 05:51 highlight the column with the subgroup size Click the Select button.
• 05:55 That column should now show in the subgroup size window.
• 05:59 You're ready now to create the chart, click the OK button at the bottom and
• 06:03 Minitab will generate it for you.
• 06:06 >> So that's the U Chart, the attribute data control chart
• 06:09 that shows us defects per unit and variable subgroup sizes

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