Locked lesson.

Upgrade

About this lesson

This lesson discusses the unique considerations associated with monitoring attribute data with control charts. It compares and contrasts the various attribute data control charts and provides some ground rules for subgroups selection.

Quick reference

Attribute Data Control Charts

There are four control charts that are normally used to monitor process attribute data.  There are specific groundrules for determining which chart to select and the size of the subgroup to be used.

When to use

If a critical process output or process parament is attribute data – in particular pass/fail defect data – an attribute control chart should be used with the process.

Instructions

Attribute data control charts are created using the control chart process discussed in an earlier module.  The data on these charts will either be defects or defectives.  The selection of which chart to use will depend upon whether charting defects or defectives and whether the sample or subgroup size being used is fixed or varies.  The table below shows the differences between the chart types.

Unlike variable data control charts, the attribute control chart is a singular chart.  There is no accompanying range chart.

The subgroup sizes for attribute charts are selected to allow an application of the central limit theorem in order to convert the pass/fail attribute data into a normal curve.   Based upon this principle, the following ground rules should be followed.

  • C charts should use subgroup sizes that create a mean of the subgroup that is greater than 2.
  • U charts should use subgroup sizes so that there are at least five defects in each subgoup.
  • P and NP should use subgroup sizes where the product of the subgroup size times the average of the subgroup proportions is greater than five, and the product of the subgroup size times the average of one minus the subgroup proportion is greater than five.   This leads to a minimum value of 10 when the proportion is 50% and it will grow as the proportion average gets farther from that value.

Hints & tips

  • You may need to try several different subgroup sizes until you find one that meets the ground rules.
  • Although the four different types of charts plot attributes with different units, you still apply the control limits and special cause criteria in the same manner.
Login to download
  • 00:04 Hello, I'm Ray Sheen.
  • 00:06 There are several control charts that are used with attribute process data.
  • 00:10 Let's do a quick overview of these charts.
  • 00:14 Attribute data control charts use discrete data typically pass fail data.
  • 00:19 There is no in between values, these charts are an adaptation of run charts
  • 00:24 that are used to track process performance.
  • 00:26 The X axis is time or sequence of units just like all the other control charts.
  • 00:32 The Y axis will be a count of the number of fails or
  • 00:34 a count of the proportion of fails in the subgroup sample.
  • 00:38 These might be things like the number of defects per order that are shipped,
  • 00:42 or the percentage of late submittals on a given week.
  • 00:46 Unlike the variable data control charts that come in pairs,
  • 00:49 the attribute control charts will be singular.
  • 00:52 There is no second chart tracking range or standard deviation.
  • 00:55 And there are four different attribute data control charts.
  • 00:59 And just like the variable data control charts depended on subgroup sample size,
  • 01:03 we use that as one of the criteria for selecting our control charts.
  • 01:07 But there are some other data characteristics that will become
  • 01:10 important also.
  • 01:12 So lets look again at the control chart selection decision tree.
  • 01:16 Recall that we start with a decision concerning what type of data is
  • 01:20 appropriate to monitor for this process.
  • 01:23 Now that data is attribute data, we pick one of these four chart types.
  • 01:27 As you can see they differ depending upon whether they are plotting actual defects
  • 01:32 or defective units which could have multiple defects.
  • 01:35 And also they differed depending upon the subgroup sample size characteristics.
  • 01:40 And of course we'll discuss the other control charts in their time.
  • 01:44 Let's go into more detail considering some of the four
  • 01:47 attributes of these data chart types.
  • 01:50 In this table, we can compare the four chart types side by side.
  • 01:54 I'll start with the two charts that focus on a count of all the defects.
  • 01:58 First, there is the C Chart, this is just basic chart of counts of the attributes
  • 02:03 normally, that means the defect within the subgroup or sample.
  • 02:07 It will always be a whole number.
  • 02:08 One constraint on this chart is that the sample sizes are equal.
  • 02:12 That way we'll know the increase in the count is truly a quality problem, and
  • 02:17 not just an increase in the process output.
  • 02:20 The U Chart still count the number of defects, but
  • 02:22 now takes to the consideration the variable subgroup sample size.
  • 02:26 So it must also count the numbers of unit to go through the process
  • 02:30 in order to normalize the count of defect.
  • 02:32 This means that the value that is plotted is a count per unit,
  • 02:36 defects per unit for the subgroup sample.
  • 02:39 This is normally a decimal or fractional number, let me be clear,
  • 02:43 we’re not counting the number of defective units.
  • 02:46 We’re looking at the total number of counts or defects per unit.
  • 02:51 All these defects could be on just one unit, or
  • 02:53 they could be spread across many units.
  • 02:56 The other two charts do focus on defective units rather than defects.
  • 03:01 First is the NP Chart,
  • 03:03 it counts the number of defectives in the sample, not the number of actual defects.
  • 03:08 For a unit to be defective, it must have at least one defect.
  • 03:12 But having more than one does not make it any more defective.
  • 03:15 The NP Chart, like the C Chart will be a whole number count.
  • 03:19 And like the C Chart, it can do this because the sample size is constant.
  • 03:24 The second chart for defective units is the P Chart.
  • 03:27 This chart plots the percentage or
  • 03:29 proportion of the defective units within the subgroup sample.
  • 03:32 This will always be a number between zero and one, since it is the proportion or
  • 03:36 percentage that are defective.
  • 03:38 And since it is a proportion, it can easily adapt to any sample size.
  • 03:44 The final question to address with these charts is how to choose a subgroup or
  • 03:48 sample size.
  • 03:50 The control group limits are definitely affected by the subgroup sample size.
  • 03:54 Not in the same way that the variable data charts have used different constants for
  • 03:58 different subgroup sizes.
  • 04:00 Rather in this case the key is normality of the data,
  • 04:03 keep in mind we're dealing with count data.
  • 04:05 And unless the central limit theorem is applied,
  • 04:07 that can often be non-normal data.
  • 04:11 So subgroup samples are usually used to normalize that data.
  • 04:15 There are some rules of thumb that we should apply to ensure that the control
  • 04:18 limit calculations will work.
  • 04:20 I know from experience that violating these can be a problem.
  • 04:23 On one occasion I tried to violate a rule thinking that,
  • 04:26 well it wouldn't really matter much.
  • 04:28 And then I found that I was trying to take the square root of a negative number.
  • 04:32 Well that doesn’t work when you’re trying to calculate control limits.
  • 04:35 So for C Charts, your subgroups are large enough that the average or
  • 04:40 mean count of defects is greater than 2.
  • 04:43 For U charts you can have a variable size subgroup, but strive for
  • 04:47 subgroup size that has at least 5 defects within that subgroup.
  • 04:51 We’ll also have to talk about the size of a unit when we get to the U Charts.
  • 04:56 The P Charts and NP Charts use the same rules.
  • 04:59 The subgroup size times the average of the defective units, n, times the average of 1
  • 05:04 minus the proportion of defective units must be greater than 5.
  • 05:08 That means a minimum size of ten units and often many more.
  • 05:15 Well attribute data can be charted easily with control charts.
  • 05:18 Just make sure you understand your data and sample size, and
  • 05:22 that you use it to select the right chart.

Lesson notes are only available for subscribers.

PMI, PMP, CAPM and PMBOK are registered marks of the Project Management Institute, Inc.

Gift this course