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About this lesson

This lesson discusses the principles of using control charts with variable data and provides ground rules for data sampling. The differences between the variable data SPC control charts are explained.

Quick reference

Variable Data

There are three control charts that are normally used to monitor variable data in processes.  Each chart has ground-rules for the subgroup size and differences in how the control limits are calculated.

When to use

If the critical product or process parameter being monitored is measured using variable data measurement techniques, that a variable data SPC control chart should be used for tracking and controlling that parameter.

Instructions

Variable data control charts are created using the control chart process discussed in an earlier lesson.  The data on these charts is measured data.  These control charts are always shown in pairs with one chart plotting the data value or a representative of the data value and the other chart plotting a measurement that represents the variation or dispersion of the data in the subgroup.   The control charts will follow the typical pattern of a time-based plot of sequential data points, with a mean value line and both upper control limits and lower control limits. 

The selection of which chart to use will defend upon the size of the data sample in the subgroup.

  • When the subgroup sample size is a single data point, use the I-MR charts.
  • When the subgroup sample size is two to ten data points, use the XbarR charts.
  • When the subgroup sample size is greater than ten data points, use the XbarS charts. 

The size of the subgroup sample is based upon several factors.  If the data collection is manual, the collection can be expensive.  In that case, you would prefer to just sample the process rather than doing 100% checking of the parameter.  If the process uses batches, the sample should represent the batching.  If the process is continuous flow, the subgroup will represent a portion of the flow.  Normally, the subgroup is selected so that each sample represents approximately the same amount of flow.  If the process is an infrequent process, the sample should represent that particular iteration of the process execution.   If the data may contain some attributes that is non-normal, the sample can apply the Central Limit Theorem which creates a normal data set from non-normal data.   It is helpful if the data is non-normal to use an odd number of data points in the sample so that there is a clear median value.

When Shewhart developed these control charts, he was using three standard deviations as his guide for control limits, but the statistical derivations had to bring into consideration the uncertainty of small sample sizes.  Ultimately, a set of tables with constants was created and these are used in the calculations of control limits.  These tables are presented here, because some of these constant values are used with multiple variable data control charts.   Notice that the first column in both tables is the subgroup sample size.

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Hints & tips

  • Use a subgroup size that makes sense for how the process works.  If each item is being uniquely processed, use the I-MR.
  • If the process works in batches use the batch as the subgroup.
  • If the process runs at set times periods, let each time period be a subgroup.
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  • 00:04 Hi, I'm Ray Sheen.
  • 00:05 Well we're now going to go through each of the different types of control charts that
  • 00:10 are typically used in business applications.
  • 00:12 I'll start with a discussion of the charts that use variable data.
  • 00:18 When I'm using the term variable or continuous data,
  • 00:21 it means data that is measurable on a scale.
  • 00:24 So every increment along the scale is meaningful.
  • 00:27 And if I had better scale, I could measure it even more significant digits.
  • 00:32 Variable data charts are an adaptation to the basic run chart that charges track to
  • 00:37 parameter over time and did not attempt to calculate control limits.
  • 00:41 Think of this now as a run chart on steroids.
  • 00:44 They have a lot more power and create better and
  • 00:46 faster insight than the basic run chart.
  • 00:49 But since it is similar to a run chart, you'll see that the x axis is the same.
  • 00:53 It's time based dimension either calendar time, like a day or a week, or
  • 00:58 a set of items being measured that are created or modified sequentially.
  • 01:02 And the y axis is the data parameter we're measuring in the appropriate units of that
  • 01:07 measurement.
  • 01:07 There are several different ways that this will be shown depending upon the control
  • 01:12 chart used.
  • 01:12 It might be the actual value of each parameter or might be the average or
  • 01:16 mean of a subgroup sample of that parameter.
  • 01:19 And these charts always come in pairs,
  • 01:22 with the second control chart of some aspect of the range among data points.
  • 01:26 It could be the range from the last point or
  • 01:29 the range from min to max within the subgroup data.
  • 01:33 And of course, since these are control charts,
  • 01:35 they have included the mean value and the upper and lower control limits.
  • 01:39 These are at approximately three standard deviations from the mean, but
  • 01:43 not precisely and we'll go through the calculations for
  • 01:46 each chart which is unique.
  • 01:48 Also some of the charts have a limit on the lower control limit.
  • 01:51 It cannot be a negative number.
  • 01:53 So if the calculation indicates a negative value, we'll replace that with zero.
  • 01:57 So let's go back to a slide that we use in another module,
  • 02:01 which shows the different types of control charts.
  • 02:04 I'm talking about the variable data control charts.
  • 02:06 There are three of them, the I- MR, which means individual moving range,
  • 02:11 the Xbar- R chart, which plots the subgroup mean and the subgroup range.
  • 02:15 And finally, the Xbar- S chart, which plots the subgroup mean and
  • 02:19 the subgroup standard deviation.
  • 02:21 Which chart you use depends upon your subgroup size,
  • 02:25 a subgroup of 1, use I- MR, a subgroup of 2 to 10 use Xbar- R,
  • 02:31 and a sub group greater than 10 use Xbar- S.
  • 02:34 We'll talk about the other control charts when we get to those sections.
  • 02:38 So since our charts selection is based upon subgroup size, let's look at that.
  • 02:43 This is one of those times when life where size matters.
  • 02:47 Data collection can be an expensive and slow process, especially if it is manual.
  • 02:52 In those cases, we often prefer to just sample the data.
  • 02:55 But then the question becomes, how is the sample selected and
  • 02:59 what is the subgroup size that it represents?
  • 03:02 There are several important considerations when selecting the size of a subgroup.
  • 03:07 If the process is a batch process, then select your samples from the same batch,
  • 03:12 not from multiple batches.
  • 03:13 If the process is a continual flow process, then determine what
  • 03:18 is a logical interval for flow, usually based upon a time interval or
  • 03:22 quantity of units and collect your samples from each time based group.
  • 03:26 If the process is an infrequent process, then each time it is run,
  • 03:31 that would represent the subgroup from which the sample is selected.
  • 03:35 One comment on the sample quantity, if the data is non normal, I recommend that
  • 03:40 an odd number of data points in your sample, so that there is a clear medium.
  • 03:45 Also a large sample size will likely result in a more normal
  • 03:49 representation of the process data due to central limit theorem.
  • 03:54 There may be other physical or
  • 03:55 business considerations that lead to a logical subgrouping.
  • 03:59 For instance, I had a manufacturing operation that ran around the clock.
  • 04:03 But during the second and third shift, the process had to run a little differently,
  • 04:08 because some of the other business support functions only work during first shift.
  • 04:13 When plotting the cycle time data, which was one of the primary ways we control
  • 04:17 the process, there was a clear pattern that was related to each of the shifts.
  • 04:21 And that effect was bigger than the normal variation.
  • 04:25 So we would take the data from all three shifts in our subgroup to create
  • 04:29 a value for the day.
  • 04:31 This essentially zeroed out the shift effect and allowed us to establish and
  • 04:36 maintain statistical control for the process.
  • 04:39 When Shewhart developed these charts and the others who have helped to refine them,
  • 04:44 they found that the size of the subgroup samples not only affected the kind of
  • 04:48 chart to use, it also affected the control limit calculation.
  • 04:52 As we get into the calculations, you will find that we need to refer back
  • 04:56 to these tables to obtain constants that are used in the calculation.
  • 05:01 The derivation of these values is beyond what we can cover in this course.
  • 05:05 Practically speaking, if doing the calculations by hand,
  • 05:08 you will refer to a lookup table with these values, or if using statistical
  • 05:13 software like Minitab, the values are already built into the software.
  • 05:17 If you plan to sit for Lean Six Sigma Belt exam with the International Association of
  • 05:22 Six Sigma certification, the tables will be provided within the reference guide.
  • 05:27 So keep these files handy for reference while you are doing the I-MR, Xbar -R and
  • 05:32 Xbar- S charts in the next few lessons.
  • 05:35 Much of the data that we use to track process performance is variable or
  • 05:40 continuous data.
  • 05:42 When that's the data that you have available,
  • 05:45 use your subgroup size to select the appropriate variable data control chart.

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