I-MR Chart

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:06 Let's take a close look at the first of our variable data control charts,
• 00:10 the I-MR Chart.
• 00:12 The I-MR Chart stands for Individual and Moving Range.
• 00:17 I-MR is a pair of control charts that work together.
• 00:21 The individual chart is the chart of the data values that have been measured.
• 00:25 This is normally the product or process parameter that we're trying to control.
• 00:29 It might be the dimension on a product, or the cycle time for a process step.
• 00:34 Well the control limits we will calculate will help to control the process.
• 00:38 We also want to be using this second chart, the moving range chart.
• 00:42 Moving range is defined as the absolute value
• 00:46 of the difference between this data point and the previous data point.
• 00:49 In other words, the magnitude that the movement or
• 00:52 variation that we saw between adjacent individual values.
• 00:56 So when do we use an I-MR chart?
• 00:58 Well, it's the simplest and most basic of the variable data charts.
• 01:02 And I find that it is often to be very useful when I'm dealing
• 01:05 with a process that has relatively low volume, and therefore,
• 01:08 there are not many data points to work with.
• 01:11 Each data point takes on a heightened importance in that case.
• 01:14 Also, if a process works on each item uniquely and separately, so
• 01:19 that there is no logical subgrouping, then use I-MR.
• 01:23 And because it is the simplest of the variable data control charts to work with,
• 01:27 I'll often start with it when I'm first setting up and analyzing a process.
• 01:32 So let's look at an example of an I-MR chart.
• 01:35 As you can see, it is a pair of charts,
• 01:38 the individual chart normally shown above the moving range chart.
• 01:41 They usually have the exact same exact time scale, so
• 01:44 they can be lined up one above the other.
• 01:46 This makes it easier to see the impact of a special cause.
• 01:50 There are a couple of interesting points about the moving range chart.
• 01:53 First, there’s no data point that corresponds with the first
• 01:56 individual data point.
• 01:58 Remember, the moving range is the absolute value of the difference
• 02:01 between the current data point and the previous data point point.
• 02:04 Well, for the first data point, there is no previous data point, so
• 02:07 there is no moving range.
• 02:09 Also, the lower control limit is always 0.
• 02:12 The moving range value is always a positive number because it is the absolute
• 02:16 value of the difference.
• 02:17 Therefore, it's impossible to be less than 0.
• 02:21 And if two adjacent points are identical, the moving range value will be 0.
• 02:25 On this chart, we see that the points 12, 13 and 14 appear to be the same value.
• 02:31 And therefore, the moving range between them is 0.
• 02:34 Also, on this individuals chart, we have a special cause occurring at point 19.
• 02:39 There have been nine consecutive data points above the mean.
• 02:43 The process should have been stopped at that point, and
• 02:45 an investigation done to understand the cause.
• 02:48 Well, I went through the steps of creating control chart in a previous module.
• 02:52 But let's look at some of the specific or unique elements of the I-MR chart.
• 02:56 The first step is a generic step for all variable data.
• 02:59 Determine how you will sample the data.
• 03:02 Now in this case, we want every data point, so
• 03:04 the only question is when to start collecting it.
• 03:07 Next, take the measurement of the individual data point.
• 03:10 I normally put that data in one column on my spreadsheet, or
• 03:13 we next calculate the moving range.
• 03:16 It is the absolute value of the difference between this point you just measured, and
• 03:20 the previous point.
• 03:22 So, obviously there's no moving range value for
• 03:24 the individuals chart point number one.
• 03:28 Now, calculate the control limits for the moving range.
• 03:31 I'll show you how to do this on the next slide.
• 03:33 Then create the moving range chart.
• 03:36 If the moving range chart is not in control,
• 03:39 find the sources of special cause and eliminate them.
• 03:42 Once the moving range chart is in control, calculate the control for
• 03:46 the individual plot, and create the individuals chart.
• 03:49 And again, I will show you how to do that on the next slide.
• 03:52 But notice the order.
• 03:54 You must first get the moving range in control before the individuals plot.
• 03:58 That is because we'll be using the moving range value to calculate the individual
• 04:02 plot control limits.
• 04:03 If the moving range is unstable, you can’t trust the values you calculate for
• 04:07 the individual chart.
• 04:08 So if the individuals plot is out of control,
• 04:12 now take the action needed to correct that.
• 04:15 Let's look at how we do the calculations manually, or
• 04:17 if we were to program that in Excel.
• 04:19 The actual formulas are shown on the right side of the screen, and
• 04:23 the calculation steps will be discussed on the left side.
• 04:26 Collect and store your data in order that it goes through the process.
• 04:31 I normally have the first column with a data point number, and
• 04:34 a second column with the actual data value that was measured.
• 04:38 Then in the third column, I'll calculate the moving range by taking the absolute
• 04:42 value of the difference between this data point and the previous one.
• 04:46 Now, calculate the mean or average value for the individual values, and
• 04:51 the moving range values.
• 04:53 Calculate the upper control limit of the moving range
• 04:56 by multiplying the constant d4 times the mean of the moving range.
• 05:01 The lower control limit of the moving range is always at 0.
• 05:04 Once the moving range chart is in control, calculate the control limits for
• 05:08 the individuals plot.
• 05:10 Do this by multiplying 3 times the mean value for the moving range, and
• 05:15 dividing that product by the value of the d2 constant.
• 05:20 Take this result, and add it to the mean value of the individuals plot
• 05:24 to get the upper control amount for the individual plot, and subtract this product
• 05:29 from the mean value of the individuals to get the lower control of it for
• 05:33 the individuals plot.
• 05:35 You can create the actual graphs in Excel by using the line chart option
• 05:39 on the graphics tool.
• 05:42 Now let's look at the creation of this chart in Minitab.
• 05:45 Go to the Stat menu, select Control Charts, then select Variable Chart for
• 05:50 Individual, and finally, select the I-MR Chart.
• 05:54 When you do that, you should get a panel that looks like this on your screen.
• 05:58 Place your cursor on the Variables window to activate the column displays.
• 06:03 Highlight the column where your data is located, then click the Select button.
• 06:07 Your data column should now be in the Variable window.
• 06:10 You don't need to select your moving range column,
• 06:13 Minitab will do that calculation on its own.
• 06:16 Remember, you can cut and paste data between Excel and Minitab.
• 06:20 Now, click on the OK button at the bottom of the panel, and
• 06:23 Minitab will generate your control chart.
• 06:27 So, that's the I-MR chart, the basic chart for
• 06:30 variable processed data that's collected one point at a time.

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