WEBVTT
NOTE Copyright (c) GoSkills Ltd, 2013 - 2022
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Hi, I'm Ray Sheen.
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Well now,
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let's take a look at the variable data control chart called the Xbar- S Chart.
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The Xbar and standard deviation, or Xbar- S Chart, is also a pair of charts.
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The Xbar and S chart are used when subgroups have a large sample size.
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And by large, I mean more than ten.
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With large sample size in the subgroup, the standard deviation is a better measure
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of variation than the range because it uses all the data, not just the extremes.
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Also a very significant advantage to the Xbar-S chart is that sample group size can
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vary as long as all the sample groups have at least ten data points.
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This chart relies on variable data meaning data measured on a scale
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with the possibility of even more precise values of
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using a scale with better discrimination.
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But this chart only needs a small subgroup sample of the data
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rather than every data point.
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The two plots of the Xbar and
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S chart are first the Xbar which is the mean of the subgroup sample points.
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This is the same thing that we had with the Xbar-R.
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But the second plot is different.
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The S is the standard deviation of the subgroup data points.
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In both parts, we'll have a sense of central tendency with a calculation of
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the mean and a level of variation with the calculation of the control limits.
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By using multiple points of the sample, this technique employs
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the Central Limit Theorem to increase the normality of the data.
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So let's take a look at an example of the Xbar-S Control Chart.
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Once again, it is a pair of charts.
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The Xbar chart is the plot of the mean value of each of the subgroup samples.
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The S chart plots the subgroup's standard deviation.
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The paths are aligned over each other, so
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that you can see the impact of both if a special cause occurs.
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If your subgroup size is less than 10, I recommend that you use the Xbar-R chart.
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With very few data points the subgroup standard deviation can be way off.
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The range is actually a better indication of variation with a small sample.
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Well we went through the steps of creating a control chart in previous modules.
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But let's create an Xbar-S chart now and look at anything that makes it special.
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The first step is to determine the subgroup size and
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how you'll sample the data.
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We typically look for logical, physical grouping or calender-base grouping.
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I mention that you can have different sample sizes for different sub-groups.
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Then, follow you sample plan to collect the data points for each subgroup.
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Each subgroup will have at least 10 data points.
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Now, calculate the average for each subgroup and
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determine the standard deviation for that subgroup.
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At this point, you can plot the data lines for your control charts.
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So now, we need to calculate the mean values and
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the control limits to complete those charts.
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Once you have at least 30 subgroups, you can calculate the mean and
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control limits for the standard deviation chart.
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We need this to be stable before we calculate the limits of the Xbar chart.
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If the standard deviation chart is not in statistical control, investigate,
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find the special cause, and take appropriate action.
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And of course, we've discussed how to do that in an earlier module.
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Once the standard deviation chart is in control, calculate the mean and
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control limits for the Xbar chart.
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I'll review the formulas on this on the next slide.
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And if the expert chart is not in statistical control, investigate and
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take action for that chart.
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Let's look at how to do the calculations manually or in Excel.
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The actual formulas shown on the right side of the screen and
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the calculation steps will be discussed on the left side.
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First, collect and store your data.
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I normally follow a similar approach I did with the Xbar-R chart,
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it's just that there's many more columns now for the additional data points.
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Then calculate the subgroup mean or Xbar value, you put that in
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the next free column, followed by a column with a standard deviation of the subgroup.
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Fortunately, Excel has functions which will do those calculations for you.
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Once again, you need to calculate the mean value of the mean values.
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That means that you want the average of all the Xbar values, and
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you'll need to do the same thing with standard deviation, calculate the mean or
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average value of the standard deviations.
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To calculate the upper lower control of the standard deviation chart,
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it's fairly easy.
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Upper control limit is the average of the standard deviation values
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times the constant B4 and the lower control is the average of
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the standard deviation values times the constant B3.
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The calculation for the control much for the Xbar chart are similar to what we did
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with the Xbar-R chart just with different constance.
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The upper control limit is the average of the Xbar values
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plus the constant A3 times the average standard deviation values.
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And the lower control limit is the average of the Xbar values minus
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the cost of A3 times the average for the standard deviation values.
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You can create the actual graphs on Excel by using the line chart option
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in the graphing tool.
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Let's look at creating this chart in Minitab.
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Go to the start menu, select control charts,
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then select variable chart for sub groups.
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And finally, select the Xbar-S chart.
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When you do that, you should get a pail that looks like this on your screen.
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You need to tell Minitab how to read your data.
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For all the data points in a subgroup in adjacent columns, or all in one column.
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I normally do adjacent columns.
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Next, place your cursor in the variables window to activate the call of display.
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Highlight the column, or
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columns, where your data is located, then click the select button.
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Your data column should now be in the variables window.
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And just like Xbar-R, if your data is all in just one column, you
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will need to tell minitab how many data points in the column make up one subgroup.
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Now, click on the OK button at the bottom of the panel and
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Minitab will generate your control chart.
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>> So that's the Xbar-S chart.
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Thanks to automation and the internet of things, it's gaining popularity with
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companies that are trying to use more data in their process control.
NOTE Copyright (c) GoSkills Ltd, 2013 - 2022