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Please note, there are several assumptions in what I am suggesting.

If this is correct, and a relationship can be shown to exist, and the relationship is strong, then monitoring one diameter and using this as a predictor of the other diameters may be possible.Īssuming this is the case, sampling one diameter and then predicting the others using a reduced sampling program for these diameters may be one way to approach your problem. As such, there may be a relationship between different diameters and how they change. Let’s suppose the part is made using a single form tool. but to answer this question, I will do so in the context of some assumptions. How would I setup a control chart to monitor three different diameters on the same part? You may be interested in some of these articles! For additional information on these Statistical Process Control Charts (Xbar R Chart versus Xbar S Chart) check out this resource. The Xbar R chart and Xbar S chart are awesome tools. Or, if we had n = 12 or more values per subgroup we would suggest the use the Xbar S Chart. In the case, the control limits for the Xbar Chart would be just right.īased on this simulation, we would suggest that we use the Xbar R Chart for n = 11 or less values per subgroup. In this case, the control limits for the Xbar Chart would be wider.īut notice that the average standard deviation for n = 12 or more values per subgroup estimates the population well. But, for the same range of subgroups (n = 5 to 11), the average standard deviation under-estimates the population standard deviation.īased on this observation, we’re inclined to believe that the Average Range estimates the population standard deviation well between n = 5 through n = 11 values per subgroup.īut what happens when you have n = 12 or more values in each subgroup? We can see that the standard deviation based on the Average Range over estimates the population standard deviation. Notice that the standard deviation, based on the Average Range, for n = 5 to 11 estimates the population standard deviation well. In Figure 2, I show the population standard deviation as a horizontal line through a standard deviation at 5. Plot of Standard Deviations Estimate for n=5 to n=15 Subgroupsįigure 2: Plot of Standard Deviation Estimates Based on the Range (BLUE) and Average Standard Deviation (RED) for n=5 to n=15 values per subgroup Now we can Interpret the Results I then plotted the data in tables 1 and 2 in the following graph shown in Figure 2. Table 2: Standard Deviation Estimates for n = 5 to 15 values per Subgroup Let’s Plot the Results Table of Average Standard Deviation Estimates Now I had the average standard deviation for n = 5 through n = 15 values per subgroup. Table 1: Standard Deviation Estimated From Average Range for n = 5 to 15 Let’s Estimate the Average Standard Deviationįor the next part of this simulation I computed the standard deviation for each subgroup, of n=5 to n=15 values, and then calculated the average standard deviation across all 50 subgroups. Table of Standard Deviation Estimates Based on the Range The Average Range was then divided by the appropriate d2 constant for each subgroup made up of n = 5 to n = 15 values. For each subgroup, of n=5 to 15 values, I computed the Range and then calculated the Average Range across all 50 subgroups.

This simulation examined 50 subgroups were each subgroup had n = 5 to 15 values. Simulated Values Using Mean = 50 and Standard Deviation = 5įigure 1: Simulation of 50 subgroup with up to 15 values per Subgroup Let’s Estimate the Standard Deviation based on the Range I generated 50 subgroups with 15 samples in each subgroup using a Mean of 50 and standard deviation of 5. Since we use the average range and the average standard deviation to compute the control limits for the Xbar Chart, then having a standard deviation that estimates the population best is critical. Well, the decision to use either of these Statistical Process Control Charts comes down to how the average range and the average standard deviation estimate the population. In this post, I will answer that question. I recently got a question from a reader that wanted to know when to use an Xbar R chart versus Xbar S chart. Xbar R Chart Xbar R Chart versus Xbar S Chart