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Shifting the Paradigm: Why Individuals Control Charts Are Often Better Than X-Bar and R Charts

August 2, 2011
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In my last blog , I described how one person could track a process using an x-bar and R chart, while another one could track the same process using an individuals control chart and get a very different looking plot. The behavior that someone undertakes from each process-tracking reporting methodology could be quite different.

The question that one might ask is, "which control charting technique is most appropriate?" My response to this question is, it depends on how you categorize the source of variability relative to common and special causes. To explain, I will use a manufacturing situation, though the same applies in transactional environments.

For illustration, let’s say that a supplier provides product daily from one lot and there is a lot larger difference between logs than within lots, which unknowingly affects the process output. To answer our original common vs. special cause question, we need to decide if the impact of day-to-day differences on our process should be considered a component of common or special cause variability. If these day-to-day differences are a noise variable to our process that we cannot control, we will probably use a control charting procedure that considers the day-to-day variability a common cause.

For this to occur, we need a sampling plan where the impact from this type of noise variable occurs between subgroupings; I call the plan that accomplishes this infrequent sampling/sub-grouping sampling and the view of the process at this level-the 30,000-foot-level view. When creating control charts at the 30,000-foot level, we need to include between-subgroup variability within our control chart limit calculations, as was achieved in the previously blog’s described individuals control charting procedure.

If we examine the math to create the x-bar and R chart and individuals chart, as noted in my previous blog , one will observe that this between-sub-group variability affecting our control limits requirement is achieved in the individuals control chart but not the x-bar and R chart. Hence, because of this, I am suggesting that for most situation people use the individuals control chart.

Individuals control charting when there are multiple samples within subgroups

For the situation where there are multiple samples within subgroups, at the 30,000-foot-level we can track the subgroup mean and log standard deviation using two individuals control charts to assess whether the process is in control or predictable. We need to note that for in control or predictable processes, the data can later be used to determine the overall process capability and performance metric.

For the data in Table 1 from my previous blog, this approach would lead to the individuals control charts shown in Figure 3 for the mean and the natural log of the standard deviation, where the log of the standard deviation is a normalizing transformation for standard deviation.

Our data analysis conclusion using this approach is that the process is in control or predictable, which is quite different from the conclusion we made from Figure 1 in my previous blog.

Process capability can now be reported since the process is considered stable. However, what is the best approach to describe how the process is performing in terms that everyone understands?

I will address this issue in my next blog.



Reference: The content of this blog was taken from Chapter 12 of IEE Volume III
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