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09/07/2007: "Fixed or Varying Subgroup Sizes for X-Bar charts"

We have series of individual voltage measurements taken on our sensors during testing. The sensors can be grouped into batches with varying batch size. How best can we monitor batch to batch variations across batches with varying batch size? All SPC software we find are restricted by fixed sub-group sizes which prohibit the calculation of our batch means.
Richard T., Product Assurance Engineer


Generally, SPC control charts used fixed subgroup sizes. Statistically, it's been shown that larger subgroup sizes (greater than ten or so) do not give much more information than the smaller sizes (less than three), so practitioners will generally decide on an economic subgroup size based on the cost of going out of control versus the cost of sampling.

Most SPC software (all QA products) support varying subgroup sizes, primarily for when samples within particular subgroups must be discarded due to bad data. Once a subgroup size has been specified, the software will properly re-calculate the control limits for subgroups having less data than the specified subgroup size. To use this feature when subgroup size is based on batch size, the largest batch size may be input as the subgroup size.

It should be noted that the use of the control charts in this manner must consider the concept of rational subgroups (see, for example: ). A control chart's subgroups are rational when the system of causes of process variation within the subgroups is the same system that influences between subgroup variation. The "within subgroup" variation is then a good predictor of the "between subgroup" variation. In the case of "batch to batch" variation, this requirement may not be met. For some processes, such as chemical processes, it is likely that the within batch variation is not a good predictor of between batch variation, since the components (or underlying causes) of variation are different. In cases like these, it is best to maintain two sets of control charts: one set that monitors each batch, during its course of operation; and a second control chart that plots the average batch parameter, for all batches, as an Individual data value. In this latter control chart, the Moving Range chart is used to monitor the between batch variation.
Some SPC Software (including QA's SPC Explorer and SPC IV Excel) provide an option within the X-Bar charts for Batch Means charts.
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