Monitoring Batch Variation

06/19/2009:

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 subgroup sizes which prohibit the calculation of our batch means. Richard T., Product Assurance Engineer

Generally, SPC control charts used fixed subgroup sizes. Statistically, it has 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 support varying subgroup sizes, for use primarily when observations within particular subgroups must be discarded due to bad data. Once a subgroup size has been specified, the software will properly recalculate 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. 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 use a batch means chart.

Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).