Analysis of Batch Processes using a Batch Means Chart

05/14/2010:

We are a specialty chemical manufacturer that utilizes a batch process to generate our products. From my understanding, SPC charts are basically useless for batch process. Some of our customers require SPC charts anyway. The acceptable range for the Cpk, I am told, is 1.33 to 2.00. With the previous software I was using, it was easy to manipulate the Cpk by adjusting the control limit. However, with this new program, I cannot seem to get the Cpk within the acceptable range. Is there any way to manipulate this? Also, which type of chart would be the best for me to use?

Matt S., QC Chemist

Control charts can be applied to batch processes. However, as in multi-stream processes, the traditional X-bar chart cannot be used as you might expect. When you select subgroups for the X-bar chart, subgroup observations collected from within the batch provide an estimate of the within batch variation, but do not provide a good estimate of the between batch (or longer term) variation. As such, subgroups collected as multiple observations from a batch are irrational subgroups, and not useful for defining the control limits on the X-bar chart.

One alternative is to use a batch means chart, which allows you to use the multiple observation subgroup collected from the batch, but corrects the control limits on the X-bar chart to use the variation between batches, such as is done in a moving range chart. One advantage of the batch means X-bar chart is that it controls both the within batch variation (on the range chart) and the between batch variation (on the X-bar chart). The calculated process capability uses process sigma based on the moving range between the batch averages.

The only acceptable method for forcing a capability calculation is to define the control limits based on a predefined estimate, such as from a process qualification / capability study. When control limits are predefined, the capability indices are also predefined, since they are inherently linked. This is one reason why capability indices should never been evaluated without their accompanying control chart: The control chart defines the process sigma and average values applied in the process capability calculation; those estimates are meaningless unless the process is in control relative to the process sigma and average values applied.

When the batch is essentially homogenous, and measurable variation cannot be estimated reliably, then it is only necessary to take a single observation from the batch, and apply it to an individual x/moving range chart or any of the other charts from individuals (n = 1) data, such as a moving average or EWMA 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).