A Signal-to-Noise Ratio is No Subsitute for a Brain

The relevance of control charts to signal-to-noise ratio
Mar 01, 2006


Terry Orchard
Dr. W. Edwards Deming, the renowned quality guru who led the Japanese post-war industrial revival, often told his followers that, "The control chart is no substitute for a brain."

I was reminded of this teaching when reading the article by James McAllister, "Stop Rejecting Good Batches—Use a Signal-to-Noise Transformation," which appeared in the July 2005 issue of BioPharm International.


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This is not meant as a criticism of McAllister's article—far from it. McAllister's article was valuable and stimulating. Rather, this article elaborates on the use of control charts and describes the relevance of the signal-to-noise ratio McAllister proposed.

THE USE OF CONTROL CHARTS

McAllister's article focused on the following four points:

1. When batch-to-batch variability is high, using an X-bar chart to track the batch means often results in the majority of the means falling outside the 3-sigma limits.

2. The transformation to a signal-to-noise ratio (S/N) leads to 3-sigma limits that contain most of the S/N values.

3. The S/N combines infor-mation on the replicates' variability and the degree off-target.

4. The S/N values are Normally distributed, whereas the means are not.


Figure 1. Individual chart of mean shot volume for 213 batches
McAllister's article presented three replicate results for 41 sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE) analyses. The variation among the 41 means was much larger than it was among the three replicates, and as a result, an X-bar chart was of no value. A routine solution to this problem is using an individual–moving range–R chart (I–MR–R) chart. An I–MR–R chart displays the individual means, moving ranges of the means, and ranges of the three replicates in separate panels. The component charts can be produced separately. With a package such as Minitab, the I-chart of means will require calculating the means before the chart can be produced.

Data with a similar pattern often are seen in the volume or weight of drug dispensed by metered dose devices. For these data, the test results for accepting batches are the means of the quantity delivered by a sample of 50 to 125 valves. In such cases, it is appropriate to use control charts of the means to manage the processes. As with the SDS-PAGE data described by McAllister, almost all the means would fall outside control chart limits that failed to allow for the large batch-to-batch variability.


Figure 2. Individual chart of McAllister S/N for 213 batches
An example of a typical control chart is shown in Figure 1, which shows the means of 213 batches as calculated from three replicate measurements on a sample of 125 valves. Because the average moving-range estimate of sigma is reduced by the clustering of batch means, we used the standard deviation of the 213 means for the "3-sigma" control chart limits instead of relying on the Minitab default.