A Signal-to-Noise Ratio is No Subsitute for a Brain - The relevance of control charts to signal-to-noise ratio - BioPharm International


A Signal-to-Noise Ratio is No Subsitute for a Brain
The relevance of control charts to signal-to-noise ratio

BioPharm International
Volume 19, Issue 3

McAllister pointed to the more normal distribution of S/NT as a benefit. The more normal distribution is not surprising because a log transformation reduces extreme values. However, the transformation is not necessarily beneficial. Extreme values are what control charts seek to detect and thus we should use our brains to decide if we want to use a transformation that reduces extreme values.

Figure 3. Means and ranges of three replicates
We also need to be aware that extreme values that are not typical for a process that is "in-control" should be excluded from the data used to calculate the control chart limits. For this reason, it is often worthwhile to use an outlier test to verify extreme values. The book by Iglewicz and Hoaglin is a good source of methods. A test flagged two of McAllister's SDS-PAGE means as possible outliers. These were 84.733 and 83.667. Removing them produced a distribution of raw data that, while not as close to normal as the S/NT, were not significantly different to normal.


Figure 4. Individual chart of T S/N ratio
In conclusion, although using control charts of a signal-to-noise ratio is a novel suggestion that may be useful, combining off-target and repeatability variability hides information. The problems associated with large batch-to-batch variability can be solved easily by simple standard procedures. Calculating control chart limits with the two outliers removed resulted in the charts of the means and ranges presented in Figure 3 and the S/NT chart presented in Figure 4. The separate Xbar and R charts use the same data and require about the same amount of work to produce. Those charts indicate the presence of three very low means and one very high range that are worth investigating.

Terry Orchard is statistician at Bespak Europe Blackhill Drive, Milton Keynes, MK12 5TS, UK +44.1908.525262, fax: +44.1908.525260,


1. McAllister J, Stop rejecting good batches – use a signal-to-noise transformation. BioPharm International 2005 July; 18(7):44-52.

2. Deming WE, Elementary Principles of the Statistical Control of Quality. Nippon Kagaku Gijutsu Kemmei, Tokyo 1951 p.69.

3. Iglewicz B, Hoaglin DC, How to Detect and Handle Outliers. Milwaukee. American Society for Quality, 1993.

4. Wheeler DJ, Chambers DS. Understanding Statistical Process Control, 2nd Edition. Knoxville TN. SPC Press Inc., 1992.

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