Stop rejecting Good Batches - Use a Signal-to-Noise Transformation

A control chart is used to test the hypothesis that the process is in control. If the data are not distributed normally, the Shewhart control chart may signal a false alarm. A transformation invented by Taguchi solves the problem.
Jul 01, 2005
Volume 18, Issue 7

Control charts are used to monitor the long-term performance of a process and to signal when the process goes out of control. Under certain conditions, standard control-charting methods have limitations in the way the control limits are calculated, signaling false out-of-control conditions. This can lead to unwarranted process investigations, or even worse, unnecessary rejection of batches. An example of this happening is with an SDS-PAGE (sodium dodecyl sulfate polyacrylamide gel electrophoresis), which is an analysis used in the manufacture and testing of biopharmaceutical products to assess the identity and purity of specific proteins.

The US has a long history of using statistical process control (SPC) techniques, but a relatively brief history of using the robust engineering techniques practiced in Japan. Because the terminology may be unfamiliar, see the box on page 50 for explanations. One of the most frequently used SPC tools is the Shewhart control chart, which focuses on process stability as measured in its variability. Similarly, the focus of robust engineering is to design a process that is economical and on-target with low variation.

Sauers describes a method that folds the Japanese techniques into tolerancing and capability analysis, which are currently familiar to U.S. quality engineers.1 He passed over connecting control charting and the common robust engineering transformations. This article blends these two concepts. Our application uses a signal-to-noise response variable in a Shewhart control chart of individual measurements. Similar to Shewhart control charts, the objective of robust engineering is to minimize variability of a process while keeping it on target and at low cost.

James McAllister
SHEWHART CONTROL CHARTS The objective of a control chart is to test the hypothesis that the process is in control. All processes have a certain amount of variability associated with them, and most sources of this variation are considered common cause. A process is considered out of control if special or assignable causes are present. Special causes are typically related to one of three categories: operator errors, defective raw materials, or improperly performing equipment.

An underlying concept in identifying special causes is known as rational subgrouping. This concept means that subgroups or samples should be selected so that if special causes are present, the variability between samples will be maximized, while the variability of replicates within a sample will be minimized.

One of the most popular control charts used is the X-bar chart. This is a chart of sample, or subgroup, averages. Observations within each subgroup are averaged, and the mean of the averages (overall or grand average) is used to define the process mean. The upper and lower control limits are calculated by using an estimate of the process standard deviation. This can be estimated in several ways depending on the dataset. One method is the Range chart, in which the within-subgroup range (the maximum observed value minus the minimum) is plotted and used to calculate an average range (R-bar).

A third chart has the special name of Individuals and Moving Range chart. The absolute difference between successive range measurements is plotted and used to calculate an average moving range (mR-bar).

Another method is the S-chart (standard deviation chart), where the standard deviation of the subgroup measurements is plotted and used to calculate an average standard deviation (S-bar). Typically, the S-chart is used in cases where the sample size is greater than or equal to ten. Regardless, the methods (R, mR, or S) are very similar because they all use the within-subgroup variation to estimate the variation for the process.

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