General Principles of Control Charts

The control limits are usually calculated from the mean (%) and standard deviation (s) obtained from repeated measurements on the laiown specimens by the particular analytical method that is to be controlled. The mean (3c) and standard deviation (s) are calculated from the following equations  

The initial estimate may not be entirely reliable owing to the low number of data points and possible outliers in the data. The estimates are revised when more data have been accumulated by recording n and the summations of x, and xfy then using the cumulative totals in the equations above to give cumulative means and standard deviations. The effects of outliers can be minimized by eliminating values exceeding the mean by more than 3.1 to 3.8s (where the 

Although the discussions in this chapter imply that plots are manually prepared, in actual practice, a wide variety of computer software packages are available for statistically calculating and plotting QA data. 

It is assumed that error distribution of the analytical method is Gaussian (see Chapter 14). The control limits are set to include most of the control values, usually 95% to 99.7%, which correspond to the mean 2 or 3 standard deviations. Because it should be a relatively rare occurrence to observe a value in the tails of the distribution (only 1 out of 20 times for 2 s limits and 3 out of 1000 for 3 s limits), such an observation is suspect and suggests that something has happened to the analytical method. Such an occurrence could have caused a shift in the mean (an accuracy problem), which would result in a higher probability for exceeding the limits, or it could have caused an increase in the standard deviation (a precision problem), which would widen the distribution and also result in a higher probability for exceeding the limits. 

Interpretation of the control data is guided by certain decision criteria or control rules, which define when an analytical run is judged in control (acceptable) or out of control (unacceptable). These control rules are given symbols, such as At, or tii, where A is the abbreviation for a statistic n is the number of control observations, and L refers to the control limits. For example, Gs refers to a control rule where 1 observation exceeding the mean +3s control limits is the criterion for rejecting the analytical run. 

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