Control and Range Charts

The individual observations in sequential order are compared with control limits established from a past measurement to generate the control chart in the initial case. If the mean value x and standard deviation a of a constant quantity have been established from 15 to 30 measurements, these quantities may be regarded as valid estimates of x and x for the population. Limits of 95% and 99.8% which are based on 1.96cr and 3.0c are usually designated as warning and action limits and these limits are usually set, and are based on the sensitivity and importance of the measurements. Special attention should be paid to one-sided deviations from control limits, because systematic errors cause deviation in one direction and may indicate an abnormally wide scatter. Therefore laboratories, production, test methods, or operator can be checked for consistency of measured results. 

Control charts are designed to incorporate the entire process of the analytical measurement from sampling variability, instrument stability, calibration standards and sample preparation. The chart presents data in a framework that clearly shows whether corrective actions are necessary to ensure that results reported are correct, and allows extrapolation from sample results to conclusion about the whole population with known risks of error or misinterpretation. 

The idea of monitoring accuracy and precision was developed by Walter Shewhart [18] and the target value here was the known concentration of analyte in a control standard. The range graph monitors the precision, and the target value is the capability that it is necessary to establish in order to set up the control chart. Process capability will be limited by the random errors involved in measurements rather than error in preparing the standards. 

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Figure 5 Mean control and range charts Example 1.

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