Cusum Charts
An alternative method of monitoring the behaviour of a process is the cumulative sum technique
(cusum). The cusum plot provides a simple method of diagnosing when a process begins to move out of
control. A sequence of analyses is made on the process stream at regular intervals. The values thus
obtained are compared with the target value for that particular component and the deviations aggregated
to provide the cumulative sum. For a process in control, the deviations will have small positive or
negative values and the cusum will remain close to zero, with the plot having a roughly horizontal
pattern. If the process goes out of control, the cusum will become increasingly positive or negative with
the corresponding change in slope signifying the point at which loss of control ensues. One major
advantage of such charts is that the computations required are minimal and the plotting very simple.
Thus charts may be constructed and used by operators of limited technical knowledge. Figure 2.6 shows
a cusum plot for a process going out of control.
Figure 2.6
A typical cusum plot showing a lack of control with a negative
deviation developing after 20 observations.Standardization of Analytical Methods
Quantitative analysis demands that an analytical measurement can be accurately and reliably related to
the composition of the sample in a strict proportionality (p. 2). The complexity of relationships,
especially for instrumental techniques, means that the proportionalities need to be practically
established in calibration procedures. For a typical simple calibration, a range of standards is prepared
containing varying amounts of the analyte. These are then analysed by the standard method and a
calibration curve of signal vs amount of analyte is plotted. Results for unknowns are then interpolated
from this graph (Figure 2.7). An important convention is