Shewhart-CUSUM Control Chart (1989 Guidance)
Shewhart-CUSUM Control Chart (1989 Guidance)
Graph | S-C Control Chart
See Also:
Shewhart-CUSUM Control Chart Options (1989 Guidance)
Shewhart-CUSUM Control Chart (Unified Guidance)
Description:
Control charts are a graphical method to assess contamination levels for individual wells. The 1989 guidance recommends Shewhart-CUSUM control charts for intra-well comparisons. ChemStat also provides an inter-well comparison implementation of the Shewhart-CUSUM control chart.
Four values, a decision internal value (h), a reference value (k), the Shewhart Control Limit (SCL), and the fast initial response (FIR) multiplier, are entered by the user.
For intra-well comparisons, the number of baseline measurements used to establish mean and standard deviation of the constituent level must also be specified. For the measurements collected beyond the time of the baseline sample, the standardized mean (Z) and the cumulative sum (S) are plotted for each sampling date. If S > h or Z > SCL, possible contamination is indicated at the well.
For intra-well comparisons, ChemStat can plot baseline concentrations as they are calculated from the baseline mean and standard deviation.
Use:
As a graphical method for intra-well or inter-well comparisons.
Options:
Select S-C Control Chart Options from the Options menu or from the right-mouse-button context menu to enter estimates of h, k, SCL, and FIR. Also entered from this option is the number of baseline measurements. If a positive number of baseline measurements is entered, the baseline measurements are counted from the first sampling date. If a negative number is entered, the number of baseline measurements is equal to the total number of measurements for the well minus the absolute value of the number entered. Baseline measurements are not graphed, but are used only to establish baseline mean and standard deviation.
The line style connecting points for the Z line and the S line can also be specified from S-C Control Chart Options.
There is also an option to circle data points which exceed either the k or SCL lines. Circling exceedences can make the graph easier to interpret by those unfamiliar with Shewhart-CUSUM control charts. From Select | Control Chart Options, check the Circle Exceedances check box.
Remarks:
Shewhart-CUSUM control charts may be very susceptible to false positives and are not robust with respect to outlier values. However, the graph is useful in providing a visual indication of changing trends in parameter concentrations.
Note that in specifying the number of baseline measurements, it is the actual number of measurements that is counted and not the number of sampling dates. However the graph plots a single point for each sampling date, regardless of the number of measurements collected on that date.