Quality Control charts CUSUM

Guide to Data Analysis and Quality Control Using CUSUM Techniques. Uses and Value of CUSUM Charts in Business, Industry, Commerce and Public Service , BS 5703-1 2003, British Standards Institute (BSI), London, UK, 2003. 

The quality control unit in a cosmetics company supervised the processing of the weekly batch of shampoo by determining, among other parameters, the viscosity and the dry residue. Control charts showed nothing spectacular. (See Fig. 4.10, top.) The cusum charts were just as uneventful, except for that displaying the dry residue (Fig. 4.10, middle and bottom) The change in trend in the middle of the chart was unmistakable. Since the analytical method was very simple and well-proven, no change in laboratory personnel had taken place in the period, and the calibration of the balances was done on a weekly basis, suspicions turned elsewhere. A first hypothesis,... 

The validation process begun in Phase I is extended during Phase II. In this phase, selectivity is investigated using various batches of drugs, available impurities, excipients, and samples from stability studies. Accuracy should be determined using at least three levels of concentration, and the intermediate precision and the quantitation limit should be tested. For quality assurance evaluation of the analysis results, control charts can be used, such as the Shewart-charts, the R-charts, or the Cusum-charts. In this phase, the analytical method is refined for routine use. 

Cumulative Sum Charts - Guidance on Quality Control and Data Analysis Using CUSUM Techniques , ISO/TR 7871 1997, International Organization for Standardization (ISO), Geneva,... 

The control charts discussed earlier are very useful in the diagnostic aspects of quality process improvement. They can be used to stabilize a process by identifying out-of-control situations. After the process is stabilized and brought in control, further improvement of the process can be achieved by using some special control charts such as the cumulative sum (CUSUM) control chart and the exponentially weighted moving average (EWMA) control chart. These control charts can be used when small shifts in a process are of interest. 

If the initial calculation is shown to contain a value more than 3 standard deviations from the mean, the value should be rejected and the mean and standard deviation recalculated. The standard deviation obtained may be used as the target standard deviation (s ) in preparation of Shewhart charts or a desired standard deviation can be used which might be related to medical need or to a previous period of satisfactory performance. For a practical guide to statistical techniques used in quality control of analytical methods and the preparation of cusum... 

Fig. 3. The cusum chart for valproic acid using the data shown in Fig. 1 and similar data from the high pool of quality control serum, against occasion of analysis.

Westgard JO, Groth T, Aronsson T, et al. Combined Shewhart-cusum control chart for improved quality control in chnical chemistry. Clin Chem 1977 23 1881-7. 

Cusum techniques have for many years proved valuable in industrial quality control and productivity, allowing the detection of movements away from a target level at much earlier dates than when charts are simply plotted of the basic observations from which cumulative sums are derived. These charts are not of value for displaying the results of a series that exhibits a steady trend this characteristic is rarely maintained for long in clinical chemistry, however, and cusum charts can be employed in a hospital laboratory s quality control program for the following purposes ... 

Figure 1.1 Examples of (a) Levey-Jennings and (b) cumulative sum (cusum) control charts using inter-assay quality control data from an alprazolam GC-MS assay. Since the cusum chart persents the cumulative sum of deviations from the mean, it is more sensitive to small biases that develop over time, whereas Levey-Jennings charts are most useful for detecting changes in the precision of the assay...

Cumidative sum charts Guidance on quality control and data analysis using CUSUM techniciue.s. ISO/TR 7871, first edition. International Organisation for Standardisation, Geneva, Switzerland (1997). 

Cusum charts are also used to allow the detection of drifts in methods and trends by plotting the sum of the difference between the result obtained and a reference value in relation to time [57]. Examples of control charts used for the quality control of speciation analysis are given elsewhere [31]. 

The Stepwise SPC Chart is a method that combines the functions of the CUSUM Chart and the Shewhart Control Chart. A sequential analysis is used to estimate the current mean of the process. Shewhart Control Charts are then constructed about the step functions representing the current mean. Figure 1 illustrates the Stepwise Control Chart. The step functions, based on sequential analysis, respond to process drift the same way as the CUSUM Chart. Each segment of the control chart then helps to identify the interruptions, in the same way as the Shewhart Control Chart does. With the proper choice of parameters, the Stepwise SPC Chart can effectively separate the three types of variations drift, fluctuations and interruptions, and thus help us to monitor and analyze the quality of the product. Refer to EWMA Chart. 

Bissell, A. E1990. Control charts and cusums for high precision processes. Total Quality Management. 1 (2) 221-29. 

FIG. 4. Cusum control chart calculated on the basis of the previously shown quality control data plotted in the Shewhart chart (Fig. 3). 

It should be noted that the cumulative sum (CUSUM) and exponential weighted moving average (EWMA) control charts have also been proposed for the use in high-quality processes (Yeh et al. 2008 Szarka and Woodall 2012). However, in some cases, they are very complex and complicated to understand for the practitioners. 

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