Shewhart charts

Westgard jo, Barry PL, Hunt MR (1981) A multi-rule Shewhart chart for quality control in clinical chemistry. Clin Chem 27 493-501. 

We do this by using the statistical ideas outlined above. First of all, the QC sample is measured a number of times (under a variety of conditions which represent normal day-to-day variation). The data produced are used to calculate an average or mean value for the QC sample, and the associated standard deviation. The mean value is frequently used as a target value on the Shewhart chart, i.e. the value to aim for . The standard deviation is used to set action and warning limits on the chart. 

Figure 6.6 Shewhart charts showing (a) data in control about the target value (b) data offset from the target value (c) drifting data (d) data with a step-change.

Figure 6.7 Data shown on (a) a Shewhart chart and (b) a moving average chart (n =4).

What is the difference between a Shewhart chart and a range chart Answer... 

A Shewhart chart is used to monitor the variation of individual results over time, compared to a target value. Shewhart charts are useful for identifying when bias has entered a measurement system. Non-random patterns in the data, such as drift or step-changes, indicate that bias is present. A range chart is used to monitor the precision of a measurement system, regardless of whether there is any bias present. The data on both types of chart are best evaluated by setting control limits. 

Figure SAQ 6.2 (a) Shewhart chart with warning and action limits at 2 and 3 standard deviations, respectively, (b) Moving average chart (n = 5) with warning and action limits at 2 Jn and 3 Jn standard deviations, respectively, (c) CUSUM chart, (d) CUSUM chart with V-mask.

One method of data presentation which is in widespread use is the control chart. A number of types of chart are used but where chemical data are concerned the most common types used are Shewhart charts and cusum charts. Only these types are discussed here. The charts can also be used to monitor the performance of analytical methods in analytical laboratories. 

A typical pair of Shewhart charts, (a) Averages chart and (b) ranges chart. Point A shows a lack of control of averages only, point B of ranges only and point C of both together. 

This chart corresponds to the original Shewhart-chart. For tmeness control, standard solutions, synthetic samples or RM/CRM samples may be analysed. Calibration parameters (slope and intercept) can also be used in a X-chart to check the constancy of the calibration. 

Original Shewhart-chart with single values... 

The Blank Value Chart is also very important. This is a special form of a Shewhart chart where the direct measurements (e.g. in Volts) from the analyses of blank samples are used. From this chart information can be received about contamination of reagents e g. from the enviromnent and the state of the analytical system. 

The Shewhart chart graphically tests the hypothesis that a process measurement is not different from the desired target value of that measurement. If one assumes that the measurement, yk, follow a normal distribution about the target value, y assuming that the target value y, represents the true mean ym for the given measurement, and assuming that the standard deviation a for the process is known, then... 

Shewhart charts are adept at detecting mean value shifts on the order of 3(7 or higher. To detect more subtle shifts in the mean value, the CUSUM chart has been developed [10,11]. The cumulative sum is defined as ... 

A pool of erythrocyte samples. This is made up of erythrocytes from left-over EDTA-blood of a large number of different patients. Aliquots of 300 pi suspension are stored in BHT-treated Eppendorf vials at -20°C for a maximum period of 1 year. One of these samples is included in each weekly series of analyses. The results of ten selected fatty acids are plotted on an electronic Shewhart chart. 

A pool of a large number of left-over plasma samples of patients is thoroughly mixed. Aliquots of 150 pi are put into Eppendorf vials and stored at -20°C. These samples are stable for 1 year. Each series of analyses has one pool plasma sample. The concentrations of the five analytes are introduced into an electronic Shewhart chart, which is renewed each year. 

An example of the most common control chart, the Shewhart chart, is shown in Fig. 8-46. It merely consists of measurements plotted versus sample number with control limits that indicate the range for normal process operation. The plotted data are either an individual measurement x or the sample mean x if more than one sample is measured at each sampling instant. The sample mean for k samples is cal-... 

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