Control charts Shewhart range

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-... 

Shewhart control charts enable average process performance to be monitored, as reflected by the sample mean. It is also advantageous to monitor process variability. Process variability within a sample of k measurements can be characterized by its range, standard deviation, or sample variance. Consequently, control charts are often used for one of these three statistics. 

Figure 5.10 shows plots of the individual melt indices, means, ranges, and standard deviations from Table 5.4 against shift number. The last three of these are the beginnings of so-called Shewhart x, R, and 5 control charts. 

Shewhart Mean and Range (or Standard Deviation) Control Charts... 

Figure 19-18 Shewhart mean and range control charts.

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. 

A conventional response to issues of variability in bioassays is to construct Shewhart Control Charts based on the results achieved in repeat tests within a laboratory using a reference toxicant. This effectively describes the range of results typically found within the laboratory and hence can be used to define limits within which the laboratory normally expects to operate. However, there is a flaw in such internal quality control because the more variable a laboratory s reference toxicant test results are, the wider the limits of acceptability will be. Indeed, it can serve merely to reinforce high variability or bias. 

The usage of quality control charts in the field of quality assurance is based on the assumption that the determined results are distributed normally. Typical control charts used in a LIMS for routine analysis are, for example, the Shewhart charts for mean and blank value control, the retrieval frequency control chart, and the range and single-value control chart [19]. Quality regulation charts can be displayed graphically in the system or exported to spreadsheet programs. 

The five line control charts have been introduced by Walter Shewhart and are also termed Shewhart means and Shewhart range charts. 

A form of this approach has long been followed by RT Corporation in the USA. In their certification of soils, sediments and waste materials they give a certified value, a normal confidence interval and a prediction interval . A rigorous statistical process is employed, based on that first described by Kadafar (1982,), to produce the two intervals the prediction interval (PI) and the confidence interval (Cl). The prediction interval is a wider range than the confidence interval. The analyst should expect results to fall 19 times out of 20 into the prediction interval. In real-world QC procedures, the PI value is of value where Shewhart (1931) charts are used and batch, daily, or weekly QC values are recorded see Section 4.1. Provided the recorded value falls inside the PI 95 % of the time, the method can be considered to be in control. So occasional abnormal results, where the accumulated uncertainty of the analytical procedure cause an outher value, need no longer cause concern. 

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. 

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. 

Fig. 2. Shewhart mean and range charts for valproic acid using the data shown in Fig. 1 and similar data from high, mid, and low pools of quality control serum, against occasion of analysis. -----------------=95% limits ---------------=99% limits...

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