Control charts Shewhart means

Both the EC50 values and the 3-pM point of the 2,3,7,8TCDD ealibration curve serve as quality criteria. For each participant, the results for both data points from all 96-well plates analyzed during the presented study were collected and reeorded in Shewhart control charts. The Shewhart control chart is used to identify variations on performanee of the DR CALUX bioassay brought about by unexpected or unassigned causes. The Shewhart eontrol chart shows the mean of the EC50 and 3-pM control point and the upper and lower eontrol limits. In Figure 2, a typical Shewhart control chart is shown. Over the analysis period, none of the participants exceeded the aetion levels (AVG 3 S). 

Precision data can be documented in bar charts or control charts such as Shewhart control charts (see the discussion of internal quality control in Section 8.2.3.5). Bar charts plot %RSD values with their corresponding confidence interval. Control charts plot the individual measurement results and the means of sets of measurements with their confidence level (or with horizontal lines representing limits, see below) as a function of the measurement number and the run number, respectively [15,55,56, 58,72, 85]. 

Two aspects are important for IQC (1) the analysis of control materials such as reference materials or spiked samples to monitor trueness and (2) replication of analysis to monitor precision. Of high value in IQC are also blank samples and blind samples. Both IQC aspects form a part of statistical control, a tool for monitoring the accuracy of an analytical system. In a control chart, such as a Shewhart control chart, measured values of repeated analyses of a reference material are plotted against the run number. Based on the data in a control chart, a method is defined either as an analytical system under control or as an analytical system out of control. This interpretation is possible by drawing horizontal lines on the chart x(mean value), x + s (SD) and x - s, x + 2s (upper warning limit) and x-2s (lower warning limit), and x + 3s (upper action or control limit) and x- 3s (lower action or control limit). An analytical system is under control if no more than 5% of the measured values exceed the warning limits [2,6, 85]. 

Table 4.1. Average run length (ARL)for exceeding an upper or lower control limit 1/p(total), or giving seven results on one side of the center line 1/p(7) of a Shewhart means chart for deviations from the mean indicated...

In terms of breaching the warning and control limits, it will take a long time for a Shewhart means chart to show that the process mean has shifted by a small fraction of the process standard deviation. The ARL for deviation of half a standard deviation from the mean is 155 (table 4.1), so on average 155... 

An example of this scenario is shown in spreadsheet 4.2 and figure 4.18. Here the motor octane number of a standard sample of 95 octane fuel is measured each month in duplicate. The Shewhart means chart never goes over the warning limit, let alone the control limit (see figure 4.19), but something is clearly wrong. The seven-in-a-row rule would be triggered, but CuSum also reveals that the system is out of control at about the same time. 

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. 

The relative performance of the Shewhart and CUSUM control charts is compared in Fig. 8-48 for a set of simulated data for the tensile strength of a resin. It is assumed that the tensile strength x is normally distributed with a mean of p = 70 M Pa and a standard deviation of a = 3 MPa. A single measurement is available at each sampling instant. A constant (a = 0.5a = 1.5) was added to x(k) for k >10 in order to evaluate each charts ability to detect a small process shift. The CUSUM chart was designed using K = 0.5a and H = 5a. 

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. 

The relevance of Fig. 5.11 to the problem of setting control chart limits on means is that if one is furnished with a description of the typical pattern of variation in y, sensible expectations for variation in y follow from simple normal distribution calculations. So Shewhart reasoned that since about 99.7 percent (most) of a Gaussian distribution is within three standard deviations of the center of the distribution, means found to be farther than three theoretical standard deviations (of y) from the theoretical mean (of y) could be safely attributed to other than chance causes. Hence, furnished with standard values for /x and a (describing individual observations), sensible control limits for y become... 

Chemical analysis finds important applications in the quality control of in dustrial processes. In an ideal situation a continuous analysis of the process stream is made and some aspects of this are discussed in Chapter 12. How ever, such continuous analysis is by no means always possible, and it is common to And a process being monitored by the analysis of separate samples taken at regular intervals. The analytical data thus obtained need to be capable of quick and simple interpretation, so that rapid warning is available if a process is going out of control and effective corrective action can be taken. 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 cusnm chans. Only these types are discussed here. The charts can also be used to monitor the performance of analytical methods in analytical laboratories. ... 

It is clear that the manual preparation and continual updating of the charts shown in Fig. 2 for a multilevel, multi-analyte quality control system involves a great deal of work. However, it is possible in a multilevel control system to represent all individual values at different levels on one chart which is a variant of the Shewhart mean plot. The difference of an individual value (e.g. from the target mean (x ) is divided by the target standard deviation (sQ and thus the position of the individual value is represented relative to the target mean in standard deviation intervals 1), see Fig. 1. The bias of each value, irrespective of its analyte concentration, is therefore represented on the same standard deviation scale. This is very convenient for manual and computer plotting as complex scaling is avoided. Fig. 4 shows an example of this... 

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...

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

Figure 19-18 Shewhart mean and range control charts.

Another important characteristic is that of precision. This becomes evident only when repeat measurements are made, because precision refers to the amount of agreement between repeated measurements (the standard deviation around the mean estimate). Precision is subject to both random and systematic errors. In industrial quality control and chemical analysis, Shewhart Control Charts provide a means of assessing the precision of repeat measurements but these approaches are rarely used in ecotoxicity testing. The effect is that we generally understand little about either the accuracy or the precision of most bioassays. 

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. 

Figure 1b. Shewhart (control chart) of control samples for the determination of lead in blood. Concentration in //g/L, blood samples made in own laboratory. Limits set on 10 % of mean value of control samples determined so far.

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