Two-sample charts

The design of a collaborative test must provide the additional information needed to separate the effect of random error from that due to systematic errors introduced by the analysts. One simple approach, which is accepted by the Association of Official Analytical Chemists, is to have each analyst analyze two samples, X and Y, that are similar in both matrix and concentration of analyte. The results obtained by each analyst are plotted as a single point on a two-sample chart, using the result for one sample as the x-coordinate and the value for the other sample as the -coordinate. ... 

A two-sample chart is divided into four quadrants, identified as (-P, -p), (-, -p), (-, -), and (-P, -), depending on whether the points in the quadrant have values for the two samples that are larger or smaller than the mean values for samples X and Y. Thus, the quadrant (-P, -) contains all points for which the result for sample X is larger than the mean for sample X, and for which the result for sample Y is less than the mean for sample Y. If the variation in results is dominated by random errors. 

A visual inspection of a two-sample chart provides an effective means for qualitatively evaluating the results obtained by each analyst and of the capabilities of a proposed standard method. If no random errors are present, then all points will be found on the 45° line. The length of a perpendicular line from any point to the 45° line, therefore, is proportional to the effect of random error on that analyst s results (Figure 14.18). The distance from the intersection of the lines for the mean values of samples X and Y, to the perpendicular projection of a point on the 45° line, is proportional to the analyst s systematic error (Figure 14.18). An ideal standard method is characterized by small random errors and small systematic errors due to the analysts and should show a compact clustering of points that is more circular than elliptical. 

The data used to construct a two-sample chart can also be used to separate the total variation of the data, Otot> into contributions from random error. Grand) and systematic errors due to the analysts, Osys. Since an analyst s systematic errors should be present at the same level in the analysis of samples X and Y, the difference, D, between the results for the two samples... 

Figure 38-1 Two-sample charts illustrating systematic errors for Methods A vs. B.

To use the macro, simply Open Labeler2.xls it will appear on screen and then Hide itself. It installs a new menu command, "Add Data Labels..." in the Chart menu. To view the workbook, containing the macro and two sample charts. Unhide the workbook. 

Two-sample Chart illustrating systematic errors Precision (Sr) ... 

Plot the two-sample chart for these data, and comment on the principal source of error in the collaborative trial. Estimate the overall variance, the measurement variance, and the systematic error component of the variance of the results. 

When two samples of air are brought together the condition of the mixture may be arrived at arithmetically by adding the heat flow of each and dividing by the total mass flow and similarly for the moisture flow. Alternatively, plot the condition of each onto a psychrometric chart. The mixed condition lies on a straight line between the two in a position proportional to the two quantities. 

In Section 4, two control charts for variable data are presented. Both the X control chart for monitoring the process mean and the R control chart for monitoring the process variation are presented. In Section 5, two control charts for attribute data are discussed the p control chart for monitoring percent nonconforming and the c chart for monitoring the number of defects in a sample. Furthermore, brief discussions of data patterns on control charts and recommended supplemental rules for judging nonrandom trends on a control chart are presented. 

Fig. 2. Separation of artificial mixtures of nonradioactive and radioactive standards. Fro files of radioactive and nonradioactive standards recorded simultaneously by a two-pen chart recorder connected to the UV detector and liquid scintillation flow monitor. The analyzed sample contained 75 nmoles of each nonradioactive and 80-100 picomoles of radioactive standards.

Figure 21.5 indicates that sample 5 lies beyond the UCL for both the x and s control charts, while sample 15 is very close to a control limit on each chart. Thus, the question arises whether these two samples are outliers that should be omitted from the analysis. Table 21.2 indicates that sample 5 includes a very large value... 

Figure 21.9 provides a general comparison of univariate and multivariate SPC techniques (Alt et al., 1998). When two variables, xi and X2, are monitored individually, the two sets of control limits define a rectangular region, as shown in Fig. 21.9. In analogy with Example 21.5, the multivariate control limits define the dark, ellipsoidal region that represents in-control behavior. Figure 21.9 demonstrates that the application of univariate SPC techniques to correlated multivariate data can result in two types of misclassification false alarms and out-of-control conditions that are not detected. The latter type of misclassification occurred at sample 8 for the two Shewhart charts in Fig. 21.8.

Viscosity is normally measured at two different temperatures typically 100°F (38°C) and 210°F (99°C). For many FCC feeds, the sample is too thick to flow at 100°F and the sample is heated to about 130°F. The viscosity data at two temperatures are plotted on a viscosity-temperature chart (see Appendix 1), which shows viscosity over a wide temperature range [4]. Viscosity is not a linear function of temperature and the scales on these charts are adjusted to make the relationship linear. 

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