Single-value control chart

The single-value control charts discussed in the previous sections provide a display of the differences between the observed values and the expected mean. Control rules, such as 22s, 4i5, and 10 provide one way of determining when these successive differences no longer appear to be random (too many in a row on one side of a limit). A more exact and quantitative method is the cumulative sum control procedure or cusum chart. 

Power functions for mean (or 2-test), range, and (or standard deviation) control procedures, when compared with those for previous control procedures, show higher probabilities for error detection, particularly at larger n s. The probability for false rejection can be set at a suitably low level by proper choice of control limits. Thus these control procedures appear to offer better performance characteristics than single-value control charts because they have higher error detection and lower false rejection as n increases. 

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. 

Control charts were originally developed in the 1920s as a quality assurance tool for the control of manufactured products.Two types of control charts are commonly used in quality assurance a property control chart in which results for single measurements, or the means for several replicate measurements, are plotted sequentially and a precision control chart in which ranges or standard deviations are plotted sequentially. In either case, the control chart consists of a line representing the mean value for the measured property or the precision, and two or more boundary lines whose positions are determined by the precision of the measurement process. The position of the data points about the boundary lines determines whether the system is in statistical control. 

Construction of Property Control Charts The simplest form for a property control chart is a sequence of points, each of which represents a single determination of the property being monitored. To construct the control chart, it is first necessary to determine the mean value of the property and the standard deviation for its measurement. These statistical values are determined using a minimum of 7 to 15 samples (although 30 or more samples are desirable), obtained while the system is known to be under statistical control. The center line (CL) of the control chart is determined by the average of these n points... 

Property control charts can also be constructed using points that are the mean value, Xj, for a set of r replicate determinations on a single sample. The mean for the ith sample is given by... 

When data of a single type accumulate, new forms of statistical analysis become possible. In the following, conventional control and Cusum charts will be presented. In the authors opinion, newer developments in the form of tight (multiple) specifications and the proliferation of PCs have increased the value of control charts especially in the case of on-line in-process controlling, monitors depicting several stacked charts allow floor supervi-... 

Single value charts are only used for special purposes, e.g. as original value chard for the determination of warning and control limits or, for data analysis of time series (Shumway [1988] Montgomery et al. [1990]). All the other types of charts are used relatively often and have their special advantages (Besterfield [1979] Montgomery [1985] Wheeler and Chambers [1990]). 

Here we cannot assume that a single value of standard deviation is applicable. Insert control materials in total numbers approximately as recommended above. However, there should be at least two levels of analyte represented, one close to the median level of typical test materials, and the other approximately at the upper or lower decile as appropriate. Enter values for the two control materials on separate control charts. Duplicate a minimum of five test materials, and insert one procedural blank per ten test materials. 

Product appearance was unremarkable. The pH was examined using a control chart. Because this is a single point observation, the moving range method was employed. The chart disclosed that the process operates within the calculated control limits. No trends were apparent. Individual batch results all met specification, and the process average (4.07) is close to the target value of 4.10. (See Fig. 11.)... 

Another approach suggested by Bolton (11) in constructing a quality control chart, based upon a single numerical value for each lot or batch, is to use the relative standard deviation (RSD) of the data set ... 

When fewer than about 100 measurements of the same type are needed, the use of control charts becomes impractical. A few repeat measurements made within the routinely encountered range of relevant values is sufficient to estimate the repeatability of a single measurement. Difficulty arises only when a measurement type or procedure is inordinately time-consuming or costly to replicate. Relevant examples are the measurement of an unusual trace constituent in a sample of minimal size, and a lengthy isotope dilution mass-spec-trometric determination. The analyst is then required to depend on general experience of reliability of a method and would be wise to estimate the uncertainty with special care. 

It is evident that the distance between the inhouse and the specification limits is influenced by the quality of the calibration/measurement procedure a fixed relation, such as 2(j, 3(j, as has been proposed for control charts, might well be too optimistic or too pessimistic (for a single test result exactly on the 2(7 inhouse limit, the true value would have a = 16% chance of being outside the 3(7 SL). Note that it takes at least n - 6 (resp. n = 11) values to make a z = 2 (z = 3) scheme (see Figure 1.24) even theoretically possible. For n = 4, for instance, xmean would have to be > 1.5 a in order that the largest x could be beyond 3a run a series of simulations on program CONVERGE and concentrate on the first four data points to see that an OOS... 

For case (1), a group control chart could be maintained on all streams but it suffices to plot only the two streams corresponding to the highest and lowest values. The chart limits are set up for a single stream and run rules should not be used. If the output of the heads is highly correlated, then a single chart on one stream may be used as a surrogate for all streams. 

In Fig. 8, the y-axis shows OD units. The x-axis contains columns, each one representing the data from a single plate. This chart is for plotting OD data from the Cm control. The expected mean of the Cm (given in the kit manual) and the allowed variation from the mean values are shown in the gray areas. This represents 1,2, and 3 SD from the mean. The test values obtained on a... 

Control Charts for Variables and Attributes A control chart for variables is used to monitor characteristics that can be measured and have a continuum of values, such as height, weight, or volume. A soft drink bottling operation is an example of a variable measure, since the amount of liquid in the bottles is measured and can take on a number of different values. A control chart for attributes, on the other hand, is used to monitor characteristics that have discrete values and can be counted. An attribute requires only a single decision, such as yes or no, good or bad, acceptable or unacceptable, or counting the number of defects. Both of them find wide application in the manufacturing industry. 

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