Control chart factors

The (I2 factor is used to provide an estimate of the process standard deviation a = R/d2, where the caret (") denotes an estimated value. More extensive tables of control chart factors are available. ... 

For a subgroup size of n = 5, the control chart factors taken from Table 1 were ... 

Establish control charts of instrumental performance. Day-to-day variations in pump flow rate, relative response factors, absolute response to a standard, column plate counts, and standard retention times or capacity factors are all useful monitors of the performance of a system. By requiring that operators maintain control charts, troubleshooting is made much easier. The maintenance of control charts should be limited to a few minutes per day. 

Several method performance indicators are tracked, monitored, and recorded, including the date of analysis, identification of equipment, identification of the analyst, number and type of samples analyzed, the system precision, the critical resolution or tailing factor, the recovery at the reporting threshold level, the recovery of a second reference weighing, the recovery for the control references (repeated reference injections for evaluation of system drift), the separation quality, blank issues, out of spec issues, carry over issues, and other nonconformances. The quantitative indicators are additionally visualized by plotting on control charts (Figure 23). 

In most applications, the choice between a variable control chart and an attribute control chart is clear-cut. In some cases, the choice will not be obvious. For instance, if the quality characteristic is the softness of an item, such as the case of pillow production, then either an actual measurement or a classification of softness can be used. Quality managers and engineers will have to consider several factors in the choice of a control chart, including cost, effort, sensitivity, and sample size. Variable control charts usually provide more information to analysts but cost more to implement and use. Attribute control charts are less sensitive and expensive but usually requires large samples to reach certain statistical significance. 

EWMA Control Chart An EWMA control chart plots weighted moving average values for variables data. A weighting factor is chosen by the user to determine how older data points affect the mean value compared to more recent ones. Because the EWMA chart uses information from all samples, it is a good alternative to the CUSUM chart in detecting smaller process shifts. 

Figure 4.22 Example of a control chart to test for outlying samples on the calibration set. Four factors were used to develop the model (original spectra from Figure 4.9, mean centred).

The alcohol content averaged 15.09%, or 0.09% above target. Individual batches met specification in every instance. The control chart (Fig. 12) was unremarkable in terms of trends or tests for pattern instability. Batch 3 is slightly below the process average, effectively ruling out overaddition of alcohol as a factor in the low specific gravity previously observed. 

The concentration of active ingredient D1 for batch to batch is shown in Figure 13. The mean potency of all batches is 0.1 mg/5 ml above target. The control chart did not respond to tests for unnatural patterns and trends. It is noteworthy that the calculated UCL (16.7 mg/5 mL) for the 20 batches in this study exceeds the release specification for the product (15.5 to 16.5 mg/5 ml. A probability thus exists that a batch may eventually fail to meet the release criteria. Raw material purity is not a factor in the potency of an individual batch because it is taken into consideration at the time of manufacture. A possible explanation for the wide historical control limits is the assay methodology for... 

Frequently, however, the lack of specificity in an analytical technique can be compensated for with sophisticated data processing, as described in the chemometrics chapter of this text (Chapter 8). Quinn and associates provide a demonstration of this approach, using fiber-optic UV-vis spectroscopy in combination with chemometrics to provide realtime determination of reactant and product concentrations.23 Automatic window factor analysis was used to evaluate the spectra. This technique was able to detect evidence of a reactive intermediate that was not discernable by off-line HPLC, and control charting of residuals was shown to be diagnostic of process upsets. Similarly, fiber-optic NIR was demonstrated by some of the same authors to predict reaction endpoint with suitable precision using a single PLS factor.24... 

Quality assurance (QA) measurements also are performed with a set of QA gamma-ray sources to confirm that the radiation detection instrument is functioning normally. The measurements are performed at regular intervals and the results are plotted to show the mean value and random deviations by 1 and 2 standard deviations (cr and 2cr). The factors that are considered include the count rate at characteristic control source peaks, the resolution of these peaks, and the background radiation shown by the detector. Any significant deviations beyond the 2-sigma values on the control charts require a repeated measurement and - if confirmed - corrective actions before further measurements are performed. 

Indebtedness is expressed to Prof. R. A. Fisher and Dr. Frank A. Yates for permission to reprint Tables III-VI from their book Statistical Tables for Biological, Agricultural, and Medical Research (Oliver Boyd, Edinburgh and London), and to the British Standards Institution for permission to reprint certain factors for Quality Control Charts from B.S, 600R, Quality Control Charts. ... 

Samples can be divided into two aliquots and analyzed, and the duplicates used for control purposes. This is a simple quality control procedure that does not require stable control materials and therefore can be used when stable materials are not available or as a supplemental procedure when stable control materials are available. The differences between duplicates are plotted on a range type of control chart that has limits calculated from the standard deviation of the differences. When the duplicates are obtained from the same method, this range chart monitors only random error and thus is not adequate for ensuring the accuracy of the analytical method. When the duplicates are obtained from two different laboratory methods, then the range chart actually monitors both random and systematic errors but cannot separate the two types of errors. The interpretation becomes more difficult, particularly when there are stable systematic differences or biases between the two analytical methods. Multiplicative factors may be necessary to deal with proportional differences, and additive factors may be necessary to allow for constant differences. Interpretation of observed differences becomes more qualitative nevertheless, this procedure still provides a useful way of monitoring the consistency of the data being generated by the laboratory. 

Figure 7.2 The use of a biomarker index in temporal and spatial studies. In this survey, three sites were sampled over ten different time periods. In order to sort out natural variation in time, a control chart approach is used. The median value of the pristine site is plotted with the 10th, 25th, 75th and 90th centiles. Biomarker index values outside the 90th and 10th centiles are most likely to be outside natural variability and could be associated with pollution factors.

SD itself does not yield useful information, unless compared to the mean (%CV Section 15.1). Between-assay variation is generally greater than within-assay variation, but care should be taken with the latter to reduce bias by randomly distributing the duplicates. The between-assay variation is usually of more value to estimate the accuracy of the procedure and, plotted on a quality-control chart, may indicate trends, such as deterioration of reagents (bias-type error Section 1.3). An example of the calculation of the within-assay and between-assay variability is given in Table 15.3. In this example, the SD of between-assay results is about 5-6 times higher than for the within-assay results. For a satisfactory EIA, this factor should be less than 2-3 and the between-assay variability should be less than 10%. 

Factors Used in the Quality Control Chart Technique ... 

Since there is no grouping of the measurements for X charts, the power of rational subgrouping is not available. The use of stratification and rational ordering of the measurements with X charts provides an alternative to rational subgrouping for individual charts. Stratification is the separation and classification of data according to selected variables or factors. Stratification on a control chart is done in two different ways. 

SAMMIE, see System for Aiding Man-Machine Interaction Evaluation Sampling. See also Work sampling in health care systems, 745-746 in human factors audits, 1135-1136 when using control charts, 1840 Sanden Corporation, 555 SAP AG, 87, 95, 96, 304, 306, 492, 1002,... 

An invaluable tool for troubleshooting and maintenance is the instrument control chart. Anything useful can be control charted, such as detector response factors, deviation from expected retention time, etc., but the analysis results from a check gas is one of the most popular items to chart. The most important information a control chart can show is when the instrument needs maintenance or recalibration. While it may seem like a good idea to recalibrate every day, the act of recalibration has error associated with it, and thus overcalibrating can be as much of a problem as undercalibrating. Statistical tools can... 

The accurate use of control charts depends on the distribution of data being similar to the statistical normal distribution. Statistical assumptions are not valid unless there is a sufficient sample size (accident cases per month) and there are factors that cause a sudden change in data. To assure a control chart s vahdity, there should be about 60 sampling periods (typically months). 

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