Standard deviation control chart

Construction of the Relative Standard Deviation Control Chart for Blend Uniformity... 

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

Figure 15.3 Mean and standard deviation control charts for grouped data from Figure 15.2 (n = 4)...

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. 

Some measure of dispersion of the subgroup data should also be plotted as a parallel control chart. The most reliable measure of scatter is the standard deviation. For small groups, the range becomes increasingly significant as a measure of scatter, and it is usually a simple matter to plot the range as a vertical line and the mean as a point on this line for each group of observations. 

The principal tool for performance-based quality assessment is the control chart. In a control chart the results from the analysis of quality assessment samples are plotted in the order in which they are collected, providing a continuous record of the statistical state of the analytical system. Quality assessment data collected over time can be summarized by a mean value and a standard deviation. The fundamental assumption behind the use of a control chart is that quality assessment data will show only random variations around the mean value when the analytical system is in statistical control. When an analytical system moves out of statistical control, the quality assessment data is influenced by additional sources of error, increasing the standard deviation or changing the mean value. 

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... 

Statistical quaUty control charts of variables are plots of measurement data, preferably the average result of repHcate analyses, vs time (Fig. 2). Time is often represented by the sequence of batches or analyses. The average of all the data points and the upper and lower control limits are drawn on the chart. The control limits are closely approximated by the sum of the grand average plus for the upper control limit, or minus for the lower control limit, three times the standard deviation. 

If three consecutive samples show a trend of being on either the high or the low side of the average, a fourth sample is run immediately. If this sample shows the same trend, a new calibration is performed and a new run chart is created. In this case the average is created using only 15 injections and the previous standard deviations are used to compute the new upper and lower control limits. 

The conventional control chart is a graph having a time axis (abscissa) consisting of a simple raster, such as that provided by graph or ruled stationary paper, and a measurement axis (ordinate) scaled to provide six to eight standard deviations centered on the process mean. Overall standard deviations are used that include the variability of the process and the analytical uncertainty. (See Fig. 1.8.) Two limits are incorporated the outer set of limits corresponds to the process specifications and the inner one to warning or action levels for in-house use. Control charts are plotted for two types of data ... 

Current Developments. A number of low-cost proprietary temperature loggers are being trialled in conjunction with the above IS Controller. In one form (14) these produce only a strip chart data table. Although convenient for statistical analysis these require keying into a further microcomputer plotter to draw a complete process temperature profile, as shown in Figure lb. As an illustration of the IS Controller s performance, statistics for the 150 minutes after exothermic overshoot indicate a mean temperature within 0.1"C of the set point and a standard deviation of 0.4°C. 

One can apply a similar approach to samples drawn from a process over time to determine whether a process is in control (stable) or out of control (unstable). For both kinds of control chart, it may be desirable to obtain estimates of the mean and standard deviation over a range of concentrations. The precision of an HPLC method is frequently lower at concentrations much higher or lower than the midrange of measurement. The act of drawing the control chart often helps to identify variability in the method and, given that variability in the method is less than that of the process, the control chart can help to identify variability in the process. Trends can be observed as sequences of points above or below the mean, as a non-zero slope of the least squares fit of the mean vs. batch number, or by means of autocorrelation.106... 

Probability plot Q-Q plot P-P Plot Hanging histogram Rootagram Poissonness plot Average versus standard deviation Component-plus-residual plot Partial-residual plot Residual plots Control chart Cusum chart Half-normal plot Ridge trace Youden plot... 

Analytical laboratories, especially quality assurance laboratories, will often maintain graphical records of statistical control so that scientists and technicians can note the history of the device, procedure, process, or method at a glance. The graphical record is called a control chart and is maintained on a regular basis, such as daily. It is a graph of the numerical value on the y-axis vs. the date on the x-axis. The chart is characterized by five horizontal lines designating the five numerical values that are important for statistical control. One is the value that is 3 standard deviations from the most desirable value on the positive side. Another is the value that is 3 standard deviations from the most desirable value on the negative side. These represent those values that are expected to occur only less than 0.3% of the time. These two numerical values are called the action limits because one point outside these limits is cause for action to be taken. 

A procedure or method maybe checked by the use of a quality control solution (often called a control), a solution that is known to have a concentration value that should match what the procedure or method would measure. The known numerical value is the desirable value in the control chart. The numerical value determined for the control by the procedure or method is charted. The warning and action limits are determined by preliminary work done a sufficient number of times so as to ascertain the population standard deviation. 

Here the concentration range of the analyte in the ran is relatively small, so a common value of standard deviation can be assumed. Insert a control material at least once per ran. Plot either the individual values obtained, or the mean value, on an appropriate control chart. Analyse in duplicate at least half of the test materials, selected at random. Insert at least one blank determination. 

Longer (e g. n > 20) frequent runs of similar materials Again a common level of standard deviation is assumed. Insert the control material at an approximate frequency of one per ten test materials. If the run size is likely to vary from run to run it is easier to standardise on a fixed number of insertions per run and plot the mean value on a control chart of means. Otherwise plot individual values. Analyse in duplicate a minimum of five test materials selected at random. Insert one blank determination per ten test materials. 

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. 

STL s quality-control programme includes the recovery of known additions of analyte, analysis of externally supplied standards, calibration, analysis of duplicates and control charting. Each analyte is monitored by analysing at least one AQC standard for every 20 samples. AQC results are plotted on control charts and action is taken if a point Hes outside +3 standard deviations (SD) or if two consecutive points He outside +2 SDs. 

We are starting with the case where we have a control sample that covers the whole analytical process inclnding all sample preparation steps. The matrix of the control sample is similar to that of the routine samples. Then the standard deviation of the analysis of this sample (under between-batch conditions) can be used directly as an estimate for the reproducibility within the laboratory. The standard deviation can be taken directly from a control chart for this control sample (see chapterl3). In the table two examples are shown for different concentration levels. 

If we don t have such an ideal control sample, but only one with a matrix different from the routine sample (e.g. a standard solution) than we have to consider also the uncertainty component arising from changes in the matrix. For this purpose we use the (repeatability) standard deviation calculated from repeated measurements of our routine samples (performed e.g. for a range control chart). When we estimate the reproducibility within laboratory we now have to combine both contributions by calculating the square root of the sum of squares. 

We have seen two different approaches to estimate the measurement uncertainty. One was using data from control charts, CRM analysis, PT results and/or recoveiy tests and sometimes maybe also experience of the analyst, the other was just using the reproducibility standard deviations from interlaboratory tests. In most cases the second method delivers higher estimates. 

The measurements on the control sample usually are made with each batch and finally marked on the control chart are done under between-batch conditions. Therefore the standard deviation for the calculation of the limits should also be determined under the same between-batch conditions. The most common way to estimate this standard deviation is to use the results from a pre-period of about 20 working days. The use of the repeatabihty standard deviation would result in too narrow limits whilst interlaboratory conditions would lead to limits that are too wide. 

Real samples. The move to analyze real samples represents a move toward the unknown. Not only are the results of the analysis unknown ahead of time, but other variables relating to sample inhomogeneity, sample preparation variables, additional sources of error, etc. are introduced. A large number (>30) of duplicate samples should be analyzed so that a reliable standard deviation and a reliable control chart can be established. The ultimate purpose of this work is to characterize what is a typical analysis for this kind of sample so that one can know when the method is under statistical control and when... 

Assuming a standard deviation of 0.0002, add warning limits at 2 standard deviations and action limits at 3 standard deviations to your control chart. Is there any day that you would take the balance out of service and perhaps call in a service agent Explain. 

The common values of constants c4 and A3 are tabulated in Table 4 for sample sizes from 2 to 10. Like other control charts, the values of x and s should be periodically verified to assure that they can be used to derive good estimators for the process average and process standard deviation. 

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