Control charting

It is often important in practice to know when a process has changed sufficiently so that steps may be taken to remedy the situation. Such problems arise in quality control where one must, often quickly, decide whether observed changes are due to simple chance fluctuations or to actual changes in the amount of a constituent in successive production lots, mistakes of employees, etc. Control charts provide a useful and simple method for dealing with such problems. 

The control chart is set up to answer the question of whether the data are in statistical control, that is, whether the data may be retarded as random samples from a single population of data. Because of this feature of testing for randomness, the control chart may be useful in searching out systematic sources of error in laboratory research data as well as in evaluating plant-production or control-analysis data. ... 

Special attention should be paid to one-sided deviation from the control limits, because systematic errors more often cause deviation in one direction than abnormally wide scatter. Two systematic errors of opposite sign would of course cause scatter, but it is unlikely that both would have entered at the same time. It is not necessary that the control chart be plotted in a time sequence. In any... 

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 focus of this chapter is on the two principal components of a quality assurance program quality control and quality assessment. In addition, considerable attention is given to the use of control charts for routinely monitoring the quality of analytical data. 

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... 

Construct a property control chart for the following spike recovery data (all values are for percentage of spike recovered). 

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... 

Constructing a Precision Control Chart The most common measure of precision used in constructing a precision control chart is the range, R, between the largest and smallest results for a set of j replicate analyses on a sample. 

To construct the control chart, ranges for a minimum of 15-20 samples (preferably 30 or more samples) are obtained while the system is known to be in statistical control. The line for the average range, R, is determined by the mean of these n samples... 

Construct a precision control chart using the following 20 ranges, each determined from a duplicate analysis of a 10-ppm calibration standard... 

Interpreting Control Charts The purpose of a control chart is to determine if a system is in statistical control. This determination is made by examining the location of individual points in relation to the warning limits and the control limits, and the distribution of the points around the central line. If we assume that the data are normally distributed, then the probability of finding a point at any distance from the mean value can be determined from the normal distribution curve. The upper and lower control limits for a property control chart, for example, are set to +3S, which, if S is a good approximation for O, includes 99.74% of the data. The probability that a point will fall outside the UCL or LCL, therefore, is only 0.26%. The... 

Example of the use of subrange precision control charts for samples that span a range of analyte concentrations. The precision control charts are used for... 

Examples of property control charts that show a run of data (highlighted In box) Indicating that the system Is out of statistical control. 

The same rules apply to precision control charts with the exception that there are no lower warning and lower control limits. 

Using Control Charts for Quality Assurance Control charts play an important role in a performance-based program of quality assurance because they provide an easily interpreted picture of the statistical state of an analytical system. Quality assessment samples such as blanks, standards, and spike recoveries can be monitored with property control charts. A precision control chart can be used to monitor duplicate samples. 

Once a control chart is in use, new quality assessment data should be added at a rate sufficient to ensure that the system remains in statistical control. As with prescriptive approaches to quality assurance, when a quality assessment sample is found to be out of statistical control, all samples analyzed since the last successful verification of statistical control must be reanalyzed. The advantage of a performance-based approach to quality assurance is that a laboratory may use its experience, guided by control charts, to determine the frequency for collecting quality assessment samples. When the system is stable, quality assessment samples can be acquired less frequently. 

Another important quality assessment tool, which provides an ongoing evaluation of an analysis, is a control chart. A control chart plots a property, such as a spike recovery, as a function of time. Results exceeding warning and control limits, or unusual patterns of data indicate that an analysis is no longer under statistical control. 

The use of several QA/QC methods is described in this article, including control charts for monitoring the concentration of solutions of thiosulfate that have been prepared and stored with and without proper preservation the use of method blanks and standard samples to determine the presence of determinate error and to establish single-operator characteristics and the use of spiked samples and recoveries to identify the presence of determinate errors associated with collecting and analyzing samples. 

Laquer, F. C. Quality Control Charts in the Quantitative Analysis Laboratory Using Conductance Measurement, ... 

The conductivities of a standard solution of KCl, laboratory distilled water, and synthetic-process samples are monitored weekly and evaluated using a control chart. 

This experiment demonstrates how control charts and an analysis of variance can be used to evaluate the quality of results in a quantitative analysis for chlorophyll a and b in plant material. 

Construct a precision control chart for these data, and evaluate the state of statistical control. 

Additional information about the construction and use of control charts maybe found in the following sources. 

Statistical control of an analysis or instmment is best demonstrated by SQC of a standard sample analysis. The preferred approach to demonstrate statistical control is to use a reference sample of the subject material that has been carefully analyzed or, alternatively, to use a purchased reference standard. Either material must be stored so that it remains unchanged, eg, sealed in ampuls or septum capped bottles. Periodically a sample can then be reanalyzed by the technique used for routine analysis. These results are plotted in a control chart. Any change in the stabihty of the test in question results in a lack of... 

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