Statistical methods control charts

Performance test results should be plotted on charts for trend analysis. Statistical quality control charting methods are used to detect statistically significant changes in instrument performance. Action limits can be set for test charts based on historical data so that appropriate repairs can be made when necessary. Examples of unacceptable instrument performance may be valuable in setting action limits for future performance tests. 

Method validation provides information concerning the method s performance capabilities and limitations, when applied under routine circumstances and when it is within statistical control, and can be used to set the QC limits. The warning and action limits are commonly set at twice and three times the within-laboratory reproducibility, respectively. When the method is used on a regular basis, periodic measurement of QC samples and the plotting of these data on QC charts is required to ensure that the method is still within statistical control. The frequency of QC checks should not normally be set at less than 5% of the sample throughput. When the method is new, it may be set much higher. Quality control charts are discussed in Chapter 6. 

This chapter deals with handling the data generated by analytical methods. The first section describes the key statistical parameters used to summarize and describe data sets. These parameters are important, as they are essential for many of the quality assurance activities described in this book. It is impossible to carry out effective method validation, evaluate measurement uncertainty, construct and interpret control charts or evaluate the data from proficiency testing schemes without some knowledge of basic statistics. This chapter also describes the use of control charts in monitoring the performance of measurements over a period of time. Finally, the concept of measurement uncertainty is introduced. The importance of evaluating uncertainty is explained and a systematic approach to evaluating uncertainty is described. 

This chapter has considered two key aspects related to quality assurance - the use of control charts and the evaluation of measurement uncertainty. These activities, along with method validation, require some knowledge of basic statistics. The chapter therefore started with an introduction to the most important statistical terms. 

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. 

FIGURE 1.5 An example of a control chart showing a device, procedure, process, or method that is in statistical control because the numerical values are consistently between the warning limits. 

The LIMS computer is located on the site, and several terminals may be provided for entry of data from notebooks and instrument readouts and for the retrieval of information. Bar coding for sample tracking and access codes for laboratory personnel are part of the system. Instruments may be interfaced directly with the LIMS computer to allow direct data entry without help from the analyst. The LIMS may also incorporate statistical methods and procedures, including statistical control and control chart maintenance. See Workplace Scene 6.4. 

Statistical Control for a New Method To implement a new method, a laboratory must produce a preliminary track record of its success so that quality control charts can be established and then maintained. Aside from acquiring the space, supplies, equipment, instrumentation, and manpower required, the method must be tested, modified, tested again, etc., until it is ready to go "online." Gillis and Callio (listed in Bibliography) recommend the following sequence for preparing an instrumental method for routine use. 

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... 

Two aspects are important for IQC (1) the analysis of control materials such as reference materials or spiked samples to monitor trueness and (2) replication of analysis to monitor precision. Of high value in IQC are also blank samples and blind samples. Both IQC aspects form a part of statistical control, a tool for monitoring the accuracy of an analytical system. In a control chart, such as a Shewhart control chart, measured values of repeated analyses of a reference material are plotted against the run number. Based on the data in a control chart, a method is defined either as an analytical system under control or as an analytical system out of control. This interpretation is possible by drawing horizontal lines on the chart x(mean value), x + s (SD) and x - s, x + 2s (upper warning limit) and x-2s (lower warning limit), and x + 3s (upper action or control limit) and x- 3s (lower action or control limit). An analytical system is under control if no more than 5% of the measured values exceed the warning limits [2,6, 85]. 

NIST (2006), NIST/SEMATECH e-handbook of statistical methods—6.3.2.3. CuSum control charts, http //www.itl.nist.gov/div898/handbook/ (Accessed 22 January 2006). 

The Reliability of Measurements. The Analysis of Data. The Application of Statistical Tests. Limits of Detection. Quality Control Charts. Standardization of Analytical Methods. 

Table 5.4 summarizes common acceptance criteria for laboratory QC checks. Laboratories rarely exceed these method-prescribed criteria for trace element and inorganic analyses. For organic analyses, laboratories generate their own acceptance criteria by means of statistical control charts as described in Chapter 4.6.1.3. 

Probably the two most basic generic industrial problems commonly approached using statistical methods are those of (1) monitoring and maintaining the stability/consistency of a process and (2) assessing the capability of a stable process. This section provides a brief introduction to the use of tools of control charting in these enterprises. 

The intent in this chapter is not to present in great detail the mathematics behind the statistical methods discussed. An excellent reference manual assembled by the Automotive Industry Action Group (AIAG), Fundamental Statistical Process Control, details process control systems, variation, action on special or common causes, process control and capability, process improvement, control charting, and benefits derived from using each of these tools. Reprinted with permission from the Fundamental Statistacal Process Control Reference Manual (Chrysler, Ford, General Motors Supplier uality Requirements Task Force , Measurement Systems Analysis, MSA Second Edition, 1995, ASQC Press. 

The reliability of measurements. The arrptysis of data. The application of statistical tests. Limits of detection. Quality control charts. Standardization of analytical methods. Chcmometrics. 

A control chart (quality control chart) is a graphical record of the results of the analysis of a quality control sample using a particular method. Monitoring these results over a period of time is one of the most useful ways of determining whether or not a method is in statistical control, i.e. it is performing in a consistent manner. It helps to indicate the reliability of the results. There are many forms of control chart,one of the most commonly used is the Shewhart Chart (Figure 4). 

Control charts often have a center line and two control lines with two pairs of limits a warning line at m 2s and an action line at m 3s. Statistics predict that 95.45% and 99.7% of the data will fall within the areas enclosed by the 2s and 3s limits. The center line is either the mean or the true value. In the ideal case, where unbiased methods are being used, the center line would be the true value. This would apply, for example, to precision control charts for standard solutions. 

The literature of industrial quality control is now very great. The standard work is W. A.. Shewhart s Economic Control of Quality of Manufactured Product (Macmillan r 1931). Short accounts are British Standard 600R Qualitj Control Charts, B. P. Dudding and W. J. Jennett, 1942 British Standard 1008 Quality Control A First Guide to Quality Control for F-ngineers, E. H. Sealy, H.M.S.O., 1946. A fuller account is L. E. Simon s An Engineer s Manual of Statistical Methods (Chapman Hall, 1941). 

Statistical Quality Control (SQC) or Statistical Process Control (SPC) is an effective method of monitoring a process through control charts that enable the use of objective criteria for distinguishing background variation from events of significance based on statistical techniques. 

The latter are hence extremely useful to monitor the performance of an analytical method with time by setting up control charts which allow for the statistical control of measurements (33). Reference materials are necessarily homogeneous and stable. If analyzed at regular intervals, quick and clear information can be gained on any tendency for the analytical process to go out of control when the... 

The monitoring of analytical quality by the use of statistical methods and control charts. 

The application of statistics to support analytical results is usually the final step in reporting. Statistics can reveal much information about the determined result and ensure confidence in results. It can be applied in several ways and one of its most effective uses is the generation of the control charts to monitor the routine analysis of samples to determine whether the preparation of standards and instrument parameters are correct and no contamination has crept into the sample, reagents and instrument or during sample preparation. A control chart is generated from a control standard and is a visual display of confidence in the method. It can warn the operator if the sample/insfrument parameters are in, or out of, control and whether corrections are necessary before proceeding with the analysis. 

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