Measurements statistical control charts

Statistical control applies to all parts of the analytical system - sampling process, the calibration, the blank, and the measurement. Statistical control is attained by the quality control of the entire system and Involves maintenance of realistic tolerances for all critical operations. A system of control charts is the best way to demonstrate attainment of statistical control and to evaluate the appropriate standard deviations. In the simplest form, the results of measurement of a stable check sample, obtained over a period of time, are plotted. Statistical control is demonstrated when the values are randomly distributed around their average value." Control limits are often taken as 2 or 3 standard deviation units of these replicates. Dr. Taylor also adds, "Even the ranges of duplicate measurements of the actual samples tested can be plotted in a similar manner to demonstrate a stable standard deviation. In either case, the statistics of the control charts are the best descriptors of the variability of the measurement process."... 

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. 

Fig. 4.12. Statistical process control chart for TXRF measurement systems. The sensitivity of the system can be controlled by daily calibration with an...

For an example of a control chart see Fig. 1.31 and Sections 4.1 and 4.8. Control charts have a grave weakness the number of available data points must be relatively high in order to be able to claim statistical control . As is often the case in this age of increasingly shorter product life cyeles, decisions will have to be made on the basis of a few batch release measurements the link between them and the more numerous in-process controls is not necessarily straight-forward, especially if IPC uses simple tests (e.g. absorption, conductivity) and release tests are complex (e.g. HPLC, crystal size). 

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. 

Statistical process control charts (such as the x-bar and range charts) plot measurements as a function of time [Grant and Leavenworth (1988)]. With reference to the current day, what part of these charts approximates an enumerative study What part of these charts approximates an analytic study Are the parts different Are the uses different ... 

Figure 10.2 Statistical process control charts for clearings. Top panel runs chart showing clearings as a function of measurement number. Middle panel x-bar chart with dashed upper control limit (UCL) and lower control limit (LCL) solid horizontal line is the grand mean, X. Bottom panel range chart with dashed upper control limit (UCL) solid horizontal line is the average range, r.

The top panel in Figure 10.3 shows the issues as a function of measurement number. The bottom range chart shows that the short-term variability of the issues process is stable and in statistical control. The x-bar chart shows that the issues process mean is stable and in statistical control, with one exception at subgroup 19. A cyclical pattern appears to be present in the x-bar chart, but the structure is not as well defined as it is for the clearings data. 

It is very important for any measurement process to be under statistical control in order to have some assurance that the results are reliable. An easy way to quickly see if a process or procedure is under statistical control is to maintain what is called a control chart. A control chart is a plot of a measurement or analysis result on the y-axis vs. time (usually days) on the... 

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. 

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]. 

Statistical process control (SPC), also called statistical quality control and process validation (PV), represents two sides of the same coin. SPC comprises the various mathematical tools (histogram, scatter diagram run chart, and control chart) used to monitor a manufacturing process and to keep it within in-process and final product specification limits. Lord Kelvin once said, When you can measure what you are speaking about and express it in numbers, then you know something about it. Such a thought provides the necessary link between the two concepts. Thus, SPC represents the tools to be used, while PV represents the procedural environment in which those tools are used. 

In this chapter, several types of control charts for the analysis of historical data are discussed. Explanations of the use of x and R charts, for both two or more measurements per batch and only one measurement per batch, are give, along with explanations of modified control charts and cusum charts. Starting with a brief exposition on the calculation of simple statistics, the construction and graphic analysis of x and R charts are demonstrated. The concepts of under control and out of control, as well as their relationship to test specifications, are included. The chapter concludes with consideration of the question of robustness of x and R charts. 

The licensee shall establish and maintain a statistical control system including control charts and formal statistical procedures, designed to monitor the quality of each type of program measurement. Control chart limits shall be established to be equivalent to levels of (statistical) significance of 0.05 and 0.001. Whenever control data exceed the 0.05 control limits, the licensee shall investigate the condition and take corrective action in a timely manner. 

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

Construct a control chart for the reactor from Example 1.14. Use this chart to determine whether the reactor is under statistical control for the following averages of five measurements of yield taken at hourly intervals ... 

An example of a recovery control chart is shown in Figure 4.7. The mean recovery of individual measurements is represented by the centreline. The upper warning limit (UWL) and the lower warning limit (LWL) are calculated as plus/minus two standard deviations (mean recovery + 2s) and correspond to a statistical confidence interval of 95 percent. The upper control limit (UCL) and the lower control limit (LCL) are calculated as plus/minus three standard deviations (mean recovery 3s), and represent a statistical confidence interval of 99 percent. Control limits vary from laboratory to laboratory as they depend on the analytical procedure and the skill of the analysts. 

All uncertainty estimates start with that associated with the repeatability of a measured value obtained on the unknown. It is neither required for the sake of quality control, nor could it always be economically justified, to make redundant determinations of each measured value, such as would be needed for complete statistical control. Repeat measurements of a similar kind under the laboratory s typical working conditions may have given satisfactory experience regarding the range of values obtained under normal operational variations of measurement conditions such as time intervals, stability of measurement equipment, laboratory temperature and humidity, small disparities associated with different operators, etc. Repeatability of routine measurements of the same or similar types is established by the use of RMs on which repeat measurements are made periodically and monitored by use of control charts, in order to establish the laboratory s ability to repeat measurements (see sect, entitled The responsible laboratory above). For this purpose, it is particularly important not to reject any outlier, unless cause for its deviation has been unequivocally established as an abnormal blunder. Rejection of other outliers leads a laboratory to assess its capabilities too optimistically. The repeatability in the field of a certified RM value represents the low limit of uncertainty for any similar value measured there. 

In industrial plants, large numbers of process variables must be maintained within specified limits in order for the plant to operate properly. Excursions of key variables beyond these limits can have significant consequences for plant safety, the environment, product quality and plant profitability. Statistical process control (SPC), also called statistical quality control (SQC), involves the application of statistical techniques to determine whether a process is operating normally or abnormally. Thus, SPC is a process monitoring technique that relies on quality control charts to monitor measured variables, especially product quality. 

The major objective in SPC is to use process data and statistical techniques to determine whether the process operation is normal or abnormal. The SPC methodology is based on the fundamental assumption that normal process operation can be characterized by random variations around a mean value. The random variability is caused by the cumulative effects of a number of largely unavoidable phenomena such as electrical measurement noise, turbulence, and random fluctuations in feedstock or catalyst preparation. If this situation exists, the process is said to be in a state of statistical control (or in control), and the control chart measurements tend to be normally distributed about the mean value. By contrast, frequent control chart violations would indicate abnormal process behavior or an out-of-control situation. Then a search would be initiated to attempt to identify the assignable cause or the. special cause of the abnormal behavior... 

Shewhart control charts enable average process performance to be monitored, as reflected by the sample mean. It is also advantageous to monitor process variability. Process variability within a sample of k measurements can be characterized by its range, standard deviation, or sample variance. Consequently, control charts are often used for one of these three statistics. 

Finally, there is the need for proper documentation, which can be in written or electronic forms. These should cover every step of the measurement process. The sample information (source, batch number, date), sample preparation/analytical methodology (measurements at every step of the process, volumes involved, readings of temperature, etc.), calibration curves, instrument outputs, and data analysis (quantitative calculations, statistical analysis) should all be recorded. Additional QC procedures, such as blanks, matrix recovery, and control charts, also need to be a part of the record keeping. Good documentation is vital to prove the validity of data. Analyt-... 

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. 

---