The control chart

In time-series analysis, we are interested in the development of the SHE performance indicators over time. This is done in so-called control charts, where the SHE performance indicator is calculated for consecutive periods and displayed in a diagram. These charts allow us to study changes in performance from one period to the next and trends over several periods. 

The measured LTI-rate for a period is an estimate of the underlying or true LTI-rate. From the statistical theory presented in Chapter 9 we know, however, that this estimate is uncertain and that we must expect the rate to fluctuate from period to period due to pure chance. The upper and lower control limits define the range in between which the LTI-rate will fall on average in 19 out of 20 periods, provided that the underlying accident risk at the company is unchanged. These limits are calculated from the mean LTI-rate during the studied periods, since this is considered to be the best estimate of the true LTI-rate. 

We consider a change in the LTI-rate for the latest period to be significant, if its value falls outside the control limits for earlier periods. 

The upper and lower control limits are calculated by applying the following formulas (1), (2) and (3)  

Example An aluminium plant has 2000 employees and each employee works 1800 hours a year. During the last ten years, an average of 35 losttime accidents per year was registered. For a control chart with a periodicity of one year, we calculate the following  

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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... 

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... 

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... 

Documentation verifying job set-ups should include documentation to perform the setup and records that demonstrate that the set-up has been performed as required. This requires that you record the parameters set and the sample size and retain the control charts used which indicate performance to be within the central third of the control limits. These records should be retained as indicated in clause 4.16 of the standard. 

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... 

One method of data presentation which is in widespread use is the control chart. A number of types of chart are used but where chemical data are concerned the most common types used are Shewhart charts and cusum charts. Only these types are discussed here. The charts can also be used to monitor the performance of analytical methods in analytical laboratories. 

Control Charts. The control chart approach (Montgomery, 1985), commonly used in manufacturing quality control in another form of screening (for defective product units), offers some desirable characteristics. 

There are numerous approaches to the problem of capturing all the information in a set of multi endpoint data. When the data are continuous in nature, approaches such as the analog plot can be used (Chemoff, 1973 Chambers et al., 1983 Schmid, 1983). A form of control chart also can be derived for such uses when detecting effect rather than exploring relationships between variables is the goal. When the data are discontinuous, other forms of analysis must be used. Just as the control chart can be adapted to analyzing attribute data, an analog plot can be adapted. Other methods are also available. 

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. 

Plot your measured weight on the control chart. If any irregularity is observed, report to your instructor. 

Create the standard curves (one for caffeine and one for benzoate) by plotting peak size vs. concentration. Use the spreadsheet procedure in Experiment 18. Obtain the concentrations of the unknowns and the control. Plot the results for the control sample on the control chart for this instrument posted in the laboratory. 

Copies of the control charts and duplicate value control charts or other agreed measures to monitor IQC. 

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. 

Measurements marked in the control chart are between-batch... 

Slow but constant changes of the equipment or of chemicals will lead to a trend in the control chart. After seven increasing or decreasing values the reason should be investigated. 

The Difference Chart is very similar to the range chart bnt it nses the difference between donble measurements together with its sign. The sample is measnred at the beginning and at the end of a series. The difference between the two measnrements is marked in the control chart with its sign. 

The first two contain all the transparencies in English and German language respectively and the latter two the control charts programme ExceUControl 2.1. To view the transparencies or use the programme contained in the zipped files, you will have to enter the password that you find printed at the end of Chap. 15. We strongly recommend that you download the zipped files to your own computer. 

Calculate the parameters for the control chart, that is, centerline and control limits. 

Conduct periodic audits on the parameters of the control chart. 

The control charts are shown in Figure 11. The x and s charts show that the process is in control and thus the parameters established here can be used to monitor future productions. 

The control charts discussed earlier are very useful in the diagnostic aspects of quality process improvement. They can be used to stabilize a process by identifying out-of-control situations. After the process is stabilized and brought in control, further improvement of the process can be achieved by using some special control charts such as the cumulative sum (CUSUM) control chart and the exponentially weighted moving average (EWMA) control chart. These control charts can be used when small shifts in a process are of interest. 

For quality control, 25 tablets are removed at random from the manufacturing line each hour and analyzed. The mean value of vitamin C in the 25 tablets is shown by a data point on the control chart. 

Let s next direct our attention to the testing done by quality control. The ATW at the core stage is based on the results from weighing 20 randomly selected tablets. The control chart in Figure 7 depicts a process with no single... 

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... 

Once the mechanics of retrospective validation are mastered, a decision is required as to how data analysis will be handled. The illustrated calculations may be performed manually with the help of a programmable calculator and the control charts may be hand-drawn, but computer systems are now available that can shorten the task. If the computer route is chosen, commercially available software should be considered. There are many reasonably priced programs that are more than up to the task [17]. 

When conducting an inspection, several target areas must be evaluated. Control limits or "charts" are helpful and should be established by plotting the defined limits of acceptable quality control. These charts are important tools for assessing laboratory precision, accuracy, and reproducibility. They can be based on a curve established from the high, mid, and low concentrations of a standard analyte. Either the mid level or the average of the three concentrations then becomes the mid-line for the control chart. Acceptable levels of fluctuation for routine mid-level standards,... 

There are two types of control charts accuracy chart and precision control chart. Accuracy control charts are prepared from the percent spike recoveries data obtained from multiple routine analysis. Precision control charts may be prepared from the relative percent difference (RPD) of analyte concentrations in the samples and their duplicate analytical data. Alternatively, RPDs are calculated for percent recoveries of the analytes in the matrix spike and matrix spike duplicate in each batch and twenty (or any reasonable number of data points) are plotted against the frequency or number of analysis. If the samples are clean and the analytes are not found, the aliquots of samples must be spiked with the standard solutions of the analytes and the RPD should be determined for the matrix spike recoveries. Ongoing data quality thus can be checked against the background information of the control chart. Sudden onset of any major problem in the analysis can readily be determined from the substantial deviation of the data from the average. 

These control limits are plotted on the control chart, along with the hourly yield data as shown in Fig. 1.10. 

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