Upper warning limit limits

Statistical Factors for the Upper Warning Limit and Upper Control Limit... 

Figure 5.12 A control chart showing a consistent pattern outside the upper warning limit after Day 24, indicating that an evaluation of the situation is warrented. It may indicate a component of the system is out of calibration, etc.

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]. 

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. 

When the measurement process is under control, that is when any variation in counts is basically random, the counts obtained with the RMs, in 95% of the cases, fall between the lower and upper warning limits and in 99.1% of cases between the lower and upper action limits. When the variation in the counts does not conform to the pattern that might reasonably be produced by chance variation, then it is concluded that the process is out of control. It means that one or more systematic errors have been introduced into the system. Several tests for detecting out of control situations have been developed. The purpose of each test is to detect a particular non-random pattern in the points plotted on the control chart. These tests have been evaluated by Nelson [42,43]. The following criteria are used for interpreting the microhiological control charts [38,42] ... 

UWL = upper warning limit LWL = lower warning limit UCL = upper control limit LCL = lower control limit... 

LWL and the upper warning limit UWL are defined as two-thirds of the control limits and... 

Figure 5 A Shewhart means chart. The final two points are above the upper warning limit and would trigger suspension of the analysis and investigation of the process.

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... 

The upper and lower warning limits, which are located at +2S, should only be exceeded by 5% of the data thus... 

The average range of the data is multiplied by D to give the lower control limit (Dq ooi). lower warning limit (/I(i.(i25). upper warning limit ( >0.975) and upper control limit ( >0.999). Adapted from Oakland (1992). 

The upper and lower warning limits (UWL and LWL) are drawn at 2s above and below, respectively, of the mean recovery. The upper and lower control limits (UCL and LCL) are defined at 3s value about the mean. If ary data point falls outside UCL or LCL, an error in analysis is inferred that must be determined and corrected. The recoveries should fall between both the warning limits (UWL... 

Precision control charts may, alternatively, be constructed by plotting the RPDs of duplicate analysis measured in each analytical batch against frequency of analysis (or number of days). The mean and the standard deviation of an appropriate number (e g., 20) of RPDs are determined. The upper and lower warning limits and the uppper and lower control limits are defined at 2 and 3.v, respectively. Such a control chart, however, would measure only the quality of precision in the analysis. This may be done as an additional precision check in conjunction with the spike recovery control chart. 

The data are plotted on a control chart in time sequence. This enables the analyst to readily observe changes in the measured value. The analyst can define warning and action limits on the chart to act as alarm bells when the system is going out of control. In Figure 4, it shows that all the results of the analysis of the QC samples are within the warning limits except for one result which is between the upper warning and upper action limit. 

The X-chart is based on the use of a standard reference material analyzed preferably with each batch of unknowns. After a reasonable number of analyses of reference material samples (typically n>20), the mean and standard deviation of the data are calculated and a control chart constructed. The center line represents the mean, the two outer lines represent the upper and lower control limits (UCL and LCL), or 99% confidence limits, and the two lines closest to the mean line are the 95% confidence limits, or upper and lower warning limits (UWL and LWL). One analysis outside the 95% confidence limits is not cause for alarm however, two consecutive analyses falling on one side of the mean line between the 95% and 99% limits would certainly be cause for an investigation. Control charts are very useful in visualizing trends (Fig. 10.6). 

Upper action limit Upper warning limit... 

In addition to the control limits as given for both types of charts, very frequentlv lower and upper warning values are also given as the 2a limits. These are calculated in the same fashion as the control limits in regard to sample size. The lower warning limit... 

PEL, so that it cannot be considered to warn adequately of its presence by its odor. It is a significant fire hazard in addition to being a health hazard. The lower and upper explosion limits are, respectively, 3% and 100%. It will bum without the presence of air or other oxidizers, with a flash point below (-18"C) and may decompose violently at temperatures above 800 F (444"C). It wUI polymerize violently when contaminated with aqueous alkalis, amines, mineral acids, and metal chlorides and oxides. It would be classified as a class B fire hazard for purposes of comphance with 29 CFR 1910.155. Locations defined as hazardous due to its use would be class I locations for purposes of comphance with 29 CFR 1910.307. 

Upper action limit (3.09a) Upper warning limit (1.96a) Process mean Lower warning limit (1.96a) Lower action limit (3.09a)... 

Limit Upper action Upper warning Lower warning Lower action... 

The chart shows that the system is in control during the first 6 samples analyzed, but the upper warning level has been breached by result 7. However, the next 8 results are within the warning levels, but results 17 to 20 indicate a downward trend culminating with both lower limits being breached indicating a loss of control due to one or more determinate errors. At this point, the causes should be sought and remedial action taken. 

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