Upper control limits

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

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. 

The BMS deviation is a measure of the spread of values for c around the mean. A large value of O indicates that wide variations in c occur. The probability that the controlled variable hes between the values of Cl and C9 is given by the area under the distribution between Ci and Cg (histogram). If the histogram follows a normal probabihty distribution, then 99.7 percent of aU observations should lie with 3o of the mean (between the lower and upper control limits). These Emits are used to determine the quality of control. 

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.

In preparing a control chart, the mean upper control limit (UCL) and lower control limit (LCL) of an approved process and its data are calculated. A control chart with mean UCL and LCL with no data points is created data points are added as they are statistically calculated from the raw data. (See also the chapter on control charts)... 

Center line (x) = 10.254 Upper control limit (UCL) = 11.761 Lower control limit (LCL) = 8.747... 

LCL = lower control limit, UCL = upper control limit. 

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). 

Worst-case conditions Trial 1 (lower control limit). Trial 10 (upper control limit). X variables randomly assigned. Best values to use are RSD of data set for each trial. When adding up die data by columns, + and — are now numerical values and the sum is divided by 5 (number of +s or —s). If the variable is not significant, the sum will approach zero. 

The upper control limits would be 7.08+A2(0.2) = 7.08 + (1.88)(0.2) = 7.46. Concerns over batches 2 and 4 arise naturally. The modified control chart calls for the use of 15- (a/2- 1)(1.88)(0.2) = 14.2 as the UCL and thus eliminates the questions over batches 2 and 4. In the application of process validations, these situations are frequently encountered, and modified control charts enable us to claim the validation of the process. 

Such data are shown in Table 3 and Fig. 6. Upper and lower control limits are calculated based upon n = 2 and A2 = 1.880. Thus, for 10 lots there will be 9 data points to plot, which results in a robust analysis of the quality control data for the product. Unlike a normal control chart, when you decide to use RSD values to create the quality control chart, the lower control limit (LCL) is more desirable than the upper control limit (UCL) simply because lower RSD values reflex a tighter dispersion around the mean. 

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. 

A surrogate standard recovery that is above the upper control limit is not necessarily an indication of a high bias in the sample result. It may indicate matrix interference, a preparation error, or a measurement error. 

The Shewhart chart in Fig. 8-46 has a target (T), an upper control limit (UCL), and a lower control limit (LCL). The target (or centerline) is the... 

When multiple samples are collected throughout the entire work shift, the Upper Control Limit at 95% confidence may be calculated by the following equation ... 

The R and 5 charts in Figs 5.12 and 5.13 are related representations (only one is typically made in practice) of the shift-to-shift behavior of melt index consistency. It is seen that on both charts, the shift 3 point plots above the upper control limit. The strong suggestion thus is that melt index consistency was detectably worse on that shift than on the others, so that from this point of view the process was in fact not stable over the time period represented in Table 5.4. In practice, physical investigation and hopefully correction of the origin of the... 

Around the CL are the control limits, set at 3 SE of the statistic being plotted. If the statistic value falls outside the control limits, this is a signal that the process is not in a state of statistical control. Because the standard errors are functions of the process standard deviation a, an estimate of this quantity is necessary. This can be supplied by the average range. The lower control limit (LCL) and upper control limit (UCL) are calculated as follows ... 

UCL Upper control limit of average tablet weight 101.5... 

UCLp Upper control limit for average compression force 11.5... 

As an example, consider monitoring the performance of a modern analytical balance. Both the accuracy and the precision of the balance can be monitored by periodically determining the mass of a standard. We can then determine whether the measurements on consecutive days are within certain limits of the standard mass. These limits are called the upper control limit (UCL) and the lower control limit (LCL). They are defined as... 

Figure 8-15 A control chart for a modem analytical balance. The results appear to fluctuate normally about the mean except for those obtained on day 17. Investigation led to the conclusion that the questionable value resulted from a dirty balance pan. UCL = upper control limit LCL = lower control limit.

---