Control limit lower

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 same rules apply to precision control charts with the exception that there are no lower warning and lower control limits. 

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. 

One point that occurs outside the upper or lower control limits... 

If three consecutive samples show a trend of being on either the high or the low side of the average, a fourth sample is run immediately. If this sample shows the same trend, a new calibration is performed and a new run chart is created. In this case the average is created using only 15 injections and the previous standard deviations are used to compute the new upper and lower control limits. 

If a molecular weight of Dowlex 2056 is outside the upper or the lower control limits, then the standard is rerun immediately to verify the trend. If the molecular weight of the rerun sample is again outside the control limits,... 

Figure 6.10 shows a range chart with upper and lower control limits. In this example, each batch of test samples contained four replicates of the QC sample. The range was calculated for each set of four QC results and plotted sequentially on the chart. The mean range value was 2.7. Since n = 4, the lower control limit is set at zero while the upper limit is set at 2.282 x 2.7 = 6.2. Note that each batch of analyses must contain the same number of replicates of the QC sample. 

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... 

Table 4.1. Average run length (ARL)for exceeding an upper or lower control limit 1/p(total), or giving seven results on one side of the center line 1/p(7) of a Shewhart means chart for deviations from the mean indicated...

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. 

Critical process variables should be set within their operating ranges and should not exceed their upper and lower control limits during process operation. Output responses should be well within finished product specifications. 

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. 

In a normal distribution curve 68.27% area lies between x Is, 95.45% area lies between x 2s, and 99.70% area falls between x 3s. In other words, 99.70% of replicate measurement should give values that should theoretically fall within three standard deviations about the arithmetic average of all measurements. Therefore, 3s about the mean is taken as the upper and lower control limits in control charts. Any value outside x 3s should be considered unusual, thus indicating that there is some problem in the analysis which must be addressed immediately. 

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. 

Let us establish a criterion whereby we conclude that the reactor is not in control if the mean of five measurements of yield is more than three standard deviations away from the population mean (as determined by the earlier 11 runs). Then we can establish upper and lower control limits on a control range X 3a, outside of which we initiate corrective action on the reactor operation. 

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. 

LCL LCS LCSD lower control limit laboratory control sample laboratory control sample duplicate... 

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... 

Control charts display the data (and variance) in the order they occur with statistically determined upper and lower control limits. The SPC charts are used to monitor the process for maintenance of the target to zero and then to determine whether process changes have accomplished their desired quality effect. ... 

The data in Table 26.3 are CIE LCH DH values as measured against a reference standard for several consecutive production runs. The time order for these values is given by reading down each column, beginning with the column on the left. The DH average range R from previous runs of the same product is 0.158 units when this value is divided by d2 = 1.128, we get an estimated standard deviation of 0.14 DH units. The midpoint of the DH specification for this product is 0.0. If 0.0 is taken as the central line for a control chart for individual values, then this chart will have the following upper and lower control limits (LCL, UCL) ... 

The balance of EWMA F,+i values in Table 26.4 are calculated in the same order as the original values in Table 26.3. Upper and lower control limits around the EWMA... 

Plotting the individual DH, X, EWMA, and upper and lower control limits against X,+l yields Figure 26.3. This figure varies considerably from a conventional EWMA... 

Six batches into the run, A" 8 falls below the EWIMA lower control limit XIS = -0.06 and steadily dropping. Shewhart control methodology would not indicate a process change was needed. Using the EWIMA, a decision can be made to leave the process alone or make a minor adjustment. In this case such an adjustment was made. By the end of the run, T24 = 0.0. At the start of the third run, at X21 and X21 > 0.0, the process was again adjusted downward, this time in response to greater than seven individual DH values from the MR2 chart above the mean. 

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