Upper control limit, UCL

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... 

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. 

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... 

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 ... 

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... 

A control chart is a run chart with the addition of a line indicating the mean and two lines indicating upper and lower control limits. A common upper control limit (UCL) is three standard deviations above the mean, and a common lower control limit (LCL)... 

Having established an X and R value, we can calculate an Upper Control Limit (UCL) and a Lower Control Limit (LCL). 

Step 3—Control chart. The main modification introduced in the model consists in the way in which the control chart is designed. Instead of the p-chart proposed by CCSM, the model uses a R-chart, which means Risk-chart. A R-chart is constructed by plotting the daily value of R against the date. R is the daily weighted average of all the proportion of non-conforming Risks. The Upper Control Limit (UCL) and the Lower Control Limit (LCL) are given by the formulas reported in Equation (3) and in Equation (4)... 

In order to create the control chart, it is finally necessary to estimate the average R (equation 12), the Upper Control Limit (UCL) (equation 13), and the Lower Control Limit (LCL). In order to simplify the model, the lower control limit has been set to zero. 

This value is symbolized by x (pronounced x double-bar). The center line of the R chart represents the average of the ranges of the samples. The top and the bottom lines of both charts represent the upper control limit (UCL) and the lower control limit (LCL), respectively, Generally, the control limits are three standard deviations (3a) above and below the center line. This means that the probability of measurements falling between 3 standard deviations is 99.73 percent of the observed values. Stated another way, between 3 standard deviations from the mean, one expects to find 99.73 percent of all the observed values. The values represented in Figure 16-26 are derived from the following example. 

A multivariate process is considered to be out-ofcontrol at the kXh sampling instant if T k) exceeds an upper control limit (UCL). (There is no target or lower control limit.) The UCL values are tabulated in statistics books and depend on the number of variables p and the subgroup size n. The control chart consists of a plot of T k) vs. k and an UCL. Thus, the control chart is the multivariate generalization of the x chart introduced in Section 21.2.2. Multivariate generalizations of the CUSUM and EWMA charts are also available (Montgomery, 2009). 

In phase I, a set of samples are collected and analyzed to infer statistical characteristics of the process when it is assumed to be in control (i.e., when the structure is undamaged). The aim of this step is to compute the control limits (upper control limit UCL and/or lower control limits LCL) between which the feature should be included if... 

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