X and R chart

Each hour, also check on three ampoules the length of the ampoules, sealing, particles, break ring presence, or any printing and note down in X and R charts for parenterals. 

Review and verify the fill volume/weight (X and R Chart) and hlling machine speed. 

In this chapter, several types of control charts for the analysis of historical data are discussed. Explanations of the use of x and R charts, for both two or more measurements per batch and only one measurement per batch, are give, along with explanations of modified control charts and cusum charts. Starting with a brief exposition on the calculation of simple statistics, the construction and graphic analysis of x and R charts are demonstrated. The concepts of under control and out of control, as well as their relationship to test specifications, are included. The chapter concludes with consideration of the question of robustness of x and R charts. 

Draw dotted horizontal lines for the UCL and LCL on x and R charts, respectively. 

Example Suppose there are 50 batches of retrospective data, with two potency values recorded for each batch. How would the x and R charts be constructed ... 

In the analysis of retrospective data, the use of x and R charts has advantages and disadvantages. If no data points exceed the x or R control limits, then it is reasonable to say the process has been in control and that the standard operating procedures are fulfilling their functions. While not explicidy discussed here, data obtained from new batches can be plotted on new x and R charts using the same control limits. This new plotted data can help to warn the operator when the process is close to being or is out of control. 

While a range for any batch cannot be computed, the control limits for the x chart depend on finding R. The procedure for constructing x and R charts needs to be modified and is described below in stepwise fashion, using an example. 

The factors A2, D3, and D4 used in the construction of x and R charts were derived from the assumption that all the retrospective data follow a normal distribution. However, random variation occurs in other nonsymmetrical forms. The term robustness refers to the extent to which the charts are still useful when the random variation of retrospective data is not normal. 

So, what happens if the random variation of the retrospective data is not normal, but has some other distributional form Are x and R charts useful in such a situation The x chart is probably useful, but the R chart is not. 

As an example, 80 batches with four observations per batch were each simulated for the following random variation forms normal, exponential, and lognormal, (see Fig. 5 A-C). x and R charts were constructed for each set as if the true random variation were normal. The charts appear in Figs. 2-4. The results appear in Table 2. This table shows that roughly the same number of points falls outside the x control limits, regardless of the form of the random variation. However, the lognormal distribution has many more R values outside the control limits than the other four distributions. The operator of the process would mistakenly think this process was frequently out of control. The R chart shows greater susceptibility to nonnormality in the random error structure. 

Apart from the standard Shewart charts, the analyst can also apply X-charts, on which the mean of several replicate measurements is plotted, or R-charts, where the difference between two replicate measurements is plotted. X- and R-charts give an indication of the reproducibility of the method. Drift in analytical procedure, for example, slows changes in the system caused by the aging of parts of instruments, decalibration in wavelength, or the aging of calibration stock solutions, can be detected early when a Cusum chart (cumulative sum) is applied. In Cusum charts, the analyst reports the cumulative sum of the differences between delivered and reference values. If this reference value is certified (CRM), the Cusum chart allows the accuracy of the determination to be monitored. 

Historically the tools used to learn and create centered primarily around X and R charts and, more recently for the process industries, on Cumsum, sums of the deviation from an actual process average or target value for that process and the exponentially weighted moving average (EWMA). 

Development of the x and R charts starts with the R chart. Since the control limits of the x chart depends on process variability, its limits are not meaningful before R is in-control. 

The most common means of monitoring variable data is with X the R and control chart combination. It is assum that the observations collected from the process are independent emd normally distributed. The X chart is utilized to monitor the process meem, and the R chart is used to monitor the process variation. Without exception, the X and R charts should rdways be used together. The normality assumption embeds the fact that two peuameters, the mean and variance, completely characterize the process therefore, both control charts are necesstuy to monitor the process completely. 

Example 7. Five observations have been collected from a process where the mean, /x, and the standard deviation, a, are known to be 50 and 1, respectively. Construct and plot the necessary control limits and calculated observations for both the X and R charts. The data are collected and the resulting Xj s and Rls are computed as follows ... 

Example 8 demonstrates the construction of X and R charts when standards are not known. 

The establishment of the trial control limits for the p chart follows the same practice as described for the X and R charts. That is, if a given point plots beyond the initial control limits, it is recommended that the cause of the extraordinary point be resolved and then removed from the calculation. That is, the control limits should be recalculated with the out-of-control point(s) removed. In some extreme cases, this process may have to be repeated. Once the observed data are contained within the trial hmits, continued production should be used to collect more data in an effort to validate the limits. Once process stability is obtained, that is, control is maintained for an extended period, the new control limits should become the operational standard. Furthermore, once the trial hmits are established, the AT T runs rules should be deployed in totality to ensure protection against process disturbances. 

There are two types of variable control charts. They are the X and R chart and the X and s chart. 

Median control charts are plotted in conjunction with Range charts in a similar manner to (x and R) charts. The individual measurements from each subgroup are plotted giving a vertical line. For an odd number of values, the middle value is marked, and for even number of values, a mark is placed midway between the two central values. The medians are connected with a solid line. Each subgroup s median (ic) and range (R) are plotted on the chart. The mean of the subgroup medians (ic) is calculated and drawn on the chart as the central line (Figure 18.24). 

Figure 16-2a illustrates a typical variables control chart (x and R chart). The center line of the x chart represents the average of a series of x values. 

There is a variation on the basic x and R chart idea that we wish to illustrate here next, because of its frequent usefulness in... 

---