x- and R-Charts

The x-chart shows the average of n samples drawn from a process in constant time intervals. The figure below shows the x-chart of a steel plate production line. 4 steel plates are drawn from the manufacturing process every 6 hours. The thickness of the four samples is measured and the average is entered into the control plot. The control limits are set in such a way that the chances of the mean falling outside them are well below 1 %. In fact, the control limits are set such that they span a range between and .

The problem with control charts is that the mean µ of the population is often not known, nor is the standard deviation of the population. When a process has just started to be monitored, we do not even know if the process is stable. A solution to this problem would be to estimate the true mean and the true standard deviation from n samples and using these estimated values to set the control limits.

Another control chart which is quite similar to the x-chart, but which shows the variability of the process, is the R-chart. The R-chart plots the range of successive samples along the time axis. The lower and upper control limits of an R-chart are again determined in such a way that the probability that a particular R will fall outside the control limits is low (usually below 1%).