Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Statistical Tests Control Charts x and RCharts  
See also: control charts, pand ccharts, Runs Test  
x and RChartsThe xchart shows the average of n samples drawn from a process in constant time intervals. The figure below shows the xchart 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 xchart, but which
shows the variability of the process, is the Rchart. The Rchart
plots the range of successive samples along the time axis. The lower and
upper control limits of an Rchart 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%).


Home Statistical Tests Control Charts x and RCharts 