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Using Statistical Process ControlPart 2- by Ivan

An X bar R chart is used to graph variation of a process. It helps us understand if a process is healthy or not.
As you can see in the figure below an X bar R chart,has two axes. However, the X and R are not the axes,they both denominate a section in the chart. The horizontal axis holds groups of readings or measurements of a specific step in a process; those groups may be of three to five samples. Up to 25 groups may be included in one of these charts mostly for manageability’s sake.

The vertical axis just shows a measuring line that need not necessarily start at zero. In fact, most times this graduated line begins at values other than zero, but it must include the whole range covered by the specification limits.
Now, the chart has two sections: the upper section called averages section and its symbolized by the letter X, while the lower section, called the ranges section, uses the letter R as its symbol, hence the charts name. The X actually stands for an individual measure. When we get the average of a group of measures we add a horizontal line on top of the X and call it ‘X bar’ and when we get the average of a group of averages we add a second line at the top and call it ‘X double bar’.
But, what do we graph in this chart? Each group of samples is written vertically at the top of the averages section. Then we calculate their average and graph it down on the graph grid. Out of our samples we will have a maximum and a minimum values; get the difference out of them and that will be the range of that sample group. Write it down at the top of the ranges section and graph it up. By the end of the sample groups you will see a line in the X and R section.
As stated in the beginning, these control charts help us determine if a process is healthy, there are many rules for reading a chart, as a simplified rule of thumb if the line in the X bar section is within limits then the process is healthy. In the ranges section the line drawn by healthy process is supposed to be approximately a straight line. If this line is out of limits or is going in one direction, upwards or downwards the process is considered to be out of control.
X bar R charts can be used to shrink the limits of variation in our process so we can keep it under control. By means of some calculations we can narrow the process specification tolerances and so surpass our customers requirements. Those are the limits depicted by the red and green lines in this chart.
At this point I have to leave the calculations for the next part of the article