Control Limits & Natural Process Limits

One of the most commonly used type of control chart is the Mean and Range chart. This has two plot areas, one of which shows the averages of the succesive subgroups, and the other shows the range within each subgroup. (The range is simply the difference between the largest and smallest values in the subgroup.) As we have just seen, the spread of the subgroup averages will be narrower than that for the individual values. The 3 sigma limits on a Mean and Range chart are called control limits, and cannot be directly compared to the total output of the process.

Other charts are also used to monitor the variability of a process, these include the Mean and Standard Deviation chart, and the Median and Range chart. They all provide essentially similar information, and there are advantages and disadvantages to them all. For example, the standard deviation is a more efficient measure of dispersion than the range, because it makes use of all the available data. This makes the Mean and Standard Deviation chart slightly more sensitive in certain cirumstances. However, there is considerably more work involved in calculating the standard deviation rather than the range of a set of values. The ease of use of a range chart is generally seen to outweigh the often neglible advantages to be gained by using a standard deviation chart.

If you wish to determine the expected performance of the process in terms of its individual values, then it is necessary to calculate the Natural Process Limits. These limits may be calculated from the average range () and the constant d₂. The value of d₂ depends on the size of the subgroup, and the correct value for each subgroup size can be found at the foot of most control charts. (A table of some of the more commonly used control chart constants can be accessed by clicking on the 'constants' link in the button bar.) The formula for calculating Natural Process Limits is simply:

You may note, incidentally, that the calculation will give you sigma ( X ) for a given process.

Natural Process Limits are a measure of what can be achieved by the process, given the current way in which it is operated, and assuming that it is stable and predictable. In just the same way as specification limits are the voice of the customer, and cannot be changed or influenced in any way, so the process limits for a stable process cannot be altered by any amount of cajoling or wishful thinking. They are effectively the process saying I can do this much and no more. If the process is not performing up to this standard then you must take action to eliminate the assignable causes of variation. If only chance cause variation is present, then the output will lie within theses limits, and only a fundamental change in the way the process is operated will reduce the variation.

It should be stressed that the natural process limits should never be confused with the specification limits.

The first four exercises with the bead board demonstrate how to calculate control limits and process limits for a stable process. If you wish to perform these exercises now, click on the Resources link in the shaded header and select Beadboard from the list, otherwise you may wait until the end of the course.

If you do choose to open the bead board now, you can leave it open when you return to the course window so that it is available for other exercises later on.