Calculating X-Bar, R, R-Bar and S

The calculations for X-Bar (), R, R-Bar (image\IMG00030.gif) and S are basic to the GainSeeker SPC system. The methods for calculating each depend on the subgroup size of the sample.

Calculating X-Bar and X-double bar

= the average of the values in a subgroup

image\IMG00012.gif

= the average of the averages

image\IMG00014.gif

Calculating R and R-Bar

image\IMG00015.gif

image\IMG00016.gif

image\IMG00030.gif = Average of the ranges

image\IMG00018.gif

If the subgroup size is one, image\IMG00030.gif is the average of the Moving Ranges and is calculated as follows:

R = the absolute value of the difference between successive pairs of measurements

image\IMG00021.gif

image\IMG00030.gif = Average of the moving ranges

image\IMG00023.gif

Calculating S and S-Bar

image\IMG00024.gif

If the subgroup size is one, the formula works like moving range.

image\IMG00025.gif

Assumptions

image\IMG00026.gif

n = total number of observations in a subgroup

k = total number of subgroups

References

Ford Motor Company, Product Quality Office. Continuing Process Control and Process Capability Improvement. 1985. Pages 12, 14.

General Motors Corporation. General Motors Statistical Process Control Manual. August, 1984. Pages 4-3, 4-4.

Grant, Eugene L. and Leavenworth, Richard S. Statistical Quality Control, Fifth Edition. McGraw-Hill Book Company. 1980. Pages 44 - 49.