Standard deviation is an important measurement of dispersion within or between subgroups in a statistical sampling. Two methods for estimating standard deviation are used in quality control and quality assurance. These are the Factors Method and the Sample Standard Deviation (SSD) Method.
Estimating standard deviation using the Factors Method
The Factors Method estimates standard deviation based on the range of each subgroup, divided by a constant value (which is based on the subgroup size). This method is valid only if the total number of subgroups is greater than 10. This process variation includes only common causes.
Before you can estimate standard deviation using the Factors Method, you must calculate . Formulas for calculating are given in the previous module. Standard deviation using the Factors Method is estimated according to the following formula:
Subgroup size |
d2 |
c4 |
2 |
1.128 |
0.798 |
3 |
1.693 |
0.886 |
4 |
2.059 |
0.921 |
5 |
2.326 |
0.940 |
6 |
2.534 |
0.952 |
7 |
2.704 |
0.959 |
8 |
2.847 |
0.965 |
If the subgroup size in GainSeeker SPC is one, the range is calculated as a moving range between two consecutive values. The value for d2, therefore, is 1.128.
Estimating standard deviation using the Sample Standard Deviation Method
The Sample Standard Deviation (SSD) Method estimates standard deviation based on the distance between each point and the mean. This process variation includes both common and special causes.
Assumptions
Statistics based on the Standard Deviation Method
For Normal distributions, the following statistics use the standard deviation method chosen for capability indexes:
MEAN - 3SD
MEAN + 3SD
MEAN - 4SD
MEAN + 4SD
6SD
Zl
Zu
Cpm
For other distributions, these statistics may be calculated differently. For more information, see Flow Chart Analysis of Non-Normal Data.
References
Beyer, William H. Standard Mathematical Tables, 25th Edition. CRC Press, 1981. Page 506.
Ford Motor Company, Product Quality Office. Continuing Process Control and Process Capability Improvement. 1985. Page 23.
General Motors Corporation. General Motors Statistical Process Control Manual. August, 1984. Pages 4-9.
Grant, Eugene L. and Richard S. Leavenworth. Statistical Quality Control, Fifth Edition. McGraw-Hill Book Company. 1980. Pages 44 - 49.