Calculating UCL (Upper Control Limit) and LCL (Lower Control Limit)

[Steve Prevette]

The best advice I can give you is advice that I received when I was starting out - go back and read the source material. Dr. Shewhart's Economic Control of Quality of Manufactured Product is available from ASQ (as a 50th anniversary edition). In that book, Dr. Shewhart lays out what he did to derive and empirically test SPC. Within the book, he states the use of the Tchybychev Inequality as the basis for SPC, and that is what makes SPC distribution-free.

Many authors since have made the case for distribution fitting. Dr. Deming was AGAINST distribution fitting, so is Dr. Wheeler. But on Quality Digest you'll find lots of articles by those (particularly one author) who is for distribution fitting.

 

[Bev D]

Steve has it just right!
If you can't afford Shewhart's book, you can google Dr. Wheeler's work. most of his articles are free.

 

[bobdoering]

In that book, Dr. Shewhart lays out what he did to derive and empirically test SPC. Within the book, he states the use of the Tchybychev Inequality as the basis for SPC, and that is what makes SPC distribution-free.....

...for independent variables.

 

[Kenwatch]

Hami812,

If you want to get some idea about the reason why is 3.14 times the median range instead of 2.66, look for the following books:

1) Fourth generation management: the new business consciousness
By Brian L. Joiner, Sue Reynard, Yukihiro Ando

2) Fundamental statistical process control: reference manual
(adopted by Ford, Chrysler and GM); available through the Automotive Industry Action Group (313-358-3580)
Published 1991 by AIAG in Southfield, MI (26200 Lahser St., Southfield 48075)

3) Understanding Variation: The Key to Managing Chaos
By Donald J. Wheeler

4) Understanding Statistical Process Control
By David S. Chambers, Donald J. Wheeler

5) Statistical Methods for Quality Improvement
By Hitoshi Kume

 

[bobdoering]

Many authors since have made the case for distribution fitting. Dr. Deming was AGAINST distribution fitting, so is Dr. Wheeler. But on Quality Digest you'll find lots of articles by those (particularly one author) who is for distribution fitting.

Dr. Wheeler opposes using distribution fitting to make adjustments to the traditional charting technique or to impact the decision to use traditional SPC charting. His basic notion is that the calculated control limits are always "close enough" to indicate that you have an out of control condition.

However, that should not be construed (or if he intended it to be construed, I do not agree) to avoid distribution fitting as a tool for process analysis. Dr. Wheeler’s notion that you need a zillion data points to ensure you have the correct curve within a 95% confidence level may be academically and statistically correct, but you can determine if one curve fits better (a different question than if one curve fits perfectly), and that decision helps you understand and visualize your variation. One clear indication that a precision machining process data collection is masked by variables that have not yet been controlled - yet need to be - is seeing the data net a Gaussian curve. Also, seeing a Gaussian curve when the data should be skewed is another good indication that you have not controlled your variation - especially measurement and gage error, which tends to mask correct distributions with Gaussian distributions. So, curve fitting is still an extremely valuable tool. Without it you may just be attempting to control error - which is not the point of the exercise.