Question: To have a valid control chart (or “Process Behavior Chart”), don’t I need data that’s normally distributed? In other words, a “bell curve”?
Short Answer: No
No, your data doesn’t have to fit a normal distribution or any distribution. The PBC methodology is robust for real world data.
You can read more from Donald J. Wheeler, Ph.D. about this.
“…three-sigma limits will filter out virtually all of the routine variation regardless of the shape of the [distribution].”
Three sigma limits are calculated in the PBC methodology, using the formulas of:
- Lower Limit = Average – 3 * MR-bar / 1.128
- Upper Limit = Average + 3 * MR-bar / 1.128
There’s no need to analyze the distribution of your data and there’s certainly no need to transform the data.
Wheeler also points out:
“… symmetric, three-sigma limits work with skewed data.”
For more, read this article by Donald J. Wheeler, Ph.D.:
“Myths About Process Behavior Charts“
“Myth One: It has been said that the data must be normally distributed before they can be placed on a process behavior chart.”
“Shewhart then went on to note that having a symmetric, bell-shaped histogram is neither a prerequisite for the use of a process behavior chart, nor is it a consequence of having a predictable process.”
Here is another Wheeler article:
“The Normality Myth“
In part:
“The oldest myth about process behavior charts is the myth that they require “normally distributed data.” If you have ever heard this idea, or if you have ever taught this to others, then you need to read this article.
While this myth dates back to 1935, and while Walter Shewhart exposed this idea as a myth in 1938, it continually reappears in various forms even today.”
I hope that helps.