Myths About Process Behavior Charts explanation?

[New to statistics]

Hello can someone elaborate (explain) from the article :

Myths About Process Behavior Charts​

​

To begin to understand how a process behavior chart can be used with all sorts of data, we need to begin with a simple equation from page 275 of Shewhart’s 1931 book:

Shewhart described two completely different approaches in this equation. The first of these approaches I call the statistical approach since it describes how we approach statistical inference:
1. Choose an appropriate probability model f(x) to use;
2. Choose some small risk of a false alarm ( 1 – P ) to use;
3. Find the exact critical values A and B for the selected model that correspond to this risk of a false alarm;
4. Then use these critical values in your analysis.

While this approach makes sense when working with functions of the data (i.e., statistics) for which we know the appropriate probability model, it encounters a huge problem when it is applied to the original data. As Shewhart pointed out, we will never have enough data to uniquely identify a specific probability model for the original data. In the mathematical sense all probability models are limiting functions for infinite sequences of random variables. This means that they can never be said to apply to any finite portion of that sequence. This is why any assumption of a probability model for the original data is just that—an assumption that cannot be verified in practice. (While lack-of-fit tests will sometimes allow us to falsify this assumption, they can never verify an assumed probability model.)

So what are we to do when we try to analyze data? Shewhart suggested a completely different approach to the equation above. He started by selecting some generic critical values A and B for which the risk of a false alarm, ( 1 – P ) will be reasonably small regardless of what probability model f(x) we might choose. This approach changed what is fixed and what is allowed to vary. With the statistical approach the risk of a false alarm is fixed, and the critical values vary to match the specific probability model. With Shewhart’s approach it is the critical values that are fixed (the three-sigma limits) and the risk of a false alarm that is allowed to vary. This complete reversal of the statistical approach is what makes Shewhart’s approach so hard for those with statistical training to understand.

Added in edit by Bev D
Donald J. Wheeler
Myths About Process Behavior Charts
Quality Digest
09/07/2011

Myths About Process Behavior Charts

www.qualitydigest.com

 

[Bev D]

First - you should always attribute anything that you quote, especially one that is this long. This article was written by Dr. Donald Wheeler, published in Quality Digest on 9/7/2011. He is referencing Dr. Shewhart’s Economic Control of Quality.

What is it that you don’t understand?

 

[New to statistics]

I don't quite understand the differences of these 2 approaches...hot you select/choose the critical values?

 

[John Predmore]

Hello can someone elaborate (explain)

Hello @New to statistics.

Donald Wheeler is a great (still-living!) statistical guru, who writes for SPCpress.com. He explains the important distinction between descriptive statistics (also called Enumerative) and inference statistics used for prediction (also called Analytical). I think that distinction will help you understand the two approaches you asked about.

From a different article (appeared in Quality Digest, July 9, 2018):

"The ultimate purpose for collecting data is to take action. In some cases the action taken will depend upon a description of what is at hand. In others the action taken will depend upon a prediction of what will be. The use of data in support of these two types of action will require different types of analyses. These differences and their consequences are the topic of this article."

I hope you can find enough explanation at SPCpress.com to help you understand the difference. It is a rather abstract distinction, but Donald Wheeler does a good job explaining topics in plain English. However. you do have to find an article which speaks to you where you are in your level of understanding.

 

[Bev D]

I don't quite understand the differences of these 2 approaches...hot you select/choose the critical values?

The Critical values for the first case are dependent on the applicable distribution. The critical values for the second case (the control chart method) are the control limits - the 3 sigma values for the subgroup size. This is exactly what Wheeler said that Shewhart said.

In other words the control limits are not based on any distribution nor is any distribution required for the control chart to work.

 

[New to statistics]

Donald J. Wheeler
Myths About Process Behavior Charts
Quality Digest
09/07/2011

Myths About Process Behavior Charts

www.qualitydigest.com

 

[Bev D]

Another more specific expanantion:

The first approach to determining “A & B” is that when you know (assume - Shewhart correctly stated that one can never actually know what distribution a time series set of process data has) a distribution you determine what amount of coverage you want to understand (low to high limit of variation). You determine or set the coverage amount (P or probability) and then you use the formula for the distribution to determine the coverage limits “A & B”). With SPC, Shewhart set the limits for coverage at +/- 3 SD (lower and upper control limits) and allowed or accepted that the true amount of coverage (or amount of data that naturally beyond the coverage limits) to be very small or small enough to be useful.