Signal & Noise in control charts

[#1]

Hello,

I am trying to understand signal and noise in control charts and what all are the possible relation between them?  Can someone please help me to understand this concept.

Thanks

Dheeraj Varapana  

[#2 · Accepted solution]

Here are my thoughts:  First I want to say there are a number of interpretations for the use of control charts and how they work.  The terminology also varies, somewhat dependent on how the data was gotten (experimental vs. observational).  In any case, noise is the common cause (Deming's terminology) or random/unassignable (Shewhart's terminology) variation associated with a process.  It is a function of the X's varying in the process.  A signal is special cause (Deming) or assignable (Shewhart) variation in the process.  The control limits are meant to help understand and separate these types of variation in the process. In reality, the control limits are a function of your subgrouping strategy (which should be rational and based on rational hypotheses).  The within subgroup variation (which is a function of the X's changing at that frequency) is used as a basis to establish the control limits.  The Range chart answers the question: Is the variation within subgroup consistent and stable?  Points outside the control limits are signals there is special/assignable cause variation acting within subgroup. The within subgroup variation is also the basis of the control limits on the Xbar chart.  The Xbar chart answers the questions: Is the variation between subgroup (due to the X's changing at that frequency) more than that predicted by the within subgroup variation.  Points out of control on these charts indicate the sources of variation between subgroup have greater effect or more leverage than the X's changing within subgroup (if the Xbar chart is in control, then the within sources dominate).

I suggest you read:

Wheeler, Donald, and Chambers, David (1992) “Understanding Statistical Process Control” SPC Press (ISBN 0-945320-13-2)

or the original

Shewhart, Walter A. (1931) “Economic Control of Quality of Manufactured Product”, D. Van Nostrand Co., NY

Wheeler also has a number of good papers on the subject.

There is also an SPC on-line class, but I have not reviewed this myself.
https://www.jmp.com/en_us/online-statistics-course/quality-methods.html