The most direct references are included below.

Without knowing exactly what your questions are – other than for specific references – I will caution you that the formula in the attachment you are looking at for total standard deviation is for a

*very specific application within a Gauge R&R study* where there are at least two repeat measured for each part and a limited sample size for the study.

**I rarely use this formula **instead recommending the

**use of historical data to calculate the total standard deviation using the traditional formula**. This approach alleviates the need to estimate a total standard deviation based on a small sample that specifically and intentionally ‘adds’ the measurement error to the observed results in the study. But more importantly it also avoids the larger impact of the

*bias* that can result from samples that are representative of the

*range* of the process variation but are not representative of the

*distribution *of that process variation. This bias can result in substantial over or under estimation of the total standard deviation.

Again, the direct reference for using the sample correction factor multiplier for measurement error is:

Donald J Wheeler, Craig Award Paper, “Problems With Gauge R&R Studies”, 46th Annual Quality Congress, May 1992, Nashville TN, pp. 179-185.
This is repeated in the book:

Evaluating The Measurement Process, Second Edition, SPC Press, 1988 by Donald J Wheeler, Richard W Lyday.

For references on the ICC (in addition to those above):

Donald J Wheeler, “An Honest Gauge R&R Study”, Manuscript 189, January 2009.

http://www.spcpress.com/pdf/DJW189.pdf
Donald S. Ermer and Robin Yang E-Hok, “Reliable data is an Important Commodity”, The Standard, ASQ Measurement Society Newsletter, Winter 1997, pp. 15-30.

**Ronald Fisher, Statistical Methods for Research Workers**
Futrell, David, “When Quality is a Matter of Taste, Use Reliability Indexes”, Quality Progress, Vol. 28, No. 5, May 1995, pp. 81-86

A google search will also help as Intraclass correlation coefficients are common statistics.

(be careful in your typing as int

**er**class coefficients are different than int

**ra**class…