2.
Measurement Process Characterization
2.4. Gauge R & R studies 2.4.4. Analysis of variability


Case study: Resistivity probes  Runtorun variability can be assessed graphically by a plot of check standard values (averaged over J repetitions) versus time with a separate graph for each check standard. Data on all check standards should be plotted on one page to obtain an overall view of the measurement situation.  
Advantage of pooling 
A level3 standard deviation with
(L  1) degrees of freedom is computed from the run averages.
Because there will rarely be more than two runs per check standard,
resulting in one degree of freedom per check standard, it is prudent
to have three or more check standards in the design to take
advantage of pooling. The mechanism for pooling over check standards
is shown in the table below. The pooled standard deviation has Q(L  1) degrees and is shown as the last entry in the righthand column of the table. 

Example of pooling 
The following table shows how the level3 standard deviations for a
single gauge (probe #2362) are pooled over check standards. The
table can be reproduced using R code.


Level3 standard deviations  A subset of data collected in a nested design on one check standard (#140) with probe (#2362) for six days and two runs is analyzed for betweenrun effects. The level3 standard deviation, computed from the averages of two runs, is 0.02885 with one degree of freedom. Dataplot code and R code can be used to perform the calculations for this data.  
Relationship to longterm changes, days and gauge precision  The size of the betweenrun effect can be calculated by subtraction using the standard deviations for days and gauge precision as $$ {\large s}_{runs} = \sqrt{{\large s}_3^2  \frac{1}{K} {\large s}_2^2} = \sqrt{{\large s}_3^2  \frac{1}{k} {\large s}_{days}^2  \frac{1}{KJ} {\large s}_1^2} $$ 