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


Case study: Resistivity gauges  Daytoday variability can be assessed by a graph of check standard values (averaged over J repetitions) versus day with a separate graph for each check standard. Graphs for all check standards should be plotted on the same page to obtain an overall view of the measurement situation.  
Pooling results in more reliable estimates 
The level2 standard deviations with
(K  1) degrees of freedom are computed from the check
standard values for days and pooled over runs as shown in the
table below. The pooled level2 standard deviation has degrees of
freedom L(K  1) for measurements made over:


Mechanism for pooling 
The table below gives the mechanism for pooling level2 standard
deviations over runs. The pooled value is an average of weighted
variances and is the last entry in the righthand column of the table.
The pooling can be extended in the same manner to cover check standards,
if appropriate.
The table was generated using a subset of data (shown on previous page) collected in a nested design on one check standard (#140) with probe (#2362) over six days. The data are analyzed for betweenday effects. The level2 standard deviations and pooled level2 standard deviations over runs 1 and 2 are: 

Level2 standard deviations for a single gauge pooled
over runs


Relationship to day effect  The level2 standard deviation is related to the standard deviation for betweenday precision and gauge precision by $$ {\large s}_{days} = \sqrt{{\large s}_2^2  \frac{1}{J} {\large s}_1^2} $$ The size of the day effect can be calculated by subtraction using the formula above once the other two standard deviations have been estimated reliably.  
Computation of variance component for days  For our example, the variance component for between days is 0.00028072. The negative number for the variance is interpreted as meaning that the variance component for days is zero. However, with only 10 degrees of freedom for the level2 standard deviation, this estimate is not necessarily reliable. The standard deviation for days over the entire database shows a significant component for days.  
Sample code  The calculations included in this section can be implemented using both Dataplot code and R code. The reader can download the data as a text file. 