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

2.4.4.4.

Example of calculations

Example of repeatability calculations

Short-term standard deviations based on

• J = 6 repetitions with 5 degrees of freedom
• K = 6 days
• L = 2 runs

were recorded with a probing instrument on Q = 5 wafers. The standard deviations were pooled over K = 6 days and L = 2 runs to give 60 degrees of freedom for each wafer. The pooling of repeatability standard deviations over the 5 wafers is demonstrated in the table below.

Pooled repeatability standard deviation for a single gauge

Source of variability	Sum of Squares (SS)	Degrees of freedom (DF)	Std Devs
Repeatability	\( SS_i = \nu_i \cdot {\large s}_{1i}^2 \)	\( \nu_i \)	\( {\large s}_1 = \sqrt{SS/\nu} \,\, \longrightarrow \)
Wafer #138 Wafer #139 Wafer #140 Wafer #141 Wafer #142 SUM	0.48115 0.69209 0.48483 1.21752 0.30076 3.17635	60 60 60 60 60 300	0.10290