- gage r&r via anova -

see "nomenclature" at the bottom of this page

Genesis Innovation

9811 West Charleston Boulevard

Suite 2556

Las Vegas, Nevada 89117 USA

(702) 524-2034

two-way anova without part*operator interaction
source	DF	SS	MS	F	P
part	n_part-1	n_opern_replic(xbar_part-xbar)²	SS_part/DF_part	MS_part/MS_repeat	note 4
operator	n_oper-1	n_partn_replic(xbar_oper-xbar)²	SS_oper/DF_oper	MS_oper/MS_repeat	note 5
repeatability	n_partn_opern_replic-n_part-n_oper +1	SS_total -SS_part -SS_oper	SS_repeat/DF_repeat
total

note 4: alpha level of 1 - CDF of F-distribution with v₁=DF_part, v₂=DF_repeat, and x=F_part

note 5: alpha level of 1 - CDF of F-distribution with v₁=DF_oper, v₂=DF_repeat, and x=F_oper

gage rr without partoperator interaction
source	varcomp	% variance component
total gage r&r	varcomp_repeat + varcomp_repro	varcomp_{total gage r&r} / varcomp_{total variation}
repeatability	MS_repeat	varcomp_repeat/ varcomp_{total variation}
reproducibility	varcomp_oper	%varcomp_oper
operator	(MS_oper - MS_repeat)/n_partn_replic	varcomp_oper / varcomp_{total variation}
part-to-part	(MS_part - MS_repeat)/n_opern_replic	varcomp_part-to-part / varcomp_{total variation}
total variation	varcomp_{total gage r&r} + varcomp_part-to-part	100%

process tolerance =	tol

source	stddev	studyvar (for 99% of the data; for 99.73% use 6sigma)	%study var	% tol
total gage r&r	(varcomp_{total gage r&r})^1/2	5.15sigma_{total gage r&r}	studyvar_{total gage r&r} /studyvar_{total variation}	studyvar_{total gage r&r} / tol
repeatability	(varcomp_repeat)^1/2	5.15sigma_repeat	studyvar_repeat /studyvar_{total variation}	studyvar_repeat / tol
reproducibility	(varcomp_repro)^1/2	5.15sigma_repro	studyvar_repro /studyvar_{total variation}	studyvar_repro / tol
operator	(varcomp_oper)^1/2	5.15sigma_oper	studyvar_oper /studyvar_{total variation}	studyvar_oper / tol
part-to-part	(varcomp_part-to-part)^1/2	5.15sigma_part-to-part	studyvar_part-to-part /studyvar_{total variation}	studyvar_part-to-part / tol
total variation	(varcomp_{total variation})^1/2	5.15sigma_{total variation}	100%	studyvar_{total variation} / tol

number of distinct categories =1.41(sigma_part-to-part / sigma_{total gage r&r})

nomenclature
CDF	cumulative distribution function
DF	degrees of freedom
DF_oper	operator component
DF_part	part component
*DF_partoper**	part*operator interaction component
DF_repeat	repeatability component
DF_total	total
F	F-statistic (ratio of variances)
F_oper	operator component
F_part	part component
*F_partoper**	part*operator interaction component
MS	mean sum of squares
MS_oper	operator component
MS_part	part component
*MS_partoper**	part*operator interaction component
MS_replic	replication component
n_oper	number of operators (measurement takers)
n_part	number of parts measured
n_replic	number of replicates
P	P-statistic (probability of significance)
sigma	standard deviation (what is this? click here)
sigma_oper	operator
sigma_part-to-part	part-to-part
sigma_repeat	repeatability
sigma_repro	reproducibility
sigma_{total gage r&r}	gage r&r
sigma_{total variation}	total for study
SS	sum of squares
SS_oper	operator component
SS_part	part component
*SS_{partoperator}**	part*operator interaction component
SS_repeat	repeatability component
SS_total	total
stdev	standard deviation (sigma)
studyvar	study variation
%studyvar	percent of study variation
tol	required tolerance (specification)
varcomp	variance component
varcomp_oper	operator
varcomp_part-to-part	part-to-part
varcomp_repeat	repeatability
varcomp_repro	reproducibility
varcomp_{total gage r&r}	gage r&r
varcomp_{total variation}	total
% variance component	percentage of the variance reflected by the component
x_bar	mean (what is this? click here)
xbar_{part, oper}	individual part measurement for each operator
x_{part, oper, replic}	each individual measurement
xbar	measurement of all parts
xbar_oper	by each operator
xbar_part	each part

gage rr with partoperator interaction
source	varcomp	% variance component
total gage r&r	varcomp_repeat + varcomp_repro	varcomp_{total gage r&r} / varcomp_{total variation}
repeatability	MS_repeat	varcomp_repeat/ varcomp_{total variation}
reproducibility	varcomp_oper + varcomp_oper*part	%varcomp_oper
operator	(MS_oper - MS_oper*part)/n_partn_replic	varcomp_oper / varcomp_{total variation}
*partoperator**	(MS_oper*part -MS_repeat)/n_replic	varcomp_part*oper / varcomp_{total variation}
part-to-part	(MS_part - MS_oper*part)/n_opern_rep_lic	varcomp_part-to-part / varcomp_{total variation}
total variation	varcomp_{total gage r&r} + varcomp_part-to-part	100%
process tolerance = tol
process tolerance = tol

source	stddev	studyvar (for 99% of the data; for 99.73% use 6sigma)	%study var	% tol
total gage r&r	(varcomp_{total gage r&r})^1/2	5.15sigma_{total gage r&r}	studyvar_{total gage r&r} /studyvar_{total variation}	studyvar_{total gage r&r} / tol
repeatability	(varcomp_repeat)^1/2	5.15sigma_repeat	studyvar_repeat /studyvar_{total variation}	studyvar_repeat / tol
reproducibility	(varcomp_repro)^1/2	5.15sigma_repro	studyvar_repro /studyvar_{total variation}	studyvar_repro / tol
operator	(varcomp_oper)^1/2	5.15sigma_oper	studyvar_oper /studyvar_{total variation}	studyvar_oper / tol
*partoperator**	(varcomp_part*oper)^1/2	5.15sigma_part*oper	studyvar_part*oper / studyvar_{total variation}
part-to-part	(varcomp_part-to-part)^1/2	5.15sigma_part-to-part	studyvar_part-to-part /studyvar_{total variation}	studyvar_part-to-part / tol
total variation	(varcomp_{total variation})^1/2	5.15sigma_{total variation}	100%	studyvar_{total variation} / tol
number of distinct categories =1.41(sigma_part-to-part / sigma_{total gage r%r})

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two-way anova with part*operator interaction
source	DF	SS	MS	F	P
part	n_part-1	n_opern_replic(xbar_part-xbar)²	SS_part/DF_part	MS_part/MS_part*oper	note 1
operator	n_oper-1	n_partn_replic(xbar_oper-xbar)²	SS_oper/DF_oper	MS_oper/MS_part*oper	note 2
*partoperator**	(n_part -1)(n_oper -1)	SS_total-SS_part-SS_oper-SS_repeat	SS_partoper/DF_partoper	MS_part*oper/MS_repeat	note 3
repeatability	n_partn_oper(n_replic-1)		SS_repeat/DF_repeat
total

note 1: alpha level of 1 - CDF of F-distribution with v₁=DF_part, v₂=DF_part*oper, and x=F_part

note 2: alpha level of 1 - CDF of F-distribution with v₁=DF_oper, v₂=DF_part*oper, and x=F_oper

note 3: alpha level of 1 - CDF of F-distribution with v₁=DF_part*oper, v₂=DF_repeat, and x=F_part*oper