-
7/21/2019 Guage R&R Explanation]
1/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 1
!R"R v#
Michael J. WhiteMaster Black Belt NA OSS
-
7/21/2019 Guage R&R Explanation]
2/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 2
!R"R v#
$e%initions&
M'( Me)surement '*stem +)ri)tion ,Minit)b will l)bel this Tot)l
!)-e R"R.
T( )rtTo)rt v)ri)tion
!R"R( !)-e Repe)t)bilit* )nd Reprodu1ibilit* stud*
T+( Tot)l 'tud* +)ri)tion
)ution
The 1)l1ul)tions %or the !R"R stud* )re not dependent upon
whether the
p)rts )re in spe1i%i1)tion or not3 Whether the pro1ess is in
1ontrol or not3
When *ou do ) line)rit*/)11ur)1* stud* *ou sele1t or 1re)te
p)rts th)n sp)n
the entire r)n-e o% the spe1i%i1)tion3 4% *ou use these s)me
p)rts %or the!R"R stud* *ou will )rti%i1i)ll* imp)1t the 5!R"R )nd
5T results3
4t )ssumes th)t )11ur)1* )nd st)bilit* is not )n issue3
4t is possible to 1)l1ul)te ) 7ero %or Reprodu1ibilit* 9 see
e:)mple in
)ppendi:3
-
7/21/2019 Guage R&R Explanation]
3/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 3
!R"R v#
)ution
A4A! Me)surement '*stems An)l*sis 9 M'A #rd;dition( p)-e vi
Usin- 6 inste)d o%
-
7/21/2019 Guage R&R Explanation]
4/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 4
!R"R v#
/ ) r t 0 T o 0 / ) r t
+ ) r i ) t i o n
+ ) r i ) t i o n $ u e
T o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r
B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u e
T o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m
+ ) r i ) t i o n
? v e r ) l l
+ ) r i ) t i o n
When *ou do ) !R"R stud* the over)ll v)ri)tion in the d)t) 1)n
be
de1omposed into two 1)te-ories3 +)ri)tion due to )rtTo)rt
di%%eren1es
,T. )nd v)ri)tion due the the me)surement s*stem ,M'.3 The
v)ri)tiondue to M' 1)n %urther be de1omposed into v)ri)tion due to
the -)-e
,repe)t)bilit*. )nd v)ri)tion due to di%%eren1es in oper)tors
,reprodu1ibilit*.3 4%
) si-ni%i1)nt inter)1tion e:[email protected] then the reprodu1ibilit* 1)n
be de1omposed
into oper)tor )nd oper)torb*p)rt3
Minitab Users Guide Number 2
-
7/21/2019 Guage R&R Explanation]
5/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 5
!R"R v#
/ ) r t 0 T o 0 / ) r t
+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r
B * / ) r t> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m
+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
4n ) per%e1t world )ll the v)ri)tion would be 1ontributed to the
di%%eren1es inp)rts )nd none to the M' itsel%3 Un%ortun)tel*@ this
is not usu)ll* the 1)se3
There is )lw)*s some v)ri)tion 1ontributed to the M'3 'ome is
1)used b* the
-)-e itsel% )nd some b* the oper)tors3 4% the -)-e w)s
)bsolutel* per%e1t
,no v)ri)[email protected] then the oper)tors would be the sour1e o% the
v)ri)tion )nd we
1ould )ddress ,tr)[email protected] pro1edures. th)t issue3
4n ) !R"R stud* we me)sure ) p)rt sever)l times with the s)me
oper)tor3 4%the me)surements )re not the s)[email protected] we h)ve )n estim)te
o% the l)1k o%
repe)t)bilit*3 When we me)sure ) p)rt with sever)l oper)tors )nd
the
me)surements )re not the s)me we h)ve )n estim)te o%
reprodu1ibilit*3
When we me)sure sever)l p)rts )1ross sever)l oper)tors we 1)n
obt)in )n
estim)te o% the Me)surement '*stem +)ri)tion3
-
7/21/2019 Guage R&R Explanation]
6/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 6
!R"R v#
/ ) r t 0 T o 0 / ) r t
+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r
B * / ) r t> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m
+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
When stud*in- )n acceptable gagethe B)r R 1h)rt should be in
1ontrol on
the R)n-e 1h)rt )nd out o% 1ontrol on the B)r 1h)rt3 The r)n-es
)re )
me)sure o% the repe)t)bilit* )nd reprodu1ibilit* o% the -)-e
,within -roup
v)ri)[email protected] the* should be ver* simil)[email protected] thus in 1ontrol3 ?n the
B)r 1h)rt the
1ontrol limits )re determined b* the )ver)-e r)n-e3 The
)ver)-e
me)surement o% the p)rt ,points on the B)r 1h)rt. should be mu1h
l)r-er
th)n the me)surement s*stem v)ri)[email protected] thus out o% the limits
)nd out o%1ontrol3
-
7/21/2019 Guage R&R Explanation]
7/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 7
!R"R v#
/ ) r t 0 T o 0 / ) r t
+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r
B * / ) r t> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m
+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
The purpose o% the !R"R stud* is to u)nti%* how l)r-e the
v)ri)tion1ontributed to the M' ,repe)t)bilit* " reprodu1ibilit*. is
rel)tive to ) st)nd)rd3
The st)nd)rd is usu)ll* the print toler)n1e )nd the stud*
v)ri)tion ,pro1ess
me)surements.3 ?ur tr)inin- m)teri)l re%ers to the print
Toler)n1e )s [email protected]
the stud* v)ri)tion )s 5!R"R3 Please be cautious when referring
to
them, this distinction may not be clear to everyone. our
customer may
refer to the !G"#" as the one relative to the print
tolerance.
?bviousl*@ i% *ou r)ndoml* sele1t p)rts %rom *our pro1ess the
5!R"R h)s
me)nin- rel)tive to *our pro1ess )nd )n* studies 1ompleted in
the %uture3 4%
*ou )rbitr)ril* sele1t/1re)te p)rts either ones th)t )re too
1lose to e)1h other
or too %)r )p)rt it will imp)1t the 5T3 4% too 1lose the 5T will
be l)[email protected] i% too
%)r )p)rt the 5T will be sm)ll3
-
7/21/2019 Guage R&R Explanation]
8/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 8
!R"R v#
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u e
T o ! ) - e> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u e
T o ? p e r ) t o r s> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n CetDs look )t the results o% )
!R"R stud*
th)t is p)rt o% our !reen Belt tr)inin-3 $)t)
in )ppendi:3 Toler)n1e E F
!)-e n)me&
$)te o% stud*&
Reported b*&
Toler)n1e&
Mis1&
?p)1it* Meter
8/G/0
!RR
F
0
2
#
Hoe ')ll*
b)r h)rt b* ?per)tor
')mpleMe)n
Me)nE2302UCE230GCCE3G6
0
030
03
032Hoe ')ll*
R h)rt b* ?per)tor
')mpleR)n-e
RE030G
UCE0320
-
7/21/2019 Guage R&R Explanation]
9/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 9
!R"R v#
Gage R&R
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.00705 1.!Repeatabilit" 0.001#$ 0.$$
Reproucibilit" 0.0051 0.'
perator 0.0051 0.'
art*To*art 0.550' #.7'
Total Variation 0.557'7 100.00
St+e, Stu" Var %Stu" Var %Tolerance
Source (S+) (5.15-S+) (%SV) (SVToler)
Total Gage R&R 0.0#$50 0.'$$' 11.' 10.#1
Repeatabilit" 0.0'#$5 0.0!0 5.7' 5.5
Reproucibilit" 0.071 0.$71#$ .!7 .$0
perator 0.071 0.$71#$ .!7 .$0
art*To*art 0.7'105 $.#0#1 .$7 5.5
Total Variation 0.7'!!'0 $.#'51 100.00 !.1$
/umber of +itinct Categorie 1
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
-
7/21/2019 Guage R&R Explanation]
10/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 10
!R"R v#
Gage R&R
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.00705 1.!
Repeatabilit" 0.001#$ 0.$$
Reproucibilit" 0.0051 0.'perator 0.0051 0.'
art*To*art 0.550' #.7'
Total Variation 0.557'7 100.00
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
CetDs see i% we 1)n determine how
MTB 1)l1ul)tes these v)lues3
-
7/21/2019 Guage R&R Explanation]
11/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 11
!R"R v#
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
le)se review the )l1ul)tin- the +)ri)n1e omponents %or !)-e R"R
'tud*,rossed. b* h)nd do1ument in the )ppendi: %or det)ils3
MTB uses the %ollowin- %un1tions to 1)l1ul)te the v)ri)n1e
1omponents3 4nter)1tion p
v)lue -re)ter th)n 032< dropped %rom model3
) E number o% p)rts b E number o% oper)tors n E number o%
repli1)tes+)romp %or Repe)t)bilit* E M' Repe)t)bilit*
+)romp %or ?per)tor E ,M' ?per)tor9 M' Repe)t)bilit*./)n
+)romp %or )rt E ,M' )rt 9 M' Repe)t)bilit*./bn
-
7/21/2019 Guage R&R Explanation]
12/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 12
!R"R v#
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
To 1omplete these 1)l1ul)tions we need the AI?+A t)ble3Two-Way
ANOVA Tale With !"teractio"
So#rce $% SS MS %
'"it N#(er ) *+.,/ ).)0 0.+/ .
O1erator * .*,* .*,/ )2.3* .0
O1erator4'"it N#(er ) .22 . *.3 .3*/)*
Re1eataility 3 .03, .*+/
Total 3/ *+.+2/)
Two-Way ANOVA Tale Witho#t !"teractio"
So#rce $% SS MS %
'"it N#(er ) *+.,/ ).)0 ).2, .
O1erator * .*,* .*,/ 0+.2 .
Re1eataility 3) .,) .*23
Total 3/ *+.+2/)
'in1e pv)lue o%inter)1tion is K 032
-
7/21/2019 Guage R&R Explanation]
13/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 13
!R"R v#
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
To 1omplete these 1)l1ul)tions we need the AI?+A t)ble3Two-Way
ANOVA Tale Witho#t !"teractio"
So#rce $% SS MS %
'"it N#(er ) *+.,/ ).)0 ).2, .
O1erator * .*,* .*,/ 0+.2 .
Re1eataility 3) .,) .*23
Total 3/ *+.+2/)
M' Repe)t)bilit* E 03008# M' ?per)tor E 03060G ) E < p)rts b
E 2 oper)tors
M' )rt E F3F0
-
7/21/2019 Guage R&R Explanation]
14/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 14
!R"R v#
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
+)romp Repe)t)bilit* E M' Repe)t)bilit* E 03008#
+)romp ?per)tor E ,M' ?per)tor 9 M' Repe)t)bilit*. )n E ,03060G
03008#. / 20 E 0300
-
7/21/2019 Guage R&R Explanation]
15/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 15
!R"R v#
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r
B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l
+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
+)romp Repe)t)bilit* E M' Repe)t)bilit* E 03008#
+)romp ?per)tor E ,M' ?per)tor 9 M' Repe)t)bilit*. )n E ,03060G
03008#. / 20 E 0300
-
7/21/2019 Guage R&R Explanation]
16/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 16
!R"R v#
Gage R&R
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.00705 1.!Repeatabilit" 0.001#$ 0.$$
Reproucibilit" 0.0051 0.'
perator 0.0051 0.'
art*To*art 0.550' #.7'
Total Variation 0.557'7 100.00
St+e, Stu" Var %Stu" Var %Tolerance
Source (S+) (5.15-S+) (%SV) (SVToler)
Total Gage R&R 0.0#$50 0.'$$' 11.' 10.#1
Repeatabilit" 0.0'#$5 0.0!0 5.7' 5.5
Reproucibilit" 0.071 0.$71#$ .!7 .$0
perator 0.071 0.$71#$ .!7 .$0
art*To*art 0.7'105 $.#0#1 .$7 5.5
Total Variation 0.7'!!'0 $.#'51 100.00 !.1$
/umber of +itinct Categorie 1
/ ) r t 0 T o 0 / ) r t+ ) r i ) t i o n
+ ) r i ) t i o n $ u eT o ! ) - e
> R e p e ) t ) b i l i t * >
? p e r ) t o r ? p e r ) t o r B * / ) r t
> 4 n t e r ) 1 t i o n >
+ ) r i ) t i o n $ u eT o ? p e r ) t o r s
> R e p r o d u 1 i b i l i t * >
M e ) s u r e m e n t ' * s t e m+ ) r i ) t i o n
? v e r ) l l+ ) r i ) t i o n
Io si-ni%i1)nt
inter)1tion in
this e:)mple3
-
7/21/2019 Guage R&R Explanation]
17/38
-
7/21/2019 Guage R&R Explanation]
18/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 18
!R"R v#
Gage R&R
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.00705 1.!
Repeatabilit" 0.001#$ 0.$$Reproucibilit" 0.0051 0.'
perator 0.0051 0.'
art*To*art 0.550' #.7'
Total Variation 0.557'7 100.00
St+e, Stu" Var %Stu" Var %Tolerance
Source (S+) (5.15-S+) (%SV) (SVToler)
Total Gage R&R 0.0#$50 0.'$$' 11.' 10.#1
Repeatabilit" 0.0'#$5 0.0!0 5.7' 5.5Reproucibilit" 0.071 0.$71#$
.!7 .$0
perator 0.071 0.$71#$ .!7 .$0
art*To*art 0.7'105 $.#0#1 .$7 5.5
Total Variation 0.7'!!'0 $.#'51 100.00 !.1$
/umber of +itinct Categorie 1
.23/0 is the sta"5ar5 5e6iatio" o= the MS.
.23/0 4 0.*0 : .)33) which ca1t#res //; o= the MS
.+),,) is the sta"5ar5 5e6iatio" o= the Total Variatio".
.+),,) 4 0.*0 : 3.2)0*/ which ca1t#res //; o= the Total
Variatio"
7 .)33) 8 3.2)0*/ 9 4 * : **.); : ;GR&R
7 .)33) 8 ) 9 4 * : *.2*; : ;T
Recall 1ri"t tolera"ce : ).
-
7/21/2019 Guage R&R Explanation]
19/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 19
!R"R v#
The -r)ph below shows the rel)tive si7e o% the Me)surement
'*stem +)ri)[email protected]
'tud* +)ri)tion )nd the rint Toler)n1e3 $oes not impl* rel)tive
position3
!R"R 'TU$
5!R"R E 32F5 Rel)tive To 'tud* +)ri)tion
5T E 0385 Rel)tive to rint Toler)n1e o% F
rint Toler)n1e E F
'tud* +)ri)tionM' +)ri)tion
'howin- rel)tive [email protected] not ne1ess)ril* position3
-
7/21/2019 Guage R&R Explanation]
20/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 20
!R"R v#
The -ener)l -uidelines %or interpretin- the !R"R per1ent)-e is
)s %ollows(
05 to 05 is [email protected] 05 to 205 is A11ept)[email protected] 205 to #05 is
[email protected] )nd )bove #05 is Un)11ept)ble3 The -r)phi1 below
shows therel)tive si7e o% these per1ent)-es ,)nd
-
7/21/2019 Guage R&R Explanation]
21/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 21
!R"R v#
AT;!?R4;'
ou 1)n think o% the number o% distin1t 1)te-ories )s the number
o% -roups
within the pro1ess d)t) th)t *our me)surement s*stem 1)n
distin-uish3
'uppose *ou me)sure ten di%%erent p)[email protected] )nd M4I4TAB reports the
number o%
distin1t 1)te-ories )s %our3 This me)ns th)t *our me)surement
s*[email protected] over
[email protected] 1)nnot dete1t the di%%eren1e between some o% the p)rts3
4n1re)sin- the
pre1ision o% the -)-e will in1re)se the number o% distin1t
1)te-ories3
The Automotive 4ndustr* A1tion !roup ,A4A!. st)tes&>4%
the number o% d)t) 1)te-ories is less th)n [email protected] the me)surement
s*stem is
o% no v)lue %or 1ontrollin- the pro1ess3 4t is )ll noise )nd one
p)rt 1)nnot be
s)id to be di%%erent %rom )nother3 4% the number o% 1)te-ories
is [email protected] it would
me)n th)t the d)t) 1)n be divided into hi-h )nd low [email protected]
[email protected] this is
onl* euiv)lent to )ttribute d)t)3 The number o% 1)te-ories must
be %[email protected]
pre%er)bl* [email protected] %or the me)surement s*stem to be )11ept)ble %or
the )n)l*siso% the pro1ess3>
Automotive 4ndustr* A1tion !roup ,A4A!. ,2002.3 Measurement
Systems
Analysis Reference Manual.hr*[email protected] [email protected] !ener)l Motors 'upplier
Ou)lit*
Reuirements T)sk Nor1e3
-
7/21/2019 Guage R&R Explanation]
22/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 22
!R"R v#
CetDs t)ke ) look )t the 1)te-ories or resolution o% the M'3 4n
this !R"R stud* the
number o% distin1tive 1)te-ories is 23 CetDs look )t )
visualbe%ore we -o throu-h )
ri-orous e:pl)n)tion3 Re1)ll th)t the st)nd)rd devi)tion o% the
M' w)s 0308#G< ,times
-
7/21/2019 Guage R&R Explanation]
23/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 23
!R"R v#
The -r)phi1 below indi1)tes how m)n* times the spre)d o% the M'
will -o
into the spre)d o% the stud* v)ri)tion3 4t )ppe)rs to -o in G
times3 This
indi1)tes th)t we 1)n distin-uish )t le)st nine -roups or
1)te-ories withinthe stud* v)ri)tion3 A rel)tivel* hi-h number3
!R"R 'TU$
This is not uite the 2 1)te-ories 1)l1ul)ted b* Minit)b3 But it
-ives
us ) visualo% the 1on1ept3
-
7/21/2019 Guage R&R Explanation]
24/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 24
!R"R v#
The 1)te-ories represent the number o% nonoverl)ppin-
1on%iden1es
interv)ls th)t sp)n the r)n-e o% the stud* v)ri)tion3 Minit)b
1)l1ul)tes [email protected] b*dividin- the st)nd)rd devi)tion o% the T b* the
st)nd)rd devi)tion o% the
Tot)l !)-e R"R )nd multipl*in- b* 3F3 Then roundin- to the
ne)rest
inte-er3
Roundin- o%% to the ne)rest inte-er -ives us 2 1)te-ories3
( ) 46.1241.1*08395.0/741905.0 =
-
7/21/2019 Guage R&R Explanation]
25/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 25
!R"R v#
The number o% 1)te-ories must be %[email protected] pre%er)bl* [email protected] %or
the
me)surement s*stem to be )11ept)ble %or the )n)l*sis o% the
pro1ess3>
!R"R AT;!?R4;'
Rel)tive to 'tud* +)ri)ion
Tot)l ' tud* +)ri)tion
-
7/21/2019 Guage R&R Explanation]
26/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 26
!R"R v#
The ne:t obvious uestion is where did the 3F 1ome %rom3 The
%ollowin- is
) rel)tionship between v)ri)n1es3
Total Variatio" : art-To-art Variatio" > Total Gage
R&R
ou 1)n %ind estim)tes %or these three sour1es o% v)ri)tion in
the >+)romp>
1olumn in the M4I4TAB 'ession window output %or ) !)-e R"R
)n)l*sis3
A rel)tive me)sure o% how mu1h o% the tot)l v)ri)bilit* is due
to the )rtTo
)rt v)ri)bilit* is&
r : art-To-art 8 Total Variatio"
r ,Rho. 0 P r P
Wheeler defnes the discrimination ratio as:
D = sqrt((1+r)/(1-r))1 < D < infnity
The square root is in the ormula to return the value to the
originalunits o the data (standard deviation units).
$. %. &heeler and ". &. 'yday ()*+*. -valuating the
Measurement Process, econd -dition. P/ Press, 0nc.
-
7/21/2019 Guage R&R Explanation]
27/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 27
!R"R v#
To s)ve ke* strokes let( TV : T > TG
eu)l Total Variatio" : art-To-art > Total Gage R&R
there%ore r : T 8 TV
TV
PTPTVTV
PTPTV
TV
PTPTV
PTP
r
rD
+
=
+
=
+=
1
1
1
1
TG
TGPTP
TG
PTPTGPTP
TG
PTPTV
PTPTV
PTPTVD
+++=
+=
+=
2
1222
+=+=+
=TG
PTP
TG
TG
TG
PTP
TG
TGPTPD
TG
PTP
TG
PTP
TG
PTPD 41.1*2
2===
( )
( )TGStDevPTPStDev
TG
PTP
TG
PTPD *41.141.141.1 ===
Mi"ita 5ro1s the ?*@ =or a
(ore co"ser6ati6e
7s(aller9 esti(ate a"5#ses *.)* as a" esti(ate o=
the s
-
7/21/2019 Guage R&R Explanation]
28/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 28
!R"R v#
( )( )
46.12083950.
741905.*41.1*41.1 ===
TGStDev
PTPStDevD
4n our e:)mple(Gage R&R
%Contribution
Source VarComp (of VarComp)
Total Gage R&R 0.00705 1.!
Repeatabilit" 0.001#$ 0.$$
Reproucibilit" 0.0051 0.'
perator 0.0051 0.'
art*To*art 0.550' #.7'
Total Variation 0.557'7 100.00
St+e, Stu" Var %Stu" Var %Tolerance
Source (S+) (5.15-S+) (%SV) (SVToler)
Total Gage R&R 0.0#$50 0.'$$' 11.' 10.#1Repeatabilit"
0.0'#$5 0.0!0 5.7' 5.5
Reproucibilit" 0.071 0.$71#$ .!7 .$0
perator 0.071 0.$71#$ .!7 .$0
art*To*art 0.7'105 $.#0#1 .$7 5.5
Total Variation 0.7'!!'0 $.#'51 100.00 !.1$
/umber of +itinct Categorie 1
1246.12int == egernearesttoroundingD
-
7/21/2019 Guage R&R Explanation]
29/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 29
!R"R v#
-
7/21/2019 Guage R&R Explanation]
30/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 30
!R"R v#
!R"R d)t)
-
7/21/2019 Guage R&R Explanation]
31/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 31
!R"R v#
MTB h)nd
1)l1ul)tions
-
7/21/2019 Guage R&R Explanation]
32/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 32
!R"R v#
;:)mple o% Reprodu1ibilit* E Lero
-
7/21/2019 Guage R&R Explanation]
33/38
Unpublished work TRW Automotive 2006 MTB mike8/2/06 33
!R"R v#
;:)mple o% Reprodu1ibilit* E Lero
Mis1&
Toler)n1e&
Reported b*&
$)te o% stud*&
!)-e n)me&
0
3
