Guage R&R Explanation]

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Unpublished work TRW Automotive 2006 MTB mike8/2/06 1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


2/38


!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


3/38


!R"R v#

)ution

A4A! Me)surement '*stems An)l*sis 9 M'A #rd;dition( p)-e vi

Usin- 6 inste)d o%


4/38


!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:ists@ then the reprodu1ibilit* 1)n be de1omposed

into oper)tor )nd oper)torb*p)rt3

Minitab Users Guide Number 2


5/38


!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 * >


+ ) 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)tion.@ then the oper)tors would be the sour1e o% the v)ri)tion )nd we

1ould )ddress ,tr)inin-@ 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)me@ 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


6/38


!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 e p r o d u 1 i b i l i t * >


+ ) 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)tion.@ the* should be ver* simil)r@ 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)tion@ thus out o% the limits )nd out o%1ontrol3


7/38


!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 e p r o d u 1 i b i l i t * >


+ ) 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 5T@

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)r-e@ i% too

%)r )p)rt the 5T will be sm)ll3


8/38


!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


9/38


!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 * >


> 4 n t e r ) 1 t i o n >


> R e p r o d u 1 i b i l i t * >


? v e r ) l l+ ) r i ) t i o n

Io si-ni%i1)nt

inter)1tion in

this e:)mple3


10/38


!R"R v#

Gage R&R

%Contribution


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'


/ ) 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 * >


> 4 n t e r ) 1 t i o n >


> R e p r o d u 1 i b i l i t * >


? 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


11/38


!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 * >


> 4 n t e r ) 1 t i o n >


> R e p r o d u 1 i b i l i t * >


? 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


12/38


!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 * >


> 4 n t e r ) 1 t i o n >


> R e p r o d u 1 i b i l i t * >


? 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


13/38


!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 * >


> 4 n t e r ) 1 t i o n >


> R e p r o d u 1 i b i l i t * >


? 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


14/38


!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 * >


> 4 n t e r ) 1 t i o n >


> R e p r o d u 1 i b i l i t * >


? 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


15/38


!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 e p r o d u 1 i b i l i t * >


? 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


16/38


!R"R v#

Gage R&R

%Contribution


Total Gage R&R 0.00705 1.!Repeatabilit" 0.001#$ 0.$$


perator 0.0051 0.'

art*To*art 0.550' #.7'




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 $.#'51 100.00 !.1$


/ ) 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 * >


> 4 n t e r ) 1 t i o n >


> R e p r o d u 1 i b i l i t * >


? v e r ) l l+ ) r i ) t i o n

Io si-ni%i1)nt

inter)1tion in

this e:)mple3


17/38


18/38


!R"R v#

Gage R&R

%Contribution



Repeatabilit" 0.001#$ 0.$$Reproucibilit" 0.0051 0.'

perator 0.0051 0.'

art*To*art 0.550' #.7'




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 $.#'51 100.00 !.1$


.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 : ).


19/38


!R"R v#

The -r)ph below shows the rel)tive si7e o% the Me)surement '*stem +)ri)tion@

'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 si7e@ not ne1ess)ril* position3


20/38


!R"R v#

The -ener)l -uidelines %or interpretin- the !R"R per1ent)-e is )s %ollows(

05 to 05 is $esired@ 05 to 205 is A11ept)ble@ 205 to #05 is

Borderline@ )nd )bove #05 is Un)11ept)ble3 The -r)phi1 below shows therel)tive si7e o% these per1ent)-es ,)nd


21/38


!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)rts@ )nd M4I4TAB reports the number o%

distin1t 1)te-ories )s %our3 This me)ns th)t *our me)surement s*stem@ over

time@ 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 two@ 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 two@ it would

me)n th)t the d)t) 1)n be divided into hi-h )nd low -roups@ however@ this is

onl* euiv)lent to )ttribute d)t)3 The number o% 1)te-ories must be %ive@

pre%er)bl* more@ %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*sler@ Nord@ !ener)l Motors 'upplier Ou)lit*

Reuirements T)sk Nor1e3


22/38


!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


23/38


!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


24/38


!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 it@ 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 =


25/38


!R"R v#

The number o% 1)te-ories must be %ive@ pre%er)bl* more@ %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


26/38


!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.


27/38


!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


28/38


!R"R v#

( )( )

46.12083950.

741905.*41.1*41.1 ===

TGStDev

PTPStDevD

4n our e:)mple(Gage R&R

%Contribution



Repeatabilit" 0.001#$ 0.$$


perator 0.0051 0.'

art*To*art 0.550' #.7'




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 $.#'51 100.00 !.1$


1246.12int == egernearesttoroundingD


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!R"R v#


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!R"R v#

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!R"R v#

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1)l1ul)tions


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!R"R v#

;:)mple o% Reprodu1ibilit* E Lero


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!R"R v#

;:)mple o% Reprodu1ibilit* E Lero

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3

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Guage R&R Explanation]