Median Range Charts 100datospptx

8/17/2019 Median Range Charts 100datospptx

http://slidepdf.com/reader/full/median-range-charts-100datospptx 1/17

Median & RaCh

Statisti

• Alf• Gu• He

• Ló• "e

&'("%R(DAD A&)*'*MA D%L %)AD* D%M*R%L*

FAC&L)AD D% C(%'C(A +&(M(CA e ('G%'(%R



INTRODUCTION

,hat is a Control Chart-

• A statistical tool used to distin!uish .et/ee$ariation resultin! fro0 co00on causes andresultin! fro0 special causes1 ho/in! in a proceor insta.ilit2 o$er ti0e1



OBJECTIVE

• &nderstand the /a2 of doin! a 0edian and ran!ethe ad$anta!es to use it to e3plain the #ualit2 andthe process1



Median

Central $alue of a sa0ple of 4n 4 ele0ents5 /hic

are ordered fro0 lo/ to hi!h 6 or $ice $ersa7 1 (n the$ent that the sa0ple size is a e$en nu0.er of dat5 the 0edian is the a$era!e of the t/o 0iddl$alues 8 and /hen the sa0ple size is an odnu0.er of data5 the 0edian is the central $alue1

For0ula for the 0edian/hen is an odd nu0.er99



,hen is it used-

&se the 0edian chart /hen 2ou /ant to plot all the 0easured $a

su.!roup statistics1 )his 0a2 .e the case /hen su.!roup ran!es

deal5 as sho/in! all the points /ill e0phasize the spread1 (t

indi$idual data points can fall outside the control li0its5 /hile

location is /ithin the li0its1

&se the 0edian chart /hen 2ou can ans/er 2es to these #uestions

• Do 2ou need to assess s2ste0 sta.ilit2-

• (s the data in $aria.les for0-

• (s the data collected in su.!roups lar!er than one-

• (s the ti0e order of su.!roups preser$ed-

• Do 2ou /ant to see indi$idual data points-



Ad$anta!es to use the 0edi

)he 0edian has ad$anta!es as a 0eancontrollin! the position for those cases /herecontrolled population is not nor0al and presestron! as200etr21 Also has an ad$anta!e in eause1



)his 0eans that the 0edian lea$es the sanu0.er of $alues .elo/ than a.o$e5 does re#uire perfor0in! an2 calculation for o.tainin! as0all sa0ple sizes 6as are usuall27 is o.tained

inspection of the sa0ple 9 for e3a0ple in a sa0size of <$e ti0es the 0edian is the third $alu.oth !oin! fro0 lo/ to hi!h and hi!h to lo/1

%3a0ple9et data pair9

=5>5?5@55B55=5?55>5

Data are ordered fro0lo/est to hi!hest9=5 =5 >5 >5 ?5 ?5 5 5 5 B@

)he 0edian is9?1

%3a0ple9*dd data set9

=5>5?555B55=5?

Data are ordered fro0lo/est to hi!hest9=5 =5 >5 ?5 ?5 5 5 B5

)he 0edian is9?



Co0ponents of the Control Gra

&CL EEE &pper CoLi0it

CL EEE Central Li

LCL EEE Lo/er CoLi0it



Median chart,hat is it-

• A 0edian chart is a special purpose $ariation of the )his chart uses the 0edian instead of the su.!roup sho/ the s2ste0s central location1

• )he 0edian is the 0iddle point /hen data points arfro0 hi!h to lo/1 )he chart sho/s all the indi$idual re

• Althou!h 0edian charts sho/.oth central location and spread5

the2 are often paired /ith ran!e charts1



Ran!e Chart

Althou!h 0edian charts sho/ .oth central location athe2 are often paired /ith ran!e charts1

• ,hats a Ran!e-

Ran!e is an esti0ate of spread in a set of data pdierence .et/een the hi!hest and lo/est $alues iset1



Median and Range chart formul

Median For!las"

&pper control li0it9

Lo/er control li0it9

Range"

&pper control li0it9

Lo/er control li0it9



E#$MP%E

A hotel 0easures custo0ersatisfaction /ith a sur$e2 thatrecords a ratin! fro0 I 6/orst#ualit27 to I 6.est #ualit271 %$er2/eeK the hotel calculates a$era!eratin!s for the /eeK1

)he 0ana!er desires to Kno/ if#ualit2 is consistent or chan!in!

o$er ti0e1 ,eeKl2 ratin!s for aseries of /eeKs are 15 1I5 1@5@1=5 1=5 15 1B5 @15 1=5 15and B11 )he 0ana!er isconcerned a.out the last /eeKsratin! of B11 Does it represent astatistical ano0al25 or is it si0pl2 aresult of rando0 $ariation-1

o5 one thin! 0ana!er 0a2 /ant Kno/ is if that B1 <ts rando0 pattern of other data5 or if it donot1

otelSatis'action

%C%LM('()A

http://var/www/apps/conversion/tmp/Desktop/ejemplo%20Excel%20Medianas%20y%20rangos.xlsx

http://var/www/apps/conversion/tmp/Desktop/ejemplo%20Excel%20Medianas%20y%20rangos.xlsx



,e ha$e the follo/in!0easure0ents9

Day X values Median R

1 48 45 45 45 50 45 5

2 45 48 46 50 46 46 5

4! 51 46 4" 45 47 64 41 40 42 41 42 41 2

5 4! 46 48 48 44 47 4

6 46 44 45 4 42 44 3

! 4 40 52 48 4" 48 12

8 50 4! 42 40 42 42 7

" 4 4 51 41 4 43 10

10 42 42 45 46 44 44 4

11 42 45 41 50 51 45 10

12 46 4" 40 4! 46 46 9

1 42 40 45 40 46 42 6

14 40 41 46 45 4! 45 7

15 45 50 50 44 48 48 6

16 4" 48 48 42 42 48 6

1! 46 42 50 46 42 46 8

18 4 44 42 4" 48 44 7

1" 42 48 48 4! 51 48 9

20 4! 45 50 48 42 47 8

45.5 6.5



A',%R %C%

L

A',%R

M('()A

I I = =>@

?I

?>

?

?B

?@

I

Median Chart

LCL CL &CL Median

a0ples

Medians

I

=

?

I

I=

I?

I

Ran!e Cha

LCL CL &C

a0ple

Ran!es

Range

#$% $%

14&165

Median

&CL CL LCL1I= ?1 ?1B=

http://var/www/apps/conversion/tmp/Desktop/ejemplo%20Excel%20Medianas%20y%20rangos%20resuelto.xlsx






C%$SS $CTIVIT(

Diaeters o' Parts

I = > ?

I I1??

I1

I1?

I1??

I1=

= I1?

I1>

I1

I1=

I1I

> I1

I1I

I1?B

I11?

I1?=

? I1> I1= I1 I1@ I1

I1=

I1?>

I1??

I1?

I1

I1?

I1?

I1I

I1?

I1

B I1

>

I1

I

I1?

I1?

I1?

Diaeters o' Parts

I = > ?

I I1??

I1

I1?

I1??

I1=

= I1?

I1>

I1

I1=

I1I

> I1

I1I

I1?B

I11?

I1?=

? I1> I1= I1 I1@ I1

I1=

I1?>

I1??

I1?

I1

I1?

I1?

I1I

I1?

I1

B I1

>

I1

I

I1?

I1?

I1?

) * +

I> I1

I1B=

I1?

I? I1?B

I1>

I1

I I1>

I1

I1

I I1I

I1>

I1=

IB I1

I1I

I1?

I I1?

I1?

I1?@

I@ I1?@

I1

I1I

= I1=

I1

I1

) * +

I> I1

I1B=

I1?

I? I1?B

I1>

I1

I I1>

I1

I1

I I1I

I1>

I1=

IB I1

I1I

I1?

I I1?

I1?

I1?@

I@ I1?@

I1

I1I

= I1=

I1

I1

)he dia0eters of certains pieces are9

%%RC(%

A',%R

%C%L

http://var/www/apps/conversion/tmp/Desktop/EJERCICIO%20EN%20CLASE.xlsx


http://var/www/apps/conversion/tmp/Desktop/EJERCICIO%20EN%20CLASE%20RESUELTO.xlsx

http://var/www/apps/conversion/tmp/Desktop/EJERCICIO%20EN%20CLASE%20RESUELTO.xlsx





CONC%USION



i.lio!raph2

• %)%RF(%LD5 D1 6=@71 Control de la Calidad. A&)*RE%D()*R1

• PQ Systems1 6I de A.ril de =I71 *.tenido dehttp9NN///1p#s2ste0s1co0N#ualit2ad$isorNDataAnal2sis)ooledian1php

• Quantitative Tools for Service Operations Management by DScott Sampson ©2!21 6> de April de =I71 *.tenido de

tatistical Orocess Control 6OC7 Anal2sis9 Control Charts9http9NNser$ices1.2u1eduNtN#uantNspc1ht0l

Documents

Median Range Charts 100datospptx