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Median & RaCh
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8/17/2019 Median Range Charts 100datospptx
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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
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OBJECTIVE
• &nderstand the /a2 of doin! a 0edian and ran!ethe ad$anta!es to use it to e3plain the #ualit2 andthe process1
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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
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,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$idual data points-
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Ad$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
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)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?
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Co0ponents of the Control Gra
&CL EEE &pper CoLi0it
CL EEE Central Li
LCL EEE Lo/er CoLi0it
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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
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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 $alues iset1
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Median and Range chart formul
Median For!las"
&pper control li0it9
Lo/er control li0it9
Range"
&pper control li0it9
Lo/er control li0it9
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E#$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 $ariation-1
o5 one thin! 0ana!er 0a2 /ant Kno/ is if that B1 <ts rando0 pattern of other data5 or if it donot1
otelSatis'action
%C%LM('()A
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,e ha$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
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CONC%USION
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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