SPCChapter 7.docx

SPCChapter 7.docx

《SPCChapter 7.docx》由会员分享，可在线阅读，更多相关《SPCChapter 7.docx（19页珍藏版）》请在冰豆网上搜索。

SPCChapter7

StatisticsatWork

HARDWORKANDBADPARTS

Weallworkhard.Weworkharderwhenthingsaregoingbadly.Whenthingsaregoingwell,ourworkseemsaloteasier.Weallwantthingseasier.

Thesameistrueforthepartsourcompanymakes.Whenpartsarebad,wegetintrouble,thecompanylosesmoney,wegetpaidless,ourfamilycomplains,lifebecomesdifficult.Badpartsmakehardwork.

SPContheotherhandmakegoodpartseasy.

MAKINGGOODPARTSBETTER

Howisthisdone?

First,wehavetoknowwhenthepartswemakearegood.That’swhytherearespecifications.Ifthepartiswithinspecifications,it’sgood.Ifitisnot,thepartisbad.Ifitisbad,thenitistoolate.Whenthespecificationcannotbemetwearebacktoworkinghardagain.

Second,weneedawayoftellingwhenourpartsarejustbeginningtogetbad…longbeforetheybecome“outofspecification”thatiswhensomethingcanbedoneaboutit.

Thefirstwaycanbedonewithinspection.ThesecondwaycanbedonewithSPC.

WHATDOESNORMALMEAN?

Toknowwhenourpartsaregettingbad,weneedtoknowwhattheylooklikewhentheyaregood.Mostofthetimeourpartsaregood,otherwisetheywouldneverbeaccepted,andwewouldn’tbeinbusiness.

Ofcourse,theyarenotallthesame.Likethevegetablesandbowlingscores,andgolfscores,they1_______________________fromparttopart.Somemaybeverylarge.Somemaybeverysmall.Butforthemostpart,theyaresomewhereinthemiddle.Thisisthewaythingsnormallyare.Thethingsmaybecucumbers,tomatoes,watermelons,rivets,men’sheights,carspeeds,bolts,cardoors,voltages,oranythingthatcanbemeasured.

Whenthefarmergroupedhisvegetablesbyweight,hefoundthesamething.Hefoundapattern,anormalpattern.ThiskindofpatterniscalledtheNormalCurve.

THENORMALCURVE–WHATISIT?

Wehavelearnedthatallthingsvary.Thereis2______________________intheworld.Thepatternofvariationweusuallyseeiscalledthe3___________________________________.

Thefarmerarrangedhisvegetablesbyweight.Thefarmerdistributedhisvegetablesbyweight.Whenhelookedatthepatternofweights,hefoundtheywerenormallydistributed.Hefoundtheywere4______________________accordingtothe5______________________________________.

Thisisthewaywetalkabouthowthingsvary.UsuallythingsvaryaccordingtoaNormalDistribution.

NormalDistributionshavecertainfeatures.Lookatthecurve.Canyoutellwhatsomeofthemare?

Wealreadyknowone.Mostofthethingsareinthemiddle.Therearefewerandfewerthingsasyougoawayfromthemiddle.Wayourattheendsthereareveryfew.

Whatelsedoyousee?

Itlooksbalanced,doesn’tit?

Therightsideofthecurvelooksliketheleft,onlyreversed.Lootatthecurvetotheleftofthetriangles.Supposeyoucutthepaperatthetrianglesandheldittoamirror.Inthemirroritwouldlooklikethecurveontherightsideofthetriangle.Therightsideisthemirrorimageoftheleftside.Indifferentwords,wesaytheNormalDistributionissymmetric.Therightsideofthecurveisthe6____________________________________________.

Whatelsedoyousee?

Thecurveskindoflookslikeabell.Ithasasinglepeakatthemiddle.Thetwoendstailoutlikethebell’srim.Therearethemostnumberofthingsatandaroundthepeak.Andthecurveis7______________________aboutthemiddle.

Let’suseallthesetechnicaltermstodescribetheNormalDistribution.Itisbell-shaped,symmetriccurve.

Ifthingsvaryintheusualway,wecanshowitbythenormalcurve.Inanormaldistributionthingsvaryinacertainway.Therewillbemorethinsinthe8______________________thanatthe9______________________.Thecurvewillbe10______________________aboutthemiddle,andthecurvewillbe11______________________-shaped.

AVERAGES

Thenormaldistributionhasanaverage.Itisrightinthemiddleofthecurve.Theaverageisdefinedinaveryexactwayinstatistics.Wedon’twanttobefuzzyorvaguewhenwetalkaboutournumbers.

Howdoeyougettheaverage?

First,lookatthethingsyouareinterestedin.Let’ssaybolts.Second,youmeasurethem,weighthem,measurethewidthorlength,orevencountthenumberofthreads.Youmaydoanynumberofthings.But,upcomeupwithanumber.Youdothisafewtime,let’ssayyoumeasurefivebolts.Addupthenumberofthefivemeasurements.Theansweryougetiscalledthesum.Finally,dividethesumbythetotalnumberofreadings,orfiveinthisexample.Thereisn’tmuchtoit.

Theaverageisanextremelyusefultoolinstatistics.Whenmostpeoplethinkofaverage,theythinkofordinary,normal,usual,everyday,common.Youuseiteveryday.Yousay,“Heisofaverageheight,”or“Shehasanaverageweight”or“Theyareaveragebowlers.”

Themostimportantpartoftheaverageisthatitshowsuswhatthingslooklikeinonenumber.Itputsallthenumbersintoonenumber.Let’slookatanexample.Let’susethebowlingscoreswesawatthebeginning.

Ourbowlerbowledfivegames.Thenumberofpinsheknockeddownwere:

129,141,135,148,and137.Whatistheaverage?

Step1:

Addupthefivescores.

129

141

135

148

137

690

Theanswer690iscalledthesum.

Step2:

Dividethesumbyfive.

690I5=138

Theaveragetellsyouwhateachscorewouldbeifallthescoreswerethesame.

138

138

138

138

138

690

Tofindtheaveragefirstwe12______________________allthenumbers.Thisgivesusthe13______________________.Inthesecondstepwe14______________________thesumbythenumberofscores.Ifwehavefivescores,wefirst15______________________thefivescorestogether.Secondwedividethesumby16______________________.Let’stryanotherexample.

Let’susethegolfscoreswesayinthebeginning.Ourgolfershot:

98,91,96,89,and94.Whatistheaverageofthesescores?

98

91

96

89

94

468

Thefirstthingwehavetodoisaddallthenumbers.Thisiscalledthesumanditequalsto468.Thenextthingwehavetodoisdivide468by5.

Let’sdothisinadifferentwaythistime.It’sveryeasytodivideby5ifyouknowalittletrick.Hereitis.Takethesumanddoubleit:

468+468=936.Togettheaverage,movethedecimalpointonplacetotheleft.Theansweris93.6,itisthateasy.

MuchoftheworkinSPCdealswithfindingtheaverageof5numbers.Mostpeoplefindthisisaneasywaytodivideby5.

Supposewefinedtheaverageofthesenumbers:

1,8,7,6,and2.Thefirstthingwedoisfindthesum.Thesumis17______________________.Nextwe18______________________thesumby2.Theansweris19______________________.Nowwemovethedecimalpointoneplacetothe20______________________.Theaverageis21______________________.Usethiswayofdividingby5.Itwillmakearithmeticaloteasier.

USINGTHENORMALCURVE

Let’sgobacktothenormalcurve.Ithasanaverage.Theaveragetellsyouwhateachmeasurementwouldbeifallthemeasurementswerethesame.It’swhereallthemeasurementsarebalanced.Theaverageputsallthenumbersintoonenumber.

Amanufacturingcompanycanmakealotofparts.Itisimpossibletoinspecteverypart.Ifwecannotinspectthemall,howdoweknowifthepartsaregood?

Usingthenormalcurve,wecantellwhatallthepartslooklikebylookingatonlyafewparts.

Amanufacturermakesinternallythreadedhardware,nuts.AnemployeebythenameofJohnjustmade500,000ofthem.Severalthingshadtobecontrolled.Eachnuthadtohavetherightheight,width,threads,etc.Everynutisslightlydifferent.John’sbosstoldhimthathewantedtoknowhowmanyofthenutshadaheightof.207inches.Johnstartedtomeasurethe500,000nuts.Hemeasuredthefirst100andgroupedthembysize.Thevaried（weredistributedlikethis:

Johncouldmeasureapartquickly.Hecouldmeasureapartinonly15seconds.Tomeasure100parts,hetookonly1,500seconds,or25minutes.Hethoughthewasdoingagoodjob.Whenhisbosscameby,heaskedifJohnwasdoneyet.Johnsaid,“Listen,youhaven’tgivenmeenoughtime.IfIdo100partsin25minutes,Ishouldbedoneinaboutayear!

”John’sbosswasnonetoobright.Johnwasgladhisbossonlywantedtheheightschecked.“Well,keepongoing,John.Measure200boltsthistime.Weneedtoknowassoonaspossible.”

So,Johnmeasured200partsandarrangedthembysize.Theweredistributedlikethis:

.206

Johnbegantonoticesomething.Bothgroupsofnutmeasurementshadpatternsthatlookedthesame.Themeasurementswerealittledifferent,butthepatternswerealike.Theybothlookedlikethenormalcurve.

NowJohnknewsomethingaboutthenormalcurve.Healsoknewsomethingaboutaverages.Hefoundtheaveragesforthetwogroupsofnutheights.Giveortake.0001inches,hefoundeachaveragewas.206.Whenhelookedatthetwodistributionshenoticedeachaveragewasrightinthemiddle.Therewerefewerandfewermeasurementstowardtheends,veryfewabove.208,andveryfewbelow.204.Thedistributionsweresymmetricandtheylookedbell-shaped.IfJohnwascorrectinthinkinghismeasurementswerenormallydistributed,whereshouldtheaverageof.206goonethenormalcurve?

Inthemiddle.

.206

Asyouknowthereis22______________________inallpartsyoumake.Whenyouarrangethemeasurementsyoutake,usuallytheywillbedistributedaccordingtothe23___________________________________________.Thenormalcurve–ornormaldistribution–issymmetric.Thatmeanstherightsideofthecurveisthe24____________________________________________oftheleft.Thecurvehastheshapeofa25______________________.Moremeasurementsoccurinthe26______________________thanattheends.Thes