SPC统计制程品管概述

按一下以編輯母片標題樣式,按一下以編輯母片,第二層,第三層,第四層,第五層,#,統計制程品管(SPC),科建顧問,KIND CONSULTING,Print by Danny.Wang,統計技,術,術之應,用,用,1。市,場,場分析,2。產,品,品設計,3。相,依,依性規,格,格，壽,命,命及耐,用,用性預,測,測,4。制,程,程管制,及,及制程,能,能力研,究,究,5。制,程,程改善,6。安,全,全評估,/,/風險,分,分析,7。驗,收,收抽樣,8。數,据,据分析,，,，績效,評,評估及,不,不良分,析,析,K ,在內之或然率,在外之或然率,0.67 ,50.00%,50.00%,1 ,68.26%,31.74%,1.96 ,95.00%,5.00%,2 ,95.45%,4.55%,2.58 ,99.00%,1.00%,3,99.73%,0.27%,常態分,配,配,常態分,配,配,95.45%,99.73%,68.26%,-3-2,-,-1,+,+1,+,+2,+,+3,+3,-3,UCL,CL,LCL,管制界,限,限的构,成,成,共同原,因,因与特,殊,殊原因,之,之變异,共同原,因,因：制,程,程中變,异,异因素,是,是在統,計,計的管,制,制,狀態下,，,，其產,品,品之特,性,性有固,定,定的分,配,配。,特殊原,因,因：制,程,程中變,异,异因素,不,不在統,計,計的管,制,制,狀態下,，,，其產,品,品之特,性,性沒有,固,固定的,分,分配。,預測,時間,共同原,因,因的變,异,异,預測,時間,特殊原,因,因的變,异,异,兩种錯,誤,誤(risk risk),-3,+3,1,2,兩种錯,誤,誤(risk risk),管制界限,值,1 ,31.74%,2 ,4.56%,3 ,0.27%,4 ,6/10 %,3,平均值移動,值,1-,值,1 ,97.72%,2.28%,2 ,84.13%,15.87%,3 ,50.00%,50.00%,4 ,15.87%,84.13%,管制圖的选择,新據性,質,質?,樣本大,小,小,n=?,數據系,不,不良數,或,或缺點,數,數,CL性,質,質?,n=,?,n,是否相,等,等,?,單位大,小,小是否,相,相關,X-R,管,製,圖,計量值,計量值,n2,n=1,不良值,缺點數,n,=3或5,n,=25,n,10,不是,是,是,不是,_,X-R,管,製,圖,_,X-,管,製,圖,X-Rm,管,製,圖,P,管,製,圖,P,n,管,製,圖,u,管,製,圖,C,管,製,圖,管制圖,的,的選擇,X-R管制圖,(,(平均,值,值与全,距,距),1.公,式,式,(1)X管制圖,CL=X,UCL,=,=X+A,2,R,LUL,=,=X-A,2,R,(2)R管制圖,CL=R,UCL,=,=D,4,R,LCL,=,=D,3,R,X-R管制圖,(,(平均,值,值与全,距,距),2.實,例,例：,某工厂,制,制造一,批,批紫銅,管,管，應,用,用X-R管制圖,來,來控制,其,其內徑,，,，尺寸,單,單位為m/m,利用下,頁,頁數据,表,表之資,料,料，求,的,的其管,制,制界限,并,并繪圖,。,。(n=5,),),X-R繪圖步,驟,驟,1.將,每,每樣組,之,之X与R算出記,入,入數据,表,表內,2.求X与R,X=X/n=1250,/,/25,=,=50,.,.16,R=,R/n=120/25=4.8,3.查系數A,2,，D,4,，D,3,A,2,=0.58，D,4,=2.11，D,3,=負值(,以,以0代,表,表),4.求,管,管制界,限,限,(1)X管制圖,CL=R=4,.,.8,-R繪圖步,驟,驟,X,UCL,=,=X+A2R,=,=50,.,.16,+,+0.58*4.8,=,=52,.,.93,LCL,=,=X-A2R,=,=50,.,.16,-,-0.58*4.8,=,=47,.,.39,(2)R管制圖,CL=R=4,.,.8,UCL,=,=D,4,R=2,.,.11,*,*4.8=10.13,LCL,=,=D,3,R=0,*,*4.8=0,5.將管制,界,界限繪,入,入管制,圖,圖,6.點,圖,圖,-R繪圖步,驟,驟,X,7.檢,討,討管制,界,界限,X管制圖,R管制圖,5.2,5.4,5.0,4.8,4.6,10,5,0,UCL,(,(52,.,.93,),),CL(50.16),LCL,(,(47,.,.39,),),UCL,(,(10,.,.15,),),CL(4.8,),),LCL,(,(0),P管制圖,(,(不良,率,率),1.公,式,式,(1),公,公組樣,本,本大小n相等時,：,：,CL=P,UCL,=,=P+3,P(1,-,-P),/,/n,LCL,=,=P-3,P(1,-,-P),/,/n,2.實例,某工厂,制,制造外,銷,銷產品,，,，每2,小,小時抽,取,取100件來,檢,檢查，,將,將檢查,所,所得之,不,不良品,數,數据，,列,列于下,表,表，利,用,用此項,數,數据，,繪,繪制不,良,良率(P)管制圖,，,，控制,其,其品質,。,。,P管制圖,(,(不良,率,率),組別,n,d,p,組別,n,d,p,組別,n,d,p,1,100,3,0.03,11,100,3,0.03,21,100,5,0.05,2,100,4,0.04,12,100,6,0.06,22,100,8,0.08,3,100,3,0.03,13,100,8,0.08,23,100,4,0.04,4,100,8,0.08,14,100,5,0.05,24,100,5,0.05,5,100,5,0.05,15,100,2,0.02,25,100,4,0.04,6,100,5,0.05,16,100,3,0.03,合計,2500,125,1.25,7,100,7,0.07,17,100,6,0.06,平均,100,5,0.05,8,100,5,0.05,18,100,2,0.02,9,100,5,0.05,19,100,7,0.07,10,100,6,0.06,20,100,5,0.05,P管制圖,繪,繪圖步,驟,驟,1.求,管,管制界,限,限,CL=P=125/2500=0,.,.05,=,=5%,UCL,=,= P,+,+3,P(100-P)/n=11.54%,LCL,=,=P-3,P(100-P)/n=0,(,(為負值,，,，視為0),2.點,繪,繪管制,圖,圖,UCL,CL,LCL,計量值,管,管制圖,常,常用之,系,系數表,n,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,A,2,1.880,1.023,0.729,0.577,0.483,0.419,0.373,0.337,0.308,0.285,0.266,0.249,0.235,0.223,0.212,0.203,0.194,0.187,0.180,D,3,0.076,0.136,0.184,0.223,0.256,0.283,0.307,0.328,0.347,0.363,0.378,0.391,0.403,0.415,D,4,3.267,2.574,2.282,2.114,2.004,1.924,1.864,1.816,1.777,1.744,1.717,1.693,1.672,1.653,1.637,1.622,1.608,1.597,1.585,d,2,1.128,1.693,2.059,2.326,2.534,2.704,2.847,2.970,3.078,3.173,3.258,3.336,3.407,3.472,3.523,3.588,3.640,3.689,3.735,管制圖,的,的判定,方,方法,正常點,子,子之動,態,態之管,制,制圖,1。多,數,數的點,子,子，集,中,中在中,心,心線附,近,近，且,兩,兩邊對,稱,稱。,2。少,數,數的點,子,子，落,在,在管制,界,界限附,近,近。,3。點,子,子之分,布,布呈隨,机,机狀態,，,，無任,何,何規則,可,可尋,4。沒,有,有點子,超,超出管,制,制界限,外,外(有,也,也很少,),),不正常,點,點子之,動,動態之,管,管制圖,1。在,中,中心線,附,附近無,點,點子。,2。在,管,管制界,限,限附近,無,無點子,。,。,3。在,點,點子逸,出,出管制,界,界限之,現,現象,A，管制圖,的,的判讀,法,法,管制圖,之,之不正,常,常型態,之,之鑒別,是,是根据,或,或然率,之,之理論,而,而加以,判,判定的,，,，出現,下,下述之,一,一項者,，,，即為,不,不正常,之,之型態,，,，應調,查,查可能,原,原因。,檢定規,則,則1：,3點中,有,有2點,在,在A區或A區以外,者,者(3,分,分之2A),UCL,LCL,X,A,B,C,B,A,C,A，管制圖,的,的判讀,法,法,檢定規,則,則2：,5點中,有,有4點,在,在B區或B區以外,者,者(5,分,分之4B),UCL,LCL,X,A,B,C,B,A,C,A，管制圖,的,的判讀,法,法,檢定規,則,則3：,有8點,在,在中心,線,線之兩,側,側，但C區并無,點,點子者,。,。(8,缺,缺C),UCL,LCL,X,A,B,C,B,A,C,A，管制圖,的,的判讀,法,法,檢定規,則,則3：,有8點,在,在中心,線,線之兩,側,側，但C區并無,點,點子者,。,。(8,缺,缺C),UCL,LCL,X,A,B,C,B,A,C,A，管制圖,的,的判讀,法,法,檢定規,則,則4：,(1),連,連續五,點,點繼續,上,上升(,或,或下降,),)-,-,-注,意,意以后,動,動態,(2)連續六,點,點繼續,上,上升(,或,或下降,),)-,-,-開,始,始調查,原,原因,(3),連,連續七,點,點繼續,上,上升(,或,或下降,),)-,-,-必有,原,原因，,應,應立即,采,采取措,施,施。,檢定規,則,則5：,點,點子出,現,現在中,心,心線的,單,單側較,多,多時，,有,有下列,狀,狀況者,a .連續11點中,至,至少有10點,b .連續14點中,至,至少有12點,C .連續17點中,至,至少有14點,d .連續20點中,至,至少有16點,A，管制圖,的,的判讀,法,法,檢定規,則,則6：,點,點出現,在,在管制,圖,圖界限,的,的近旁,時,時，一,般,般以超,出,出2,管制界,限,限的點,為,為調整,基,基准，,出,出現下,列,列情況,時,時，可,判,判定制,程,程發生,异,异常,a .連續3,點,點中有2點以,上,上時,b .連續7,點,點中有3點以,上,上時,c .連續10點中,有,有4點,以,以上時,B，數据分,配,配之連,串,串理論,判,判定法,管制圖,上,上諸點,，,，以中,心,心線(CL)為主，,划,划分兩,部,部分，,若,若一點,或,或連續,數,數點在,管,管制圖,中,中心線,之,之一方,，,，該點,或,或連續,數,數點為,一,一串，,UCL,LCL,CL,B，數据分,配,配之連,串,串理論,判,判定法,首先記,算,算此管,制,制圖之,總,總串數,在管制,圖,圖上方,者,者：6,串,串,11點,在管制,圖,圖下方,者,者：6,串,串,13點,總串數,：,：6+6=12串,點數取,大,大者為s,點數取,小,小者為r ,(,(sr),查表P=0,.,.005与表P=0,.,.05得到6,，,，8,126and128,故判定,此,此管制,圖,圖數据,之,之分配,具,具隨机,性,性。,B，數据分,配,配之連,串,串理論,判,判定法,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,6,2,7,2,3,8,3,3,3,9,3,3,3,4,10,3,3,4,4,5,11,3,4,4,5,5,5,12,3,4,4,5,5,6,6,13,3,4,5,5,5,6,6,7,14,4,4,5,5,6,6,7,7,7,15,4,4,5,6,6,7,7,7,8,8,16,4,5,5,6,6,7,7,8,8,9,9,17,4,5,5,6,7,7,8,8,8,9,9,10,18,4,5,6,6,7,7,8,8,9,9,10,10,11,19,4,5,6,6,7,8,8,9,9,10,10,10,11,11,201,4,5,6,7,7,8,8,9,9,10,10,11,11,12,12,表P=0.005,r,s,B，數据分,配,配之連,串,串理論,判,判定法,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,6,3,7,4,4,8,4,4,5,9,4,5,5,6,10,5,5,6,6,6,11,5,5,6,6,7,7,12,5,6,6,7,7,8,8,13,5,6,6,7,8,8,9,9,14,5,6,7,7,8,8,9,9,10,15,6,6,7,8,8,9,9,10,10,11,16,6,6,7,8,8,9,10,10,11,11,11,17,6,7,7,8,9,9,10,10,11,11,12,12,18,6,7,8,8,9,10,10,11,11,12,12,13,13,19,6,7,8,8,9,10,10,11,12,12,13,13,14,14,201,6,7,8,8,9,10,11,11,12,12,13,13,14,14,15,表P=0.05,r,s,C,管制系,數,數(Cf)判定法,Cf比較适,用,用于計,量,量值之,平,平均值,及,及全距,.,.,Cf=,n,x,/(R,/,/d,2,),其中,x,=,(X,i,-x),/,/(k-1,),)k,:,:組數n:樣本大,小,小R=1,/,/k,R,i,2,Cf值,判斷,0.7,Cf,1.3,Under Control,Cf1.3,Out of Control,Cf 0.7,有X不同的异質群体混在一起(建議再用層彆分析),制程能,力,力分析,1.Ca(准确度,Accuracy),Ca=,(,(X-S,C,)/(T/2,),),2.CP(精密度,Precision,),),CP=T/6,(,(雙邊規,格,格),CP=,(,(Su,-,-X),/,/3,或(X-Su)/3 (單邊規,格,格),3.Cpk(制程能,力,力,Process CapabilityIndex,),),Cpk=(1,-,-Ca,),)Cp,;,; (Su-X)/3 or,(,(X,-,-SL,),)/3,(,(取小的),制程能,力,力分析,4.不,良,良率P (綜合評,价,价),(1)Z,U,=3C,P,(1+Ca)超出下,限,限P,u,%,ZL,=,=3C,P,(1+Ca)超出上,限,限P,u,%,P%=P,U,%+P,L,%總不良,率,率,(2)Z,U=,(Su,-,-X),/,/3, ,ZL (X-SL)/3 ,5.定義,(1)X:制程平,均,均值,(,(2)T:公差,(3),:,制,制程標,准,准差,(,(4,),)Sc:規格中,心,心,制程能,力,力分析,例:某,產,產品的,電,電性規,格,格是56010m/m,經檢驗,一,一批后,求,求出X 3為5619m/m,.,.,求:(1,),)Ca,(2)Cp,(3)Cpk,(4)P%,制程能,力,力等級,判,判斷及,處,處置建,議,議,等級,Ca制程准确度,處置建議,A,|Ca |,12.5%,作業員遵守作業標准操作,并達到規格之要求,需繼續維持,B,12.5%,| Ca |,25%,有必要盡可能將其改進為A級,C,25%,| Ca |,50%,作業員可能看錯規格,不按作業標准操作,檢討規格,作業標准,D,50%,| Ca |,應采取緊急措施,全面檢討所有可能影響因素,必要停止生產,等級,Cp制程精密度,處置建議,A,1.33,Cp,(T=8,),此一制程穩定,可將規格許容差縮小或胜任更精密之工作,B,1.00,Cp,1.33 (T=6,),有發生不良危險,須注意,并設法維持不要使其變坏,追查原因,C,0.83,Cp,1.00 (T=5,),檢討規格及作業標准,可能本制程不能胜任如此精密之工作,D,Cp,0.83,應采取緊急措施,全面檢討所有可能影響因素,必要停止生產,等級,Cpk制程能力指數,處置建議,A,1.33 ,Cpk,制程能力足夠,B,1.0,Cpk,1.33,制程能力尚可.應再努力,C,Cpk,1.0,制程應加以改善,6概,念,念,1.何,謂,謂六個制程,?,?,制程精,密,密度(Cp),=,=2.0,制程能,力,力指數,(,(Cpk) 1.5,.,.,2.以六個訂為,品,品質缺,點,點的基,准,准理由,.,.,在無制,程,程變异,情,情況下,(,(Cp=Cpk=2),產生之,缺,缺點僅,為,為0.002ppm,在制程,無,無法消,除,除變异,情,情況下,Cp=2,Cpk=1.5,缺點率,為,為3.4ppm,常態分,布,布,-,+,-6,-,-5,-,-4,-,-3 ,-,-2,-,-1 ,+,+1,+,+2,+,+3,+,+4 ,+,+5 ,+,+6,68.26%,99.73%,95.44%,99.9937%,99.999943,%,%,99.9999998%,-6 -5 -4 -3 -2 -1 +1 +2 +3 +4 +5 +6 ,常態分配 (規格中心不偏移),規格下限,規格上限,K,百分比(%),百万分缺點數,1,68.26,317400,2,95.45,45500,3,99.73,2700,4,99.9937,63,5,99.999943,0.057,6,99.9999998,0.002,常態分,布,布,結束語,讓我們回,憶,憶一下,本,本次課,程,程內容,