计数值抽样计划

1、第九章计数值抽样计划抽样计划之设计生规定生产者冒险率9)之抽样计划(AQL)规定消费者冒险率(B)之抽样计划(Limit Quality Level,LQL=LTPD)米规定平均出厂质量界限(AOQL)之抽样计划抽样计划的型式：(计数值) 规准型：规定a、0为一定值(a=5%、p= 10%)oJIS Z9002(单次)。 调整型：MIL-STD-105Es CNS2779Z4006(单、双、屡次)。(3)选别型:Dodge & Romig Table(单、双次)。(4)连续生产型:MIL-STD-1235 (CSP-ls CSP-2.CSP-A. CSP-M)逐次型：连锁抽样计划连锁抽样计划

2、(Chain Sampling Plan-Chspl)Dodge开展。特殊类型。适用破坏性 检验或检验本钱昂贵质量特性之抽样计划。通常样本很小，且合格判定数(Ac)为零。送瞬批取檬本教(n)二 1T -检酶结果檬本敷不合格品数卷0，即允收送瞬批。倘不合格品数悬1，在最近速 i批波有不合 格品,即允收送瞬批。反之，拒收。允收机率：连锁抽样之允收机率属超几何分配（样本很小)，但二项分配简化之。Pa = p()+ pi po 了=C(n, O)p(l-p)n + C(n, l)pi(lp)n”C(n, 0)p(l.p)ni不合格品率不合格品率Chsp-l Sampling Plann = 5, Ac

3、 = 0, i = 2, p = 0.15Pa= po+ pitpo1PoPiPa= po+ pi p()20.4437053130.3915046880.520782565P0=binomdist(0,5,0.15,false)Pa = po + pi po2逐次抽样计划逐次抽样计划(Sequential Sampling)每次样本数 n=l,即判定该批为允收与否，倘无法判定时，那么继续 抽样。其优点为平均样本数(ASN)较其他抽样方式为 少。检验费较少，适用于破坏性试验。属于二项分配(N/n N 10、不合格品率固定)，假设从无 限大的母体或批量中随机抽取n样本，其中有d个不 合格品，那么

4、机率为：(AQLfpo ; LTPD9 pi)Pd = C(n, d) pd (l-p)n-d (d = 1, 2,p =不合格品率) 其逐次机率比(Sequential Probability RatioSPR)SPR= C(n, d) pid (l-pi)n-d / C(n, d) p()d (Lpo严 SPR = (pi/ po)d(l-pi) / (l-po)nd判定法那么：(a = 0.05, p = 0.10)p/(l-a) SPR (Lp)/a 继续抽验SPR (lp)/a一拒收判定线之计算：da = -ha + SIl允收线hr + sn拒收线累tt不合品教Whereha =

5、b/(gl + g2)； hr = a/(gl + g2)； S = g2/(gl + g2)；a = log(l-P)/a ; b = Iog(l-a)/pgl = log(pi / po) ； g2 = 10g(l-po )/(l-pi)Whend hr + sn -Reject 范例一:AQL = 0.05s a = 0.05、LTPD = 0.30s p = ().10 逐次抽样计划：(1)：po = AQL = 0.05, a = 0.05pi = LTPD = 0.30, p = 0.10gi = log(pi/ po) = log(0.3/0.05) = 0.7782g2 = l

6、og(l-po )/(l-pi)= log(0.95/0.7) = 0.1326a = Iog(l-p)/a= Iog(0.90/0.05) =1.3553b = log(l-a)/p= log (0.95/0.10) = 0.9777ha = b/(gi + g2) =0.9777/(0.7782+0.1326) = 1.007hr = a/(gi + g2) =1.2553/(0.7782+0.1326) = 1.037s = g2/(gi + g2) = 0.1326/(0.7782+0.1326) = 0.145 判定线da = - ha + sn = -1.007 + 0.145nh

7、r + sn = 1.037 + 0.145nSequential Sampling Plan球唱蚪 rj* rjw rjw rjw rjw rjw rjw rjw rjw rj* rj rjw rjw rjw rj rj rj rj rj rj rj rj* rj* ej* rj rjw rj rjw rjw rjw送验批的不合格率等于AQL(po)时送验批被拒收的机 率极低(5%)。送验批中含有很少不合格品，但因抽样 关系而被拒收，而造成生产者的损失。XProducers Risk (CR)。Type I Erroro aoX调整型抽样计划以美军标准MIL.STD-105E为代表，须注意考

8、虑:(1)缺点与不合格品分级严重、主要、次要(2)百件缺点数与不合格品率(平均制程)(3) a、AQL(po)、ASN(4)批量N、样本大小代字、样本数n、合格判定数Ac(5) 此规范亦有(选别型)AOQ、AOQL、LQ (Limit Quality = LTPD) 之封照言十算N=8500s AQL=1%、一般H级检验水平、单次。抽样计划：正常、N=8500s Code=Ls n=200s Ac=5s Re=6o严格、N=8500s Code=L、n=200s Ac=3s Re=4o减量、N=8500s Code=Ls n=80s Ac=2s Re=5oSimple Sampling Pla

9、n (N=8500, p=0.01)poissoii(5,200*001,tnie)NormalPa = 0.983436; AOQ=Pa*p=0.()0983436AOQL=y(l/nl/N)=3.172(l/200l/8500)=0.(H5486824poisson(3,200*0.01,true)TightenedPa = 0.857123; AOQ=Pa*p=().()()857123AOQL=y(l/nl/N)=L946(l/200l/8500)=0.009501059poisson(2,80*0.0htme)一ReducedPa = 0.952577 AOQ=Pa*p=0.0095

10、2577Nomieil, Tiglitaied, Reduced Simple SamplingNomieil, Tiglitaied, Reduced Simple Sampling. NormalFattened Reduced范例二：N=8500s AQL=1%、一般H级检验水平、双次。抽样计划：正常、N=8500s Code=Ls nl=125s Acl=2s Rel=5 ;n2=125、 Ac2=6s Re2=7o严格、N=8500s Code=Lx nl=125s Acl=ls Rel=4 ;n2=125、 Ac2=4s Re2=5o减量、N=8500s Code=Lx nl=50

11、s Acl=Os Rel=4 ;n2=50s Ac2=3s Re2=6oExample for MILSTD105EDouble Sampling Plan(N= 8500, p= 0.01)poisson(2J25Pa = Pal +Pa2 = 0.98207426 道奇罗敏抽样计划Dodge & Romig Table选别型以AOQL & LTPD为基础。仅单与双次抽样计划。选别检验。判定为拒收的送验批，不退回卖主，将送 验批采全检，剔除不合格品而以合格品代之。最少的平均总检验件数(ATI)。两种保证AOQL & LTPD (LQL, pi)o不适用破坏性检验、检验本钱太高、无法实施选别检

12、验。Dodge & Romig 抽檬表(l)LTPD 型一(A)罩次(SL)、(B)矍次(DL)(2)AOQL 型一(A理次(SA)、(B)矍次(DA)Dodge & Romig Table之LTPD抽样计划程序，如下：(1)选定送验批。(2)决定单次或双次。(3) 选定LTPD (LQL,3)。共分8种0.5%、1.0%.2.0%. 3.0%. 4.0%x 5.0%s 7.0%、10.0%o (p= 0.1)o(4)设订制程平均不合格率。(5)求出合格判定数、决定样本数与AOQL。范例一：N=1500s LTPD=1 %s p = 0.5%、单次。抽样计戈II ： N=1500s n = 6

13、10、Ac = 3、AOQL = 0.22% oLTPD相对允收机率Pa = poisson(3, 610*0.01,true) = 0.143送验批被允收机率：Pa = poisson(69125*0.005, true) = 0.636范例二：N = 8500s LTPD = 1%、p = 0.13%、双次。抽样计划：N = 8500s nl=280s Acl= 0 ; n2 = 590 x Ac2=4sAOQL = 0.3% o001，tnie)一Normal TOC o 1-5 h z Pal = 0.86846767Pa2 = 0.11500548Pa = Pal +Pa2 . 0.

14、98347314poissoii(l,125*001,triie)-TightenedPal = 0.64463579Pa2 = 0.25451159Pa = Pal +Pa2 . 0.89914739-poisson(0,50*0.01,true)ReducedPal . 0.60653066Pa2 = 0.3755436,2* *2*2* !* ,!*a?* .2* *i*2* *2* *1* *1* *.2* * * .1,.卜 99 99 彳. .1 9f9 rj 彳 ,1 rjw .1 . 99 彳J rjw .1 .1 .1 rj* r rj ejw 1 .1 rjw .1彳彳rJ rj送验批的不合格率等于LTPD(LQL, pi)时送验批被允 收的机率极低(10%)。送验批中含有很多不合格品，但 抽样关系而被允收，而造成消费者的损失。X Consumers Risk (CR)。Type II Erroro 0。! .?，7，. * ! * ! t f 一小 小 k 7， 7 9 1* 1 rjw r| rj rjw rj rjrj rj rj* rj