sampling(ppt文档).ppt

Scientific SamplingSome symbols and termsN,number of items in a given lotn,number of items in a sampleD,number of defective items in a given lotr,number of defective items in a given sample of sizec,acceptance numberp,fraction defective,In a given submitted lot,it is D/N,in a given sample,it is r/np,true process average fraction defective of a product submitted for inspection ,average fraction defective in observed samplesA batch of products with a very big population,its real nonconforming ratio is p.When randomly taking one sample from the population,the probability of nonconforming is p.and taking n sample from the population,the probability of taking r nonconforming item is:Hyper-geometric distributionOperational characteristics curven=20r=2pL(p)p0p1A sampling planImportant parameters:the probability of rejection when population ratio is p0,or producers risk:customers riskp0:Acceptable Quality Level,AQLp1:Lot tolerance Percent Defective,LTPDGenerally,AQL=p0.95 LTPD is the lot quality when p1=0.1An ideal OC curve1.00.0p00.120.90.810.65Different sampling planwith the same sampling ratio,10%The acceptance probabilityat the same quality level.In these four plans,which oneis more preferable to customerand which one is preferable to the producer?Lot-by-Lot acceptance using single sampling by attributesDifferent sampling planswith the same sample sizeshow almost the same probability of acceptance0.665,Plan 10.654,Plan 20.638,Plan 30.600,Plan 42.2%Plan 1 N=1000 n=240 c=2 pa=0.1Plan 2 N=1000 n=170 c=1 pa=0.11Plan 3 N=1000 n=100 c=0 pa=0.108the pa were obtained by Binomial distribution.Which plan is better?to producer to customerpsychologicallyType A and Type B OC curvesType A:based on lot quality,definite population,discontinuous,Hypergeometric probabilities,Type B:based on product quality,infinite population,continuous,Binomial probabilities.when sample size is no more than one-tenth of the lot size,Type A and Type B curve may be considered as identical for practical purposes.Different sampling plan with the same ratio of acceptance number to sample sizewhich one is better?to whom?Average outgoing quality and AOQLthe decision to acceptthe decision to reject:100%inspection,or screening inspection,or detailing the outgoing quality will increasep=0.006n=75c=1pa=0.925(Binomial distribution)suppose totally 40 lot are submitted40X0.925=37 lots will be accepted3 lots will be rejected.the 3 lots will be totally inspected.in each lot,0.006X75=0.45 item willbe removed replenished.The AOQ=37X0.006/40=0.555%Max AOQ=AOQL=1.12%Agreement:who will do the screening?AOQ and AOQL求该式的极大值，就是AOQLA double sampling planNn1c1n2c2p=0.020.4830.90.994A double sampling planningN 1000n1 36c1 0n2 59c2 3Sampling procedureInspect a first sample of 36 from a lot of 1000.Accept it if the sample contains 0 defectives.Reject the lot if the sample contains more than 3 defectives.Inspect a second sample of 59 if the first one contains 1,2 or 3 defectives.Accept the lot if the combined sample of 95 contains 3 or less defectives.Reject the lot if the combined sample contains more than 3 defectives.OC curve of a double samplingAverage total inspectionMinimize ATIrather thansample size Single,double and multiple sampling planAcceptance and rejection of a multiple samplingp=0.02multiple sampling planOC curves of different samplingRandomness in acceptance samplingTables of random numbersAQL SystemAQL system:Acceptable quality level MIL-STD-105,ANSI/ASQC,or ABC standardDefinition of AQLIn order to establish acceptance criteria for any particular quality characteristic of a product,it is first necessary to prescribe a maximum percent defective that,for acceptance sampling purposes only,is considered acceptable as a process average.This acceptable quality level usually has been abbreviated AQL.Sample size codeSingle sampling planPa=96.7%GB/T 13262-91 Probabilities of acceptance of lots having AQL percent defectiveIn all AQL systems,the acceptance criteria under normal inspection have chosen to protect the producer against rejection of lots meeting the quality standard.the smaller the sample size,the greater the producers risk.the consumers risk of accepting a lot much worse than the AQL is also much greater with a small sample size.Why tightened or reduced sampling?Economically(reduced)dont know the quality history(tightened)to protect the customer against accepting lots whose quality is worse than AQLProcedure for Normal inspectiontightened inspectionand reduced inspectiontightened samplingNormal tightened%87.881.89180.996.386.998.793.9Reduced samplingthe difference between accept reject criteria is not 1.what is the decision when defective number is within the range.Conditions for reducedIts not easy to be sampling-free if someones qualityis not really good.