Supplement 10 Acceptance Sampling McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc All Rights Reserved Supplement 10: Learning Objectives • You should be able to: – Explain the purpose of acceptance sampling – Contrast acceptance sampling and process control – Compare and contrast single- and multiple-sampling plans – Determine the average outgoing quality of inspected lots 10S-2 Acceptance Sampling • Acceptance sampling – A form of inspection applied to lots or batches of items before or after a process, to judge conformance with predetermined standards – May be applied to both attribute and variable inspection 10S-3 Sampling Plan • Sampling plans: – Plans that specify lot size, sample size, number of samples, and acceptance/rejection criteria • Single-sampling plan • Double-sampling plan • Multiple-sampling plan 10S-4 Single-Sampling Plan • Single-sampling plan – One random sample is drawn from each lot – Every item in the sample is inspected and classified as “good” or “bad” – If any sample contains more than a specified number of defectives, c, the lot is rejected 10S-5 Double-Sampling Plan • Double-Sampling Plan – Allows the opportunity to take a second sample if the results of the initial sample are inconclusive • Two values are specified for the number of defective items – A lower level, c1 – An upper level, c2 • If the number of defectives in the first sample is – ≤ c1 the lot is accepted and sampling is terminated – > c2 the lot is rejected and sampling is terminated – Between c1 and c2 a second sample is collected • The number of defectives in both samples is compared to a third value, c3 – If the combined number of defectives does not exceed this value, the lot is accepted; otherwise, it is rejected 10S-6 Multiple-Sampling Plan • Multiple-sampling plan – Similar to a double-sampling plan except more than two samples may be required – A sampling plan will specify each sample size and two limits for each sample • The limit values increase with the number of samples • If, for any sample, the cumulative number of defectives found exceeds the upper limit specified, the lot is rejected • If for any sample the cumulative number of defectives found is less than or equal to the lower limit, the lot is accepted • If the number of defectives found is between the two limits, another sample is taken • The process continues until the lot is accepted or rejected 10S-7 OC Curve 10S-8 Sampling Plan Discrimination • No sampling plan perfectly discriminates between good and bad quality • The degree to which a sampling plan discriminates is a function of the graph’s OC curve – Steeper OC curves are more discriminating 10S-9 Acceptable Defect Levels • Acceptable quality Level (AQL) – The percentage level of defects at which consumers are willing to accept lots as “good” • Lot tolerance percent defective (LTPD) – The upper limit on the percentage of defects that a consumer is willing to accept 10S-10 Risk • Consumer’s risk – The probability that a lot containing defects exceeding LTPD will be accepted • Manufacturer’s risk – The probability that a lot containing the acceptable quality level will be rejected 10S-11 An OC Curve 10S-12 Constructing an OC Curve • When sample size is small relative to lot size, it is reasonable to use the binomial distribution to obtain the probabilities that a lot will be accepted for various lot qualities • When n > 20 and p < 05, the Poisson distribution is useful in constructing OC curves for proportions – In effect, the Poisson distribution is used to approximate the binomial 10S-13 Average Outgoing Quality • Average outgoing quality – Average of rejected lots (100 percent inspection) and accepted lots (a sample of items inspected) N −n AOQ = Pac × p N where Pac = Probability of accepting the lot p = Fraction defective N = Lot size n = Sample size 10S-14