Chapter 14

Acceptance SamplingIntroduction

The Acceptance-Sampling Problem Acceptance sampling is concerned with inspection and decision making regarding products.The Acceptance-Sampling Problem Three aspects of sampling are important:Involves random sampling of an entire lotAccept and Reject Lots (does not achieve quality improvement) Lot sentencingThree approaches to lot sentencing:Accept with no inspection100% inspectionAcceptance samplingQuality Audit tool Why Acceptance-Sampling100 % inspection not possibleEconomic in useIf vendor has excellent quality historyStrong motivation to improve, as the entire lot is rejected.But it runs a risk of rejecting a good lot (producers risk) and accepting a poor lot (consumer risk)The Acceptance-SamplingAdvantages and Disadvantages of Sampling AdvantagesLess expensiveReduced damageReduces the amount of inspection errorDisadvantagesRisk of accepting bad lots, rejecting good lots.Less information generatedRequires planning and documentationProducers and consumer riskThe risk associated with rejecting a lot of good quality. It is desirable to accept lot of this quality (Acceptable quality level), for which a numerical value may be prescribed by ANSI/ASQC. The maximum no. of /% of non conformities a lot can be considered satisfactory on averageConsumer risk is the risk of accepting a poor quality lot. It is desirable to reject lot of this quality (limiting quality level), for which a numerical value may be prescribed by ANSI/ASQC. The no. of /% of non conformities in a lot consumer whishes the probability of acceptance to be a specified low levelAmerican National Standards Institute/American Society of Quality ControlTypes of Sampling Plans Single sampling plan (One sample at a time)Double-sampling plan (Two sample at a time)Multiple-sampling plan (Multiple sample at a time)Sequential-samplingLot FormationConsiderations before inspection:Lots should be homogeneousLarger lots more preferable than smaller lotsRandom SamplingThe units selected for inspection should be chosen at random.

Random samples are not used, bias can be introduced.

If any judgment methods are used to select the sample, the statistical basis of the acceptance-sampling procedure is lost.Single-Sampling PlansDefinition of a Single-Sampling PlanA single sampling plan is defined by sample size, n, and the acceptance number c. Say there are N total items in a lot. Choose n of the items at random. If at least c of the items are unacceptable, reject the lot.N = lot sizen = sample sizec = acceptance numberd = observed number of defectivesThe acceptance or rejection of the lot is based on the results from a single sample - thus a single-sampling plan.The OC CurveThe operating-characteristic (OC) curve measures the performance of an acceptance-sampling plan.The OC curve plots the probability of accepting the lot versus the lot fraction defective.The OC curve shows the probability that a lot submitted with a certain fraction defective will be either accepted or rejected.

OC Curve DefinedWhat is an Operations Characteristics Curve?the probability of accepting incoming lots vs. the proportions of non conformities in that lot.The perfect OC curve should be 0 and 1.But it is not possible practically, so OC curve is plotted using hyper geometric distribution/ binomial/poisson distribution depending on the condition.

13A graph used to determine the probability of accepting lots as a function of the lots or processes quality level when using various sampling plans.Summers(526)An Operating Characteristic Curve (OCC) is a probability curve for a sampling plan that shows the probabilities of accepting lots with various lot quality levels (% defectives).Operating Characteristic Curve (OCC)00.10.20.30.40.50.60.70.80.910.05.10.15.20Probability of accepting lotLot quality (% defective)Under this sampling plan, if the lot has 3% defective . the probability of accepting the lot is 90% . the probability of rejecting the lot is 10% If the lot has 20% defective . it has a small probability (5%) of being accepted . the probability of rejecting the lot is 95%OCC, AQL & Producers Risk0.20.30.40.50.60.70.80.91Probability of accepting lot00.10.05.10.15.20Lot quality (% defective)AQL - percentage level of defects at which a customer is willing to acceptAcceptable LotProducers Risk = probability acceptable lot is rejectedOCC, LQL & Consumers Risk0.20.30.40.50.60.70.80.91Probability of accepting lot00.10.05.10.15.20Lot quality (% defective)limiting quality levelConsumers Risk = probability unacceptable is acceptedUnacceptable LotProperties of OC CurvesThe acceptance number and sample size are most important factors.Decreasing the acceptance number is preferred over increasing sample size.The larger the sample size the steeper the curve. When sample sizes are increased the curve becomes steeper and provides better protection for both consumer and producer.

17Properties of OC CurvesBy changing the acceptance level, the shape of the curve will change. All curves permit the same fraction of sample to be nonconforming.

18Average Outgoing QualityRectifying inspection applies to a lot that is rejected through sampling plan. Such a lot go through 100% inspection, known as screening, where non conforming items are replaced.AOQ is the average quality level of a series that leave the inspection station. The average outgoing quality is the average defective or defect rate in released lot assuming rejected lots are 100% inspected and all defectives/defects are removed. The outgoing quality is better than the incoming quality as a result of the 100% inspection of rejected lots.= (Pa p( N-n))/NWhere Pa is the probability of accepting a batch (Can be found using Poisson distribution) , p is the % of non conformities, N is the lot size and n is the sample size.The AOQ curve shows how outgoing quality (y-axis) depends on the incoming quality (X axis).

Average Outgoing Quality LimitThe AOQ curve initially increases as more defectives/defects are produced, more are released. As more and more lots are rejected, 100% inspections become more common and the AOQ curve starts to decrease as a result. The maximum value of the AOQ curve is called theAverage Outgoing Quality Level (AOQL).The maximum AOQ is the average quality level, or the worst average quality that would leave the inspection station regardless of rectification.Average Total inspectionThe average total inspection per lot depends on the incoming quality, the probability that the lot will be accepted, and the sample and lot sizes. When incoming quality is very good (for example, no product in the lot has a defect), then you inspect the specified sample size. When the incoming quality is very bad (for example, every product in the lot has a defect), then you resort to 100% inspection. Because the quality levels varies between lots, the average number inspected across many lots falls between 0% and 100% of the lot size.ATI is the average no. of items inspected per lot.ATI= n+(1- Pa ) (N-n)The average total inspection (ATI) plot depicts the relationship between the quality of the incoming material and the number of items that need to be inspected, assuming that rejected lots will be 100% inspected and that a rectifying inspection of defective items will be performed. In a rectifying inspection, defective items are either removed, reworked, or replaced.