G CCEPTANCE SAMPLING PLANS - Pearson Education

1 LEARNING GOALSA fter reading this supplement, you shouldbe able between single- SAMPLING ,double- SAMPLING , and sequential-samplingplans and describe the uniquecharacteristics of an operating characteristic curvefor a single- SAMPLING plan and estimate theprobability of accepting a lot with a givenproportion a single- SAMPLING the average outgoing quality fora single- SAMPLING SAMPLING is an inspection proce-dure used to determine whether to acceptor reject a specific quantity of material. Asmore firms initiate total quality management (TQM)programs and work closely with suppliers to ensurehigh levels of quality, the need for acceptancesampling will decrease. The TQM concept is that nodefects should be passed from a producer to acustomer, whether the customer is an external orinternal customer. However, in reality, many firmsmust still rely on checking their materials basic procedure is A random sample is taken from a large quantityof items and tested or measured relative to thequality characteristic of If the sample passes the test, the entire quantityof items is If the sample fails the test, either (a) the entirequantity of items is subjected to 100 percentinspection and all defective items repaired orreplaced or (b) the entire quantity is returned tothe first discuss the decisions involved in settingup acceptance SAMPLING PLANS .

2 We then address sev-eral attribute SAMPLING and the Companion Website many tools,activities, and resources designed for this GACCEPTANCE SAMPLING PLANSA CCEPTANCE SAMPLING plan DecisionsAcceptance samplinginvolves both the producer (or supplier) of materials and the consumer(or buyer). Consumers need acceptance SAMPLING to limit the risk of rejecting good-qualitymaterials or accepting bad-quality materials. Consequently, the consumer, sometimes in con-junction with the producer through contractual agreements, specifies the parameters of theplan. Any company can be both a producer of goods purchased by another company and aconsumer of goods or raw materials supplied by another and Risk DecisionsTwo levels of quality are considered in the design of an acceptance SAMPLING plan . The firstis the acceptable quality level (AQL), or the quality level desired by the consumer.

3 The pro-ducer of the item strives to achieve the AQL, which typically is written into a contract or pur-chase order. For example, a contract might call for a quality level not to exceed one defectiveunit in 10,000, or an AQL of The producer s risk ( )is the risk that the SAMPLING planwill fail to verify an acceptable lot s quality and, thus, reject it a type I error. Most often theproducer s risk is set at , or 5 producers are interested in low risk, they often have no control over the con-sumer s acceptance SAMPLING plan . Fortunately, the consumer also is interested in a low pro-ducer s risk because sending good materials back to the producer (1) disrupts the consumer sproduction process and increases the likelihood of shortages in materials, (2) adds unnecessarilyto the lead time for finished products or services, and (3) creates poor relations with the second level of quality is the lot tolerance proportion defective (LTPD), or theworst level of quality that the consumer can tolerate.

4 The LTPD is a definition of bad qualitythat the consumer would like to reject. Recognizing the high cost of defects, operationsmanagers have become more cautious about accepting materials of poor quality from sup-pliers. Thus, SAMPLING PLANS have lower LTPD values than in the past. The probability ofaccepting a lot with LTPD quality is the consumer s risk ( ), or the type II error of the common value for the consumer s risk is , or 10 PlansAll SAMPLING PLANS are devised to provide a specified producer s and consumer s , it is in the consumer s best interest to keep the average number of items inspected(ANI) to a minimum because that keeps the cost of inspection low. SAMPLING PLANS differwith respect to ANI. Three often-used attribute SAMPLING PLANS are the single- SAMPLING plan ,the double- SAMPLING plan , and the sequential- SAMPLING plan .

5 Analogous PLANS also havebeen devised for variable measures of PlanThe single- SAMPLING planis a decision rule to accept or reject alot based on the results of one random sample from the lot. The procedure is to take a ran-dom sample of size (n) and inspect each item. If the number of defects does not exceed aspecified acceptance number (c), the consumer accepts the entire lot. Any defects found inthe sample are either repaired or returned to the producer. If the number of defects in thesample is greater than c, the consumer subjects the entire lot to 100 percent inspection orrejects the entire lot and returns it to the producer. The single- SAMPLING plan is easy to usebut usually results in a larger ANI than the other PLANS . After briefly describing the othersampling PLANS , we focus our discussion on this PlanIn a double- SAMPLING plan , management specifies two sample sizes() and two acceptance numbers ().

6 If the quality of the lot is very good or verybad, the consumer can make a decision to accept or reject the lot on the basis of the first sample,which is smaller than in the single- SAMPLING plan . To use the plan , the consumer takes a randomsample of size . If the number of defects is less than or equal to , the consumer accepts thelot. If the number of defects is greater than , the consumer rejects the lot. If the number ofdefects is between , the consumer takes a second sample of size . If the combinednumber of defects in the two samples is less than or equal to , the consumer accepts the , it is rejected. A double- SAMPLING plan can significantly reduce the costs of inspectionrelative to a single- SAMPLING plan for lots with a very low or very high proportion defectivebecause a decision can be made after taking the first sample. However, if the decision requirestwo samples, the SAMPLING costs can be greater than those for the single- SAMPLING PlanA further refinement of the double- SAMPLING plan is thesequential- SAMPLING plan , in which the consumer randomly selects items from the lot andinspects them one by one.

7 Each time an item is inspected, a decision is made to (1) reject the lot,c2n2c1 and c2(c2)(c1)n1c1 and c2n1 and n2 BAacceptance samplingAn inspection procedure used todetermine whether to accept or reject aspecific quantity of quality level (AQL)The quality level desired by s risk ( )The risk that the SAMPLING plan will fail toverify an acceptable lot s quality and,thus, reject it (a type I error).Alot tolerance proportiondefective (LTPD)The worst level of quality that theconsumer can s risk ( )The probability of accepting a lot withLTPD quality (a type II error).Bsingle- SAMPLING planA decision to accept or reject a lot basedon the results of one random samplefrom the planA plan in which management specifiestwo sample sizes and two acceptancenumbers; if the quality of the lot is verygood or very bad, the consumer canmake a decision to accept or reject the loton the basis of the first sample, which issmaller than in the single- SAMPLING planA plan in which the consumer randomlyselects items from the lot and inspectsthem one by SAMPLING PLANSSUPPLEMENT GG-3(2) accept the lot, or (3) continue SAMPLING , based on the cumulative results so far.

8 The analystplots the total number of defectives against the cumulative sample size, and if the number ofdefectives is less than a certain acceptance number ( ), the consumer accepts the lot. If thenumber is greater than another acceptance number ( ), the consumer rejects the lot. If thenumber is somewhere between the two, another item is inspected. Figure illustrates a deci-sion to reject a lot after examining the 40th unit. Such charts can be easily designed with the helpof statistical tables that specify the accept or reject cut-off values as a function of thecumulative sample ANI is generally lower for the sequential- SAMPLING plan than for any other form ofacceptance SAMPLING , resulting in lower inspection costs. For very low or very high valuesof the proportion defective, sequential SAMPLING provides a lower ANI than any comparablesampling plan .

9 However, if the proportion of defective units falls between the AQL and theLTPD, a sequential- SAMPLING plan could have a larger ANI than a comparable single- ordouble- SAMPLING plan (although that is unlikely). In general, the sequential- SAMPLING planmay reduce the ANI to 50 percent of that required by a comparable single-samplingplan and, consequently, save substantial inspection and c2c2c1 FIGURE Chart01234567810203040506070 Number of defectivesCumulative sample sizeRejectDecision to rejectContinue samplingAcceptOperating Characteristic CurvesAnalysts create a graphic display of the performance of a SAMPLING plan by plotting the probabil-ity of accepting the lot for a range of proportions of defective units. This graph, called anoperating characteristic (OC) curve, describes how well a SAMPLING plan discriminates betweengood and bad lots.

10 Undoubtedly, every manager wants a plan that accepts lots with a qualitylevel better than the AQL 100 percent of the time and accepts lots with a quality level worse thanthe AQL 0 percent of the time. This ideal OC curve for a single- SAMPLING plan is shown inFigure However, such performance can be achieved only with 100 percent typical OC curve for a single- SAMPLING plan , plotted in red, shows the probability a of rejectinga good lot (producer s risk) and the probability of accepting a bad lot (con-sumer s risk). Consequently, managers are left with choosing a sample size nand an acceptance number to achieve the level of performance specified bythe AQL, , LTPD, and .Drawing the OC CurveThe SAMPLING distribution for the single- SAMPLING plan is the binomial distrib-ution because each item inspected is either defective (a failure) or not (a suc-cess).