1. 1 SMU EMIS 7364 NTU TO-570-N Acceptance Sampling Basic Concepts and Mathematical Basis Updated: 5.07.02 Statistical Quality Control Dr. Jerrell T. Stracener, SAE Fellow

2. 2 Basic Concepts of Acceptance Sampling Inspection of raw materials, semi finished products, or finished products is one aspect of quality assurance. When inspection is for the purpose of acceptance or rejection of a product, based on adherence to a standard, the type of inspection procedure employed is usually called acceptance sampling.

3. 3 Basic Concepts of Acceptance Sampling (continued) Purpose of acceptance sampling  To sentence lots, not to estimate the lot quality.  Most acceptance-sampling plans are not designed for estimation purposes. Acceptance-sampling plans do not provide any direct form of quality control. Acceptance sampling simply accepts and rejects lots. Even if all lots are of the same quality, sampling will accept some lots and reject others, the accepted lots being no better than the rejected ones.

4. 4 Basic Concepts of Acceptance Sampling (continued) The most effective use of acceptance sampling is not to ‘inspect quality into the product’ but rather as an audit tool to ensure that the output of a process conforms to requirements.

5. 5 Three Approaches to Lot Sentencing 1. Accept with no inspection. 2. 100% inspection - that is, inspect every item in the lot, removing all defective units found (defectives may be returned to the vendor, reworked, replaced with known good items, or discarded). 3. Acceptance sampling.

6. 6 Applications of Acceptance Sampling 1. When testing is destructive. 2. When the cost of 100% inspection is extremely high. 3. When 100% inspection is not technologically feasible or would require so much calendar time that production scheduling would be seriously impacted. 4. When there are many items to be inspected and the inspection error rate is sufficiently high that 100% inspection might cause a higher percentage of defective units to be passed than would occur with the use of a sampling plan.

7. 7 Applications of Acceptance Sampling (continued) 5. When the vendor has an excellent quality history, and some reduction in inspection from 100% is desired, but the vendor’s capability is sufficiently low as to make no inspection an unsatisfactory alternative. 6. When there are potentially serious product liability risks, and although the vendor’s process is satisfactory, a program for continuously monitoring the product is necessary.

8. 8 Advantages of Acceptance Sampling 1. It is usually less expensive because there is less inspection. 2. There is less handling of the product, hence reduced damage. 3. It is applicable to destructive testing. 4. Fewer personnel are involved in inspection activities. 5. It often greatly reduces the amount of inspection error.

9. 9 Disadvantages of Acceptance Sampling 1. There are risks of accepting ‘bad’ lots and rejecting ‘good’ lots. 2. Less information is usually generated about the product or about the process than manufactured the product. 3. Acceptance sampling requires planning and documentation of the acceptance sampling procedure whereas 100% inspection does not.

10. 10 Acceptance Sampling Objectives Assure quality levels for consumer/producer Maintain quality as a target Assure average outgoing quality levels Reduce inspection, with small sample sizes, good quality history Reduce inspection after good quality history Assure quality no worse than target

11. 11 Summary Acceptance sampling is a “middle ground” between the extremes of 100% inspection and no inspection. It often provides a methodology for moving between these extremes as sufficient information is obtained on the control of the manufacturing process that produces the product. Although there is no direct control of quality in the application of an acceptance sampling plan to an isolated lot, when that plan is applied to a stream of lots from a vendor, it becomes a means of providing protection for both the producer of the lot and the consumer.

12. 12 Summary (continued) Acceptance Sampling provides for an accumulation of quality history regarding the process that produces the lot, and it may provide feedback that is useful in process control determining when process controls at the vendor’s plant are not adequate. Acceptance Sampling may place economic or psychological pressure on the vendor to improve the production process.

13. 13 Sampling Plans Classification of Sampling Plans  Attributes Quality characteristics that are expressed in a “go, no-go” basis.  Variables Quality characteristics that are measured on a numerical scale.

14. 14 Sampling Plans Types of Sampling Plans  Single-sampling plan A lot-sequencing procedure in which one sample of n units is selected at random from the lot, and the disposition of the lot is determined based on the information contained in that sample.  Double-sampling plan Based on two single-sampling plans where the second lot is taken only if the first lot passes. If the second lot is taken, the results of both lots are combined in order to reach a decision whether to accept or reject the lot.

15. 15 Sampling Plans Types of Sampling Plans  Multi-sampling plan An extension of the double-sampling procedure. Sample sizes in multiple sampling are usually smaller than they are in either single or double sampling.  Sequential-sampling plan The ultimate extension of multiple sampling. Units are selected from the lot one at a time, and following inspection of each unit, a decision is made to either accept the lot, reject the lot, or select another unit.

16. 16 True Situation DecisionH 0 trueH 0 false Accept H 0 correct decisionType II error Reject H 0 Type I errorcorrect decision (Accept H 1 ) Application of Tests of Hypotheses to Acceptance Sampling Null Hypothesis – H 0 Lot quality meets spec Alternative Hypothesis – H 1 Lot quality does not meet spec

17. 17 Testing Decision Risks The decision risks are measured in terms of probability.  = P(Type I error) = P(reject H 0 |H 0 is true) = Producers risk  = P(Type II error) = P(accept H 0 |H 1 is true) = Consumers risk Remark: 100% ·  is commonly referred to as the significance level of a test. Note: For fixed n,  increases as  decreases, and vice versa, as n increases, both  and  decrease.

18. 18 Power Function Before applying an acceptance sampling plan, i.e., a decision rule, we need to analyze its discriminating power, i.e., how good the test is. A function called the power function enables us to make this analysis. Power Function() = P(rejecting H 0 |true parameter value, ) OC Function () = P(accepting H 0 |true parameter value, ) = 1 - Power Function () where OC is Operating Characteristic.

19. 19 Power Function A plot of the power function vs the test parameter value is called the power curve and 1 - power curve is the OC curve. 1 0 PR()PR() ideal power curve H0H0 H1H1 

20. 20 Power Function The power function of a statistical test of hypothesis is the probability of rejecting H0 as a function of the true value of the parameter being tested, say , i.e., PF() = PR() = P(reject H 0 |) = P(test statistic falls in C R |)

21. 21 Operating Characteristic Function The operating characteristic function of a statistical test of hypothesis is the probability of accepting H 0 as a function of the true value of the parameter being tested, say , i.e., OC()= P A () = P(accept H 0 |) = P(test statistic falls in A R |)