Acceptance sampling

Statistics

1. Acceptance Sampling - A form of inspection PRESENTED BY : SeNARATHNE d.M.U.S | S/09/598

2. Outline Introduction Usage Sampling Plans Single, Double and multiple Sampling Plans Operating Characteristic Curve and Acceptance Levels Sampling Risks Average Outgoing Quality Advantages and Disadvantages Conclusion acceptance sampling 2

3. Introduction A form of inspection applied to lots or batches of items before or after a process to judge conformance to predetermined standards It is a decision making tool by which a conclusion is reached regarding the acceptability of lot. acceptance sampling 3

4. Acceptance Sampling Used in… acceptance sampling When testing is destructive When the cost of 100% inspection is extremely high and it is not technologically feasible When the vendor has an excellent quality history, and some reduction in inspection from 100% is desired, but the vendor’s process capability is sufficiently low as to make no inspection an unsatisfactory alternative 4

5. Sampling Plans acceptance sampling Sampling Plans specify the lot size, sample size, number of samples and acceptance/rejection criteria. Sampling plans involve Random sample Lot 5

6. Single Sampling Plan acceptance sampling A representative sample of n items is drawn from a lot size of N items. Each item in the sample is examined and classified as good/defective If the number of defective exceeds a specified rejection number (C - cut off point) the whole lot is rejected; otherwise the whole lot is accepted Random sample (n items) Lot (N items) Random sample (n items) Lot (N items) 6

7. Double Sampling Plan acceptance sampling A Double Sampling Plan allows the opportunity to take a second sample if the results of the original sample are inconclusive. Specifies the lot size, size of the initial sample, the accept/reject/inconclusive criteria for the initial sample ( CL - lower level of defectives, CU - upper level of defectives ) Specifies the size of the second sample and the acceptance rejection criteria based on the total number of defective observed in both the first and second sample ( CT- total allowable defectives ) It works like the following example 7

8. Double Sampling Plan… acceptance sampling Compare number of defective found in the first random sample to CL and CU and make appropriate decision. CL CU Accept Lot Reject Lot First sample inconclusive, take second sample First Random sample Lot 8

9. Double Sampling Plan… acceptance sampling Compare the total number of defective in both samples to CT and make the appropriate decision Accept Lot Reject Lot CT Lot First Random sample Second Random sample 9

10. Multiple Sampling Plans acceptance sampling A Multiple Sampling Plan is similar to the double sampling plan in that successive trials are made, each of which has acceptance, rejection and inconclusive options. Which Plan you choose depends on Cost and time Number of samples needed and number of items in each sample 10

11. Operating Characteristic Curve(OCC) 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). acceptance sampling 11

12. Customers Acceptance Levels acceptance sampling Most customers understand that 100% inspection is impractical and are generally willing to accept that a certain level of defectives will be produced . The Acceptable Quality Level (AQL) is the percentage level of defects at which a customer is willing to accept as lot as “ good ”. The Lot Tolerance Percent Defective (LTPD) is the upper limit on the percentage of defectives that a customer is willing to accept . Customers want lots with quality better than or equal to the AQL but are willing to live with some lots with quality as poor as the LTPD , but prefer not to accept lots with quality levels worse than the LTPD . 12

13. Defining good and bad lot Very Good Ok! But not great Very Bad Instead of good and bad we will define “ really good ”, “ really bad ”, “ ok, but not great ” acceptance sampling 13

14. Customers Acceptance Levels… Therefore the sampling plan must be designed to assure the customer that they will be receiving the required AQL and LTPD . The Consumer’s Risk is the probability that an unacceptable lot (e.g. above the LTPD ) will be accepted . The Producer’s Risk is the probability that a “good” lot will be rejected. acceptance sampling 14

15. Sampling Risks AQL LTPD Producer’s Risk = Probability acceptable is rejected Consumer Risk = Probability unacceptable is accepted Acceptable lot Unacceptable lot aceptancae sampling 15

16. Average Quality Of Inspected Lots The result of acceptance sampling (assuming rejected lots are 100% inspected) is that the level of inspection automatically adjusts to the quality of the lots being inspected . The Average Outgoing Quality (AOQ) is the average of rejected lots (100% inspection) and accepted lots ( a sample of items inspected). AOQ = where; = Probability of accepting a lot = Fraction defective N = Lot size n = Sample size The maximum outgoing quality level is referred to as the AOQL   acceptance sampling 16

17. Constructing OC Curve Proportion non-conforming Probability of acceptance 1 0.01 0.986 0.02 0.922 0.04 0.677 0.06 0.416 0.08 0.226 0.1 0.112 0.15 0.014 0.2 0.001 OC curve for n=50, c=2 acceptance sampling 17

18. Advantages It is usually less expensive because there is less inspection. There is less handling of the product, hence reduced damage. It is applicable to destructive testing. Fewer personnel are involved in inspection activities. It often greatly reduces the amount of inspection error. The rejection of entire lots are opposed to the sample return of defectives often provides a stronger motivation to the vendor for quality improvements. acceptance sampling 18

19. Disadvantages There are risk of accepting “bad” lots and rejecting “good” lots. Less information is usually generated about the product or about the process that manufactured the product. Acceptance sampling requires planning and documentation of the acceptance sampling procedure whereas 100% inspection does not. acceptance sampling 19

20. Conclusion Acceptance sampling is a statistical procedure used to determine whether to accept or reject a production lot of material. A wide variety of sampling plans are available. Plans have an accepted AQL & a rejected LTPD & an AOQL. Acceptance sampling tables are there to supply a set of accepted procedures with known properties &verified results. Sampling provides rational means of verification that a production lot confirms with requirements of technical specifications. acceptance sampling 20

21. THANK YOU acceptance sampling 21