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# 10S

10S. Acceptance Sampling. Learning Objectives. 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. Sampling Plans.

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## 10S

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1. 10S Acceptance Sampling

2. Learning Objectives • 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

3. Sampling Plans • Acceptance sampling: Form of inspection applied to lots or batches of items before or after a process, to judge conformance with predetermined standards • Sampling plans: Plans that specify lot size, sample size, number of samples, and acceptance/rejection criteria • Single-sampling • Double-sampling • Multiple-sampling

4. Acceptance Sampling • Acceptance Sampling most useful when • A large number of items must be processed in a short time • The cost consequences of passing defects are low • Destructive testing is required • Fatigue or boredom leads to inspection errors

5. Operating Characteristic Curve • Operating Characteristic (OC) Curve: Probability curve that shows the probabilities of accepting lots with various fractions defective.

6. Typical OC Curve 1 0.9 0.8 0.7 0.6 0.5 Probability of accepting lot 0.4 0.3 0.2 3% 0.1 0 0 .05 .10 .15 .20 .25 Lot quality (fraction defective) Figure 10S.1

7. Decision Criteria 1.00 Ideal Not very discriminating Probability of accepting lot “Good” “Bad” 0 Lot quality (fraction defective) Figure 10S.2

8. Sampling Terms • Acceptance quality level (AQL): the percentage 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 • Consumer’s risk: the probability that a lot contained defectives exceeding the LTPD will be accepted • Producer’s risk: the probability that a lot containing the acceptable quality level will be rejected

9. Consumer’s and Producer’s Risk 1  = .10 0.9 0.8 0.7 0.6 0.5 Probability of accepting lot LTPD 0.4 0.3 “Good” Indifferent “Bad” 0.2 0.1  = .10 0 0 .05 .10 .15 .20 .25 Lot quality (fraction defective) AQL Figure 10S.3

10. 1 .9139 0.9 0.8 .7361 0.7 0.6 .5443 0.5 Probability of acceptance 0.4 .3758 0.3 .2440 0.2 .1493 .0860 0.1 0 .10 .20 .30 .40 .50 0 Fraction defective in lot QC Curve for n = 10, c = 1 Figure 10S.4

11. Average Quality Pac = Probability of accepting lot p = Fraction defective N = Lot size n = Sample size • Average outgoing quality (AOQ): Average of inspected lots (100%) and uninspected lots

12. Example S-2: AOQ Approximate AOQL = .082 AOQ (Fraction defective out) Incoming fraction defective

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