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OC curve for the single sampling plan N = 3000, n=89, c= 2 1

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Probabilities of Acceptance for the Single Sampling Plan n = 89, c = 2 Assumed Process QualitySample size, n np 0 Probability of acceptance, P a Percent of Lots Accepted 100P a P0P0 100P 0 0.011.0890.90.93893.8 0.022.0891.80.73173.1 0.033.0892.70.49449.4 0.044.0893.60.30230.2 0.055.0894.50.17417.4 0.066.0895.30.10610.6 0.077.0896.20.0555.5 2

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Double Sampling Plan Inspect a sample of 150 from lot of 2400 If 1 or less Nonconforming units accept lots and stop If 4 or more Nonconforming units the lot is not accepted and stop If 2 or 3 nonconforming units, inspect a second sample of 200 If 5 or less Nonconforming units On both samples, Accept the lot If 6 or more Nonconforming units On both samples The lot is not accepted Graphical description of the double sampling plan: N=2400,n 1 =150, c 1 =1, r 1 =4, n 2 =200, c 2 =5, and r 2 =6 3

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OCC for Double Sampling Plan 4

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OCC for a Multiple Sampling Plan 5

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Type-A and Type-B OC curves: 6

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Effect of n and c on OC curves: 7

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Other Aspects of OC Curve Behavior 8

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Average Outgoing Quality (AOQ). A common procedure, when sampling and testing is non-destructive, is to 100% inspect rejected lots and replace all defectives with good units. In this case, all rejected lots are made perfect and the only defects left are those in lots that were accepted. 9

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) The Average Outgoing Quality (AOQ) is the average of rejected lots (100% inspection) and accepted lots ( a sample of items inspected ) Average Outgoing Quality Note that as the lot size N becomes large relative to the sample size n, AOQ P ac p 10

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Typically the term (N-n)/N is very close to 1; therefore, the equation most often used is: Average Quality of Inspected Lots 11

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Example If N = 10,000, n = 89, and c = 2, and that the incoming lots are of quality p = 0.01. What is AOQ? AOQ = P ac p(N-n)/N = ? 12

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Average Outgoing Quality (AOQ) for the Single Sampling Plan n = 89, c = 2 Assumed Process QualitySample size, n np 0 Probability of acceptance, P a AOQ 100P ac p P0P0 100P 0 0.011.0890.90.93893.8 0.022.0891.8? 0.033.0892.70.4941.482 0.044.0893.6? 0.055.0894.5? 0.066.0895.30.1060.636 0.077.0896.20.0550.385 13

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AOQ and Acceptance Sampling ProducerN=3000n=89c=2 Consumer 15 lots 2% nonconforming 11 lots 2% nonconforming 4 lots 2% nonconforming 4 lots 0% nonconforming Figure 9-15 How acceptance Sampling works 14

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AOQ and Acceptance Sampling Total Number Number Nonconforming 11 lots- 2% Nonconforming 11(3000)=33,00033,000(0.02)=660 4 lots- 0% Nonconforming 4(3000)(0.98)=11,7 60 0 44,760660 Percent Nonconforming (AOQ) = 660/44,760 X 100 =1.47% Figure 9-15 contd.

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Average Outgoing Quality curve for the sampling plan N = 3000, n = 89, and c = 2

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A plot of the AOQ (Y-axis) versus the incoming lot p (X-axis) will start at 0 for p = 0, and return to 0 for p = 1 (where every lot is 100% inspected and rectified). In between, it will rise to a maximum. This maximum, which is the worst possible long term AOQ, is called the Average Outgoing Quality Level AOQL. Average Outgoing Quality Level 17

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Average Total Inspection (ATI) When rejected lots are 100% inspected, it is easy to calculate the ATI if lots come consistently with a defect level of p. For a LASP (n,c) with a probability pa of accepting a lot with defect level p, we have: ATI = n + (1 - pa) (N - n) where N is the lot size. 18

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Example If a lot size N = 10,000, and sample size n = 89, number of acceptance c = 2, find ATI at p = 0.01 19

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Average Sample Number (ASN) For a single sampling (n,c) we know each and every lot has a sample of size n taken and inspected or tested. For double, multiple and sequential plans, the amount of sampling varies depending on the number of defects observed. 21

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Average Sample Number (ASN) For any given double, multiple or sequential plan, a long term ASN can be calculated assuming all lots come in with a defect level of p. A plot of the ASN, versus the incoming defect level p, describes the sampling efficiency of a given plan scheme. ASN = n1 + n2 (1 P1) for a double sampling plan. 22

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Sampling Plan Design Suppose is known and the AQL is also known then : Sampling plan with stipulated producers risk Sampling plan with stipulated consumers risk Sampling plan with stipulated producers and consumers risk can be designed. 23

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Sampling Plan Design Stipulated Producers Risk = 0.05 AQL = 1.2% Pa=0.95 P0.95= 0.012 Assume values for C, find np0.95 for this c value, calculate n 24

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Sampling Plan Design Stipulated Consumers Risk = 0.10 LQ = 6.0% Pa=0.10 P0.10= 0.060 Assume values for C, find np0.95 for this c value, calculate n 25

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Sampling Plan Design Stipulated Producers and Consumers risk = 0.10 = 0.10 AQL=0.9 LQ= 7.8 Find the ratio of P0.10/P0.95. From table 9-4 C is between 1 and 2. Find n for c =1 and n for c =2. 26

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Sampling Plan Design Have 4 plans. Select plan based on: Lowest sampling size Greatest sampling size Plan exactly meets consumers stipulation and is as close as possible to producers stipulation Plan exactly meets producers stipulation and is as close as possible to consumers stipulation 27