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© 2007 Pearson Education AQL LTPD Acceptance Sampling Plans Supplement I

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© 2007 Pearson Education Sequential Sampling Chart 8 8 – 7 7 – 6 6 – 5 5 – 4 4 – 3 3 – 2 2 – 1 1 – 0 0 – Reject Continue sampling Accept Cumulative sample size ||||||| 10203040506070 Number of defectives

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© 2007 Pearson Education Sequential Sampling Chart 8 8 – 7 7 – 6 6 – 5 5 – 4 4 – 3 3 – 2 2 – 1 1 – 0 0 – Reject Decision to reject Continue sampling Accept Cumulative sample size ||||||| 10203040506070 Number of defectives

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© 2007 Pearson Education Operating Characteristic Curve Ideal OC curve Probability of acceptance Proportion defective

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© 2007 Pearson Education Operating Characteristic Curve Ideal OC curve Typical OC curve Probability of acceptance Proportion defective

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© 2007 Pearson Education Operating Characteristic Curve 1.0 Ideal OC curve Typical OC curve AQL LTPD Probability of acceptance Proportion defective

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© 2007 Pearson Education Constructing an OC Curve Example I.1 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance

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© 2007 Pearson Education Probability Proportionof c or less defectivedefects (p)np(P a )Comments n = 60 c = 1 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Constructing an OC Curve Example I.1

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© 2007 Pearson Education Probability Proportionof c or less defectivedefects (p)np(P a )Comments n = 60 c = 1 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance np012.05.951.9991.000.10.905.9951.000.15.861.990.999.20.819.982.999.25.779.974.998.30.741.963.996.35.705.951.994.40.670.938.992.45.638.925.989.50.607.910.986.55.577.894.982.60.549.878.977.65.522.861.972 Constructing an OC Curve Example I.1

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© 2007 Pearson Education Probability Proportionof c or less Defectivedefects (p)np(P a )Comments 0.01 (AQL)0.6 n = 60 c = 1 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance np012.05.951.9991.000.10.905.9951.000.15.861.990.999.20.819.982.999.25.779.974.998.30.741.963.996.35.705.951.994.40.670.938.992.45.638.925.989.50.607.910.986.55.577.894.982.60.549.878.977.65.522.861.972 Constructing an OC Curve Example I.1

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© 2007 Pearson Education Probability Proportionof c or less defectivedefects (p)np(P a )Comments 0.01 (AQL)0.60.878 n = 60 c = 1 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance np012.05.951.9991.000.10.905.9951.000.15.861.990.999.20.819.982.999.25.779.974.998.30.741.963.996.35.705.951.994.40.670.938.992.45.638.925.989.50.607.910.986.55.577.894.982.60.549.878.977.65.522.861.972 Constructing an OC Curve Example I.1

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© 2007 Pearson Education Probability Proportionof c or less defectivedefects (p)np(P a )Comments 0.01 (AQL)0.60.878 n = 60 c = 1 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance np012.05.951.9991.000.10.905.9951.000.15.861.990.999.20.819.982.999.25.779.974.998.30.741.963.996.35.705.951.994.40.670.938.992.45.638.925.989.50.607.910.986.55.577.894.982.60.549.878.977.65.522.861.972 Constructing an OC Curve Example I.1

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© 2007 Pearson Education Probability Proportionof c or less defectivedefects (p)np(P a )Comments 0.01 (AQL)0.60.878 n = 60 c = 1 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Constructing an OC Curve Example I.1

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – 0.663 |||||||||| 12345678910 0.308 0.199 0.048 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Probability Proportionof c or less defectivedefects (p)np(P a )Comments 0.01 (AQL)0.60.878 = 1.000 – 0.878 = 0.122 0.021.20.663 0.031.80.463 0.042.40.308 0.053.00.199 0.06 (LTPD)3.60.126 = 0.126 0.074.20.078 0.084.80.048 0.095.40.029 0.106.00.017 n = 60 c = 1 Constructing an OC Curve Example I.1

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 0.878 0.663 0.463 0.308 0.199 0.126 0.078 0.048 0.029 0.017 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Constructing an OC Curve Example I.1

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 0.878 0.663 0.463 0.308 0.199 0.126 0.078 0.048 0.029 0.017 = 0.122 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance = 0.126 Constructing an OC Curve Example I.1

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© 2007 Pearson Education Drawing the OC Curve Application I.1

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© 2007 Pearson Education Finding (probability of rejecting AQL quality: p =.03 np =5.79 Pa =Pa = 0.965 = 1 –.965 = 0.035 Drawing the OC Curve Application I.1 Cumulative Poisson Probabilities

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© 2007 Pearson Education Finding (probability of accepting LTPD quality: p =.08 np =15.44 Pa =Pa = 0.10 = P a = 0.10 Drawing the OC Curve Application I.1 Cumulative Poisson Probabilities

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© 2007 Pearson Education Drawing the OC Curve Application I.1

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© 2007 Pearson Education Drawing the OC Curve Application I.1

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© 2007 Pearson Education Understanding Changes in the OC Curve (with c = 1) 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk n (p = AQL)(p = LTPD)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk n (p = AQL)(p = LTPD) 600.1220.126 Understanding Changes in the OC Curve (with c = 1)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk n (p = AQL)(p = LTPD) 600.1220.126 800.1910.048 Understanding Changes in the OC Curve (with c = 1)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk n (p = AQL)(p = LTPD) 600.1220.126 800.1910.048 1000.2640.017 Understanding Changes in the OC Curve (with c = 1)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk n (p = AQL)(p = LTPD) 600.1220.126 800.1910.048 1000.2640.017 1200.3320.006 Understanding Changes in the OC Curve (with c = 1)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance n = 60, c = 1 n = 80, c = 1 n = 100, c = 1 n = 120, c = 1 Operating Characteristic Curves (with c = 1)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk c (p = AQL)(p = LTPD) Understanding Changes in the OC Curve (with n = 60)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk c (p = AQL)(p = LTPD) 10.1220.126 Understanding Changes in the OC Curve (with n = 60)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk c (p = AQL)(p = LTPD) 10.1220.126 20.0230.303 Understanding Changes in the OC Curve (with n = 60)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk c (p = AQL)(p = LTPD) 10.1220.126 20.0230.303 30.0030.515 Understanding Changes in the OC Curve (with n = 60)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance Producer’sConsumer’sRisk c (p = AQL)(p = LTPD) 10.1220.126 20.0230.303 30.0030.515 40.0000.726 Understanding Changes in the OC Curve (with n = 60)

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© 2007 Pearson Education 1.0 – 0.9 – 0.8 – 0.7 – 0.6 – 0.5 – 0.4 – 0.3 – 0.2 – 0.1 – 0.0 – |||||||||| 12345678910 (AQL) (LTPD) Proportion defective (hundredths) Probability of acceptance n = 60, c = 1 n = 60, c = 2 n = 60, c = 3 n = 60, c = 4 Operating Characteristic Curves (with n = 60)

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© 2007 Pearson Education Acceptance Sampling Plan Data AQL BasedLTPD Based 00.050952.299638 10.3552363.887565 20.8112815.321789 31.36751376.6697111 41.96801977.9894133 52.62562639.2647154 63.283832810.5139175 73.979439811.7726196 84.693646912.9903217 95.423754214.2042237 106.163561615.4036257 AcceptanceExpectedSampleExpectedSample NumberDefectivesSizeDefectivesSize

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© 2007 Pearson Education Average Outgoing Quality Example I.2 1.6 – 1.2 – 0.8 – 0.4 – 0 – ||||||||12345678||||||||12345678 Defectives in lot (percent) Average outgoing quality (percent) ProportionProbability Defectiveof Acceptance (p)np(P a ) 0.011.100.974 0.022.200.819 0.033.300.581= (0.603 + 0.558)/2 0.044.400.359 0.055.500.202= (0.213 + 0.191)/2 0.066.600.105 0.077.700.052= (0.055 + 0.048)/2 0.088.800.024 For p = 0.01:0.01(0.974)(1000 – 110)/1000 = 0.0087 For p = 0.02:0.02(0.819)(1000 – 110)/1000 = 0.0146 For p = 0.03:0.03(0.581)(1000 – 110)/1000 = 0.0155 For p = 0.04:0.04(0.359)(1000 – 110)/1000 = 0.0128 For p = 0.05:0.05(0.202)(1000 – 110)/1000 = 0.0090 For p = 0.06:0.06(0.105)(1000 – 110)/1000 = 0.0056 For p = 0.07:0.07(0.052)(1000 – 110)/1000 = 0.0032 For p = 0.08:0.08(0.024)(1000 – 110)/1000 = 0.0017 Noise King uses rectified inspection for its single-sampling plan with n = 110, c = 3, N = 1000 Estimate the probabilities of acceptance for portion defective values from 0.01 to 0.08 in steps of 0.01

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© 2007 Pearson Education Average Outgoing Quality Example I.2 1.6 – 1.2 – 0.8 – 0.4 – 0 – ||||||||12345678||||||||12345678 Defectives in lot (percent) Average outgoing quality (percent) ProportionProbability Defectiveof Acceptance (p)np(P a ) 0.011.100.974 0.022.200.819 0.033.300.581= (0.603 + 0.558)/2 0.044.400.359 0.055.500.202= (0.213 + 0.191)/2 0.066.600.105 0.077.700.052= (0.055 + 0.048)/2 0.088.800.024

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© 2007 Pearson Education 1.6 – 1.2 – 0.8 – 0.4 – 0 – ||||||||12345678||||||||12345678 Defectives in lot (percent) Average outgoing quality (percent) Average Outgoing Quality Example I.2

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© 2007 Pearson Education AOQL 1.6 – 1.2 – 0.8 – 0.4 – 0 – ||||||||12345678||||||||12345678 Defectives in lot (percent) Average outgoing quality (percent) Average Outgoing Quality Example I.2

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© 2007 Pearson Education AOQ Calculations Application I.2 Management has selected the following parameters:

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© 2007 Pearson Education AOQ Calculations Application I.2

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© 2007 Pearson Education Solved Problem 1.0 — 0.9 — 0.8 — 0.7 — 0.6 — 0.5 — 0.4 — 0.3 — 0.2 — 0.1 — 0 — |||||||||| 12345678910 Proportion defective (hundredths)(p) Probability of acceptance (P a ) (AQL)(LTPD) 1.000 0.996 0.951 0.810 0.587 0.363 0.194 0.092 0.039 0.015 = 0.092 = 0.049

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