krm8_ism_i - Supplement I Acceptance Sampling Plans...

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Unformatted text preview: Supplement I Acceptance Sampling Plans PROBLEMS 1. Alpha is the producers risk. To find Alpha, p is set equal to the acceptable quality level (AQL = 0.5%). Then np = (200 0.005) = 1.00. From Table I.1 where c = 4, ( 29 0.996 P x c = . Alpha ( 29 1 0.996 0.004 =- = , or 0.4 percent. Beta is the consumers risk. To find Beta, p is set equal to the lot tolerance proportion defective. (LTPD = 4%). Then np = (200 0.04) = 8.0. From Table I.1 where c = 4, ( 29 0.100 P x c = . Beta = 0.100, or 10 percent. 2. a. A variety of sampling plans will satisfy the requirements. One such plan is n = 280, c = 6. To find Alpha: ( 29 280 0.01 2.8 np = = . Then ( 29 0.976 P x c = and Alpha ( 29 1 0.976 0.024 =- = , or 2.4 percent. To find Beta, np = (280 0.04) = 11.2. Then ( 29 0.071 P x c = and Beta = 0.071, or 7.1 percent. Another plan is n = 232, c = 5. In this case, Alpha = 3.1% and Beta = 10 percent. The tradeoff between this plan and the other one is that you have a smaller sample size but the producers and consumer risks increase. 2 l SUPPLEMENT I b. The OC curve is: c. The maximum value of the AOQ over various possible values of the proportion defective is 0.0122. The AOQL is therefore 1.22 percent defective when the lot proportion defective is 0.02. Here we have used n = 280 and c = 6. ( 29 ( 29 a p P N n AOQ N- = Proportion Defective ( p ) np a P ( N n / N ) AOQ 0.000 0.0 1.000 0.907 0.0000 0.005 1.4 0.999 0.907 0.0045 0.010 2.8 0.976 0.907 0.0089 0.015 4.2 0.867 0.907 0.0118 0.020 5.6 0.670 0.907 0.0122 0.025 7.0 0.450 0.907 0.0102 0.030 8.4 0.267 0.907 0.0073 0.035 9.8 0.143 0.907 0.0045 0.040 11.2 0.071 0.907 0.0026 0.071 0.976 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 P r o b a b i l i t y o f A c c e p t a n c e , ( P a ) Acceptance Sampling Plans l SUPPLEMENT I l 3 3. SunSilk Shampoo Company. AQL = 5/500, or 1%; LTPD = 5%. a. Again, a variety of sampling plans will satisfy the requirements. One plan is n = 160, c = 4. To find Alpha: np = (160 0.01) = 1.6. Then ( 29 0.976 P x c = and Alpha = (1 0.976) = 0.024, or 2.4 percent. To find Beta, np = (160 0.05) = 8.0. Then ( 29 0.100 P x c = and Beta = 0.100, or 10.0 percent. Another plan is n = 134, c = 3. Alpha = 4.7 percent and Beta = 9.9 percent....
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This note was uploaded on 12/19/2009 for the course MANAGEMENT 00123 taught by Professor Ahmed during the Spring '09 term at Albany College of Pharmacy and Health Sciences.

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krm8_ism_i - Supplement I Acceptance Sampling Plans...

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