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MIE364S_T_1_09 - MIE364H1S Methods of Quality Control and...

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MIE364H1S Methods of Quality Control and Improvement Course Instructor: Prof. V. Makis Tutorial #1 1. A quality engineer is interested in setting target values for two independent quality characteristics of a paper roll. The first quality characteristic, , is the weight of a paper roll which follows a normal distribution, 1 X ) 1 , ( ~ 1 µ N X . The lower specification limit for is = 52.5 lb per roll. The second quality characteristic, , is the number of brownish spots per roll and it is Poisson distributed, 1 X 1 l 2 X ) ( ~ 2 λ Poisson X . The upper specification limit for is = 3. The producer’s revenue is a 2 X 2 l 1 = $20 for an accepted roll and a 2 = $5 for a rejected roll. A roll is accepted when both , otherwise it is rejected. The production cost function for a paper roll has a form 1 52.5 3 X and X 2 ) exp( 2 2 2 1 1 X l c X c c + + with c = $4, c 1 =$0.05, and c 2 =$0.1. a. Derive the expected profit function and discuss a procedure for finding the optimal target values µ * and λ *. b. What is the expected profit when µ = 53 lb and λ = 1?
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