hw2_new_new_solns

hw2_new_new_solns - Solutions to HW 2 IEOR 130 Prof...

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IEOR 130 Prof. Leachman 1. (a) μ = 97.5, R-bar = 5.21, n=5 σ = 5.21 / d 2 = 5.21 / 2.326 = 2.24 X-bar chart: UCL = 97.5 + 3(2.24)/5^0.5 = 100.5 LCL = 97.5 - 3(2.24)/5^0.5 = 94.5 R-chart: LCL = d 3 *R-bar = 0 UCL = d 4 *R-bar = 2.1(5.21) = 10.99 (b) Prob {94.5 < X-bar < 100.5 | μ = 100} = Prob { (94.5-100.0)/{2.24/5^0.5} < Z < (100.5-100.0)/{2.24/5^0.5} } = Prob { -5.495 < Z < 0.5043 } = Φ (0.5043) - Φ (-5.495) = Φ( 0.5043) = 0.6887 (c) (0.6887)^5 = 0.155 2. (a) UCL= μ + 3σ / n^0.5, LCL= μ − 3σ / n^0.5 μ = (UCL+LCL)/2 = 11 (b) UCL - LCL = 6* σ / n^0.5 n^0.5 = 6*6.6/(13.8-8.2) = 7.071 n = 50 3. (a) R-bar = 3.825, n=6 σ = 3.825 / d 2 = 3.825 / 2.534 = 1.51 LCL = d 3 *R-bar = 0 UCL = d 4 *R-bar = 2*3.825 = 7.65 (b) UCL= μ + 3σ / n^0.5, LCL= μ − 3σ / n^0.5 UCL - LCL = 6* σ / 6^0.5 = 3.70 4. (a) Use a c-chart. (b) We are given UCL = 70, USL = 60. C pk = (USL – μ )/3* σ , so we need to find μ and σ . Now μ = c, σ = c 0.5 , so we need to find c. UCL = c + 3*[c
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This note was uploaded on 03/16/2010 for the course ORMS 130 taught by Professor Leachman during the Spring '10 term at Berkeley.

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hw2_new_new_solns - Solutions to HW 2 IEOR 130 Prof...

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