hw1sol

hw1sol - ME 363 HW #1 Solution 1 T = TA 2 + TB2 + TC 2 + TP...

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Unformatted text preview: ME 363 HW #1 Solution 1 T = TA 2 + TB2 + TC 2 + TP 2 2 2 2 2 = ⎡( 0.006 ) + ( 0.006) + ( 0.014 ) + ( 0.010) ⎤ 2 ⎣ ⎦ = 0.0192 or ± 0.0096 1 All Unilateral Part A = 3.519+0.006 −0 Part B = 4.749+0.006 −0 Part C = 13.344+0.014 −0 + Part D = 7.268−0.010 0 Bilateral Part A = 3.522 ± 0.003 Part B = 4.752 ± 0.003 Part C = 13.351 ± 0.007 Part D = 7.273 ± 0.005 2. (a ) Ra = ∑y i −y n y = 0.833 Ra = 1 ⎛ 3.167 + 18.167 + 22.167 + 15.167 + 31.833 + 20.833 ⎞ ⎟ 12 ⎜ +27.833 + 19.167 + 30.167 + 12.167 + 15.833 ⎝ ⎠ 1 ( 224.5) = 20.03 12 2 = ( b) ∑ ( yi − y ) Rq = n ⎡ 1 ⎛ 3.167 + 18.167 + 22.167 + 15.167 + 31.833 + 20.833 =⎢ ⎜ 2 2 2 2 2 ⎢ 12 ⎝ +27.833 + 19.167 + 30.167 + 12.167 + 15.833 ⎣ 2 2 2 2 2 2 ⎞⎤ ⎟⎥ ⎠⎥ ⎦ 1 2 ⎡1 ⎤2 = ⎢ ( 5536 ) ⎥ ⎣ 12 ⎦ = 21.46 1 (c) 20.03 0.030 ⊥ 3 Prob. 3 sample number 1 2 3 4 5 6 7 Average x1 0.55 0.59 0.55 0.54 0.58 0.6 0.57 x2 0.6 0.55 0.5 0.57 0.58 0.61 0.6 x3 0.57 0.6 0.55 0.5 0.6 0.55 0.54 x4 0.55 0.58 0.51 0.5 0.56 0.59 0.57 0.568 0.580 0.528 0.528 0.580 0.588 0.570 R 0.05 0.05 0.05 0.07 0.04 0.06 0.06 Average 0.563 (a) x = 0.563 R = 0.054 The sample size is 4 and # of samples is 7. From Table 36.3, A 2 = 0.729 D 4 = 2.282 and D3 = 0 UCL x = x + A 2 ⋅ R = 0.563 + 0.729 × 0.054 = 0.602 LCL χ = x − A 2 ⋅ R = 0.56 − 0.729 × 0.05 = 0.524 UCL R = D 4 ⋅ R = 2.282 × 0.054 = 0.123 LCL R = D3 ⋅ R = 0 × 0.054 = 0 (b) σ= ∑(x − x ) n −1 2 = 0.025 Cp = USL-LSL 6σ 0.602 − 0.524 = 0.52 6 × 0.025 min { USL − x , LSL − x } 3σ min {( 0.602 − 0.563) , ( 0.524 − 0.563)} 3 × 0.025 = C pk = = = 0.52 ...
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