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ISyE3039_Tsui_Fall 04_hw3solns

# ISyE3039_Tsui_Fall 04_hw3solns - ISyE 3039 HW3 Solutions...

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ISyE 3039 HW3 Solutions 5-1. (a) for n = 5, A 2 = 0.577, D 4 = 2.114, D 3 = 0 1 2 1 2 x 2 x x 2 R 4 R R 3 34.5 34.2 34.2 34.00 24 3 4 2 4.71 24 UCL 34.00 0.577(4.71) 36.72 CL 34.00 LCL 34.00 0.577(4.71) 31.29 UCL 2.115(4.71) 9.96 CL 4.71 LCL 0(4.71) 0.0 m m x x x x m R R R R m x A R x x A R D R R D R + + + + + + = = = + + + + + + = = = = + = + = = = = - = - = = = = = = = = = L L L L 0 X-bar Chart for Bearing ID (all samples in calculations) 15 12 27.0 29.0 31.0 33.0 35.0 37.0 39.0 41.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Sample No. x-bar UCL = 36.72 CL = 34.00 LCL = 31.29 5-1 R chart for Bearing ID (all samples in calculations) 0 2 4 6 8 10 12 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Sample No. R UCL = 9.96 CL = 4.71 LCL = 0

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5-1 (a) continued The process is not in statistical control; x is beyond the upper control limit for both Sample No. 12 and Sample No. 15. Assuming an assignable cause is found for these two out-of-control points, the two samples can be excluded from the control limit calculations. The new process parameter estimates are: 2 x x x R R R ˆ 33.65; 4.5; / 4.5/ 2.326 1.93 UCL 36.25;CL 33.65;LCL 31.06 UCL 9.52;CL 4.5;LCL 0.00 x x R R d σ = = = = = = = = = = = x-bar Chart for Bearing ID (samples 12, 15 excluded) 15 12 27.0 29.0 31.0 33.0 35.0 37.0 39.0 41.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Sample No.
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ISyE3039_Tsui_Fall 04_hw3solns - ISyE 3039 HW3 Solutions...

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