# ch08 - Chapter 8 Note to the Instructor Some of the revised...

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Unformatted text preview: Chapter 8 Note to the Instructor: Some of the revised control charts provided in the solutions retain the removed points only as place holders. Other revised control charts have been created by removing the out-of-control point from the worksheet and constructing the control charts again. Section 8-4 8.1. a) 48 . 28 r A CL LCL 95 . 33 CL 42 . 39 r A CL UCL chart x 2 2 =- = = = + = ) 35 . 5 ( r D LCL 35 . 5 CL 77 . 13 r D UCL chart R 3 4 = = = = = = 20 10 Subgroup 40 35 30 Sample Mean 1 X=33.95 3.0SL=39.42-3.0SL=28.48 15 10 5 Sample Range R=5.350 3.0SL=13.77-3.0SL=0.00E+00 Xbar/R Chart for x1-x3 b) 22 . 29 LCL 28 . 34 CL 34 . 39 UCL chart x = = = ) 947 . 4 ( r D LCL 947 . 4 CL 74 . 12 UCL chart R 3 = = = = = 1 20 10 Subgroup 40 35 30 Sample Mean X=34.28 3.0SL=39.34-3.0SL=29.22 15 10 5 Sample Range R=4.947 3.0SL=12.74-3.0SL=0.00E+00 Xbar/R Chart for x1-x3 8-2. a) 39 . 20 80 . 7 r 925 . 18 20 50 . 378 x = = = = 64 . 18 ) 39 . ( 729 . 925 . 18 r A CL LCL 925 . 18 CL 21 . 19 ) 39 . ( 729 . 925 . 18 r A CL UCL chart x 2 2 =- =- = = = + = + = ) 39 . ( r D LCL 39 . CL 89 . ) 39 . ( 282 . 2 r D UCL chart R 3 4 = = = = = = = b) 2 ˆ 18.925 0.39 ˆ 0.1894 2.059 x r d μ σ = = = = = 8-3. a) The trial control limits are as follows. 08 . 12 LCL 14 . 15 CL 20 . 18 UCL chart x = = = LCL 2 . 4 CL 581 . 9 UCL chart R = = = 2 20 10 Subgroup 19 18 17 16 15 14 13 12 Sample Mean X=15.14 3.0SL=18.20-3.0SL=12.08 10 5 Sample Range 1 R=4.200 3.0SL=9.581-3.0SL=0.00E+00 Xbar/R Chart for Problem 8-3 Based on the control charts, there is a single observation beyond the control limits. Observation 14 is above the upper control limit on the R chart. b) With Observation 14 removed, the control limits and charts are as follows. 31 . 12 LCL 14 . 15 CL 98 . 17 UCL chart x = = = LCL 895 . 3 CL 885 . 8 UCL chart R = = = 20 10 Subgroup 18 17 16 15 14 13 12 Sample Mean X=15.14 3.0SL=17.98-3.0SL=12.31 10 5 Sample Range R=3.895 3.0SL=8.885-3.0SL=0.00E+00 Previous Xbar/R Chart for 8-3 All points are within the control limits. The process is said to be in statistical control. 8-4. 5476 . 3 ) 534 . 2 ( 4 . 1 r giving 534 . 2 d 4 . 1 d r . 20 x 2 2 = = = = = 29 . 18 ) 5476 . 3 ( 483 . . 20 r A CL LCL . 20 CL 71 . 21 ) 5476 . 3 ( 483 . . 20 r A CL UCL chart x 2 2 =- =- = = = + = + = ) 5476 . 3 ( r D LCL 5476 . 3 CL 11 . 7 ) 53476 . 3 ( 004 . 2 r D UCL chart R 3 4 = = = = = = = 3 8-5. a) 2 . 47 25 1180 r 28 . 306 25 7657 x = = = = 87 . 271 ) 2 . 47 ( 729 . 28 . 306 r A CL LCL 223 CL 69 . 340 ) 2 . 47 ( 729 . 28 . 306 r A CL UCL chart x 2 2 =- =- = = = + = + = ) 2 . 47 ( r D LCL 2 . 47 CL 71 . 107 ) 2 . 47 ( 282 . 2 r D UCL chart R 3 4 = = = = = = = b) 92 . 22 059 . 2 2 . 47 d r ˆ 28 . 306 x ˆ 2 = = = = = σ μ 8-6. a) 06237 . LCL 06294 . CL 06352 . UCL chart x = = = LCL 000996 . CL 002106 . UCL chart R = = = 25 20 15 10 5 Subgroup 0.064 0.063 0.062 Sample Mean 1 1 1 1 X=0.06294 3.0SL=0.06352-3.0SL=0.06237 0.003 0.002 0.001 0.000 Sample Range 1 R=9.96E-04 3.0SL=0.002106-3.0SL=0.00E+00 Xbar/R Chart for x1-x5...
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## This note was uploaded on 03/15/2009 for the course IE 315 taught by Professor Kapur during the Spring '09 term at University of Washington.

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ch08 - Chapter 8 Note to the Instructor Some of the revised...

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