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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Page1 / 38

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online