mont4e_sm_ch16_sec05 - CHAPTER 16 Note to the Instructor:...

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CHAPTER 16 Note to the Instructor: Many of the control charts and control chart summaries were created using Statgraphics. Minitab can be used to provide similar results. Section 16-5 16-1 a) 286 . 34 35 1200 223 35 7805 = = = = r x 0 ) 286 . 34 ( 0 286 . 34 51 . 72 ) 286 . 34 ( 115 . 2 22 . 203 ) 286 . 34 ( 577 . 0 223 223 78 . 242 ) 286 . 34 ( 577 . 0 223 3 4 2 2 = = = = = = = = = = = = + = + = r D LCL CL r D UCL chart R r A CL LCL CL r A CL UCL chart x b) 74 . 14 326 . 2 286 . 34 ˆ 223 ˆ 2 = = = = = d r x σ μ 16-2 a) 1456 . 0 25 64 . 3 344 . 0 25 60 . 8 510 . 14 25 75 . 362 = = = = = = s r x 0 ) 344 . 0 ( 0 344 . 0 728 . 0 ) 344 . 0 ( 115 . 2 312 . 14 ) 344 . 0 ( 577 . 0 510 . 14 510 . 14 708 . 14 ) 344 . 0 ( 577 . 0 510 . 14 3 4 2 2 = = = = = = = = = = = = + = + = r D LCL CL r D UCL chart R r A CL LCL CL r A CL UCL chart x 16-1
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b) c 4 = 0.94 0 0129 . 0 94 . 0 1 94 . 0 1456 . 0 3 1456 . 0 1 3 1456 . 0 3041 . 0 94 . 0 1 94 . 0 1456 . 0 3 1456 . 0 1 3 417 . 14 25 94 . 0 1456 . 0 3 510 . 14 3 510 . 14 603 . 14 25 94 . 0 1456 . 0 3 510 . 14 3 2 2 4 4 2 2 4 4 4 4 = = = = = + = + = = = = = = + = + = c c s s LCL CL c c s s UCL chart S n c s CL LCL CL n c s CL UCL chart x 16-3 a) 58 . 13 20 6 . 271 223 20 4460 = = = = s x 0 61 . 3 1512 . 0 9213 . 0 58 . 13 3 58 . 13 1 3 58 . 13 77 . 30 1512 . 0 9213 . 0 58 . 13 3 58 . 13 1 3 89 . 200 20 9213 . 0 58 . 13 3 223 3 223 11 . 245 4 9213 . 0 58 . 13 3 223 3 2 4 4 2 4 4 4 4 = = = = = + = + = = = = = = + = + = c c s s LCL CL c c s s UCL chart S n c s CL LCL CL n c s CL UCL chart x b) Process mean and standard deviation 74 . 14 9213 . 0 58 . 13 ˆ 223 ˆ 4 = = = = = c s x σ μ 16-2
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16-4 a) 5476 . 3 ) 534 . 2 ( 4 . 1 534 . 2 4 . 1 0 . 20 2 2 = = = = = r d d r x 0 ) 5476 . 3 ( 0 5476 . 3 11 . 7 ) 53476 . 3 ( 004 . 2 29 . 18 ) 5476 . 3 ( 483 . 0 0 . 20 0 . 20 71 . 21 ) 5476 . 3 ( 483 . 0 0 . 20 3 4 2 2 = = = = = = = = = = = = + = + = r D LCL CL r D UCL chart R r A CL LCL CL r A CL UCL chart x 043 . 0 0946 . 0 ) 5 . 1 ( 3 427 . 1 1 3 427 . 1 811 . 2 0946 . 0 ) 5 . 1 ( 3 427 . 1 1 3 427 . 1 so 9515 . 0 16 . 18 6 / ) 5 . 1 ( 3 0 . 20 3 0 . 20 84 . 21 6 / ) 5 . 1 ( 3 0 . 20 3 5 . 1 / where 2 4 4 2 4 4 4 4 4 4 = = = = = + = + = = = = = = = = + = + = = c c s CL LCL CL c c s CL UCL s c chart S n c s CL LCL CL n c s CL UCL c s chart x 16-5 a) X-bar and Range - Initial Study Problem 16-1 X-bar | Range ----- | ----- UCL: + 3.0 sigma = 37.5789 | UCL: + 3.0 sigma = 11.9461 Centerline = 34.32 | Centerline = 5.65 LCL: - 3.0 sigma = 31.0611 | LCL: - 3.0 sigma = 0 | out of limits = 1 | out of limits = 0 -------------------------------------------------------------------------------- Chart: Both
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mont4e_sm_ch16_sec05 - CHAPTER 16 Note to the Instructor:...

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