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Unformatted text preview: Chapter 9 Exercise Solutions Note: Many of the exercises in this chapter were solved using Microsoft Excel 2002, not MINITAB. The solutions, with formulas, charts, etc., are in Chap09.xls. 91. ˆ ˆ 2.530, 15, 101.40 ˆ ˆ 2.297, 9, 60.444 ˆ ˆ 1.815, 18, 75.333 ˆ ˆ 1.875, 18, 50.111 A A A B B B C C C D D D n n n n σ μ σ μ σ μ σ μ = = = = = = = = = = = = Standard deviations are approximately the same, so the DNOM chart can be used. ˆ 3.8, 2.245, 3 R n σ = = = x chart: CL = 0.55, UCL = 4.44, LCL =  3.34 R chart: CL = 3.8, UCL = 4 D R = 2.574 (3.8) = 9.78, LCL = 0 Stat > Control Charts > Variables Charts for Subgroups > XbarR Chart Sample Sample Mean 20 18 16 14 12 10 8 6 4 2 4 224 _ _ X= 0.55 UCL= 4.438 LCL= 3.338 Sample Sample Range 20 18 16 14 12 10 8 6 4 2 10.0 7.5 5.0 2.5 0.0 _ R= 3.8 UCL= 9.78 LCL= 0 XbarR Chart of Measurements (Ex91Xi) Process is in control, with no samples beyond the control limits or unusual plot patterns. 91 Chapter 9 Exercise Solutions 92. Since the standard deviations are not the same, use a standardized x and R charts. Calculations for standardized values are in: Excel : workbook Chap09.xls : worksheet : Ex92. 3 4 2 4, 0, 2.282, 0.729; 19.3, 44.8, 278.2 A B C n D D A R R R = = = = = = = Graph > Time Series Plot > Simple Ex92Xsi Ex92Part Ex92Samp C C C C C B B A A A 20 18 16 14 12 10 8 6 4 2 1.5 1.0 0.5 0.00.51.0A2 = 0.729A2 = 0.729 +A2 = 0.729 +A2 = 0.729 Control Chart of Standardized Xbar (Ex92Xsi) Ex92Rsi Ex92Part Ex92Samp C C C C C B B A A A 20 18 16 14 12 10 8 6 4 2 2.5 2.0 1.5 1.0 0.5 0.0 D4 = 2.282 D4 = 2.282 1.006 1.006 D3 = 0 D3 = 0 Control Chart of Standardized R (Ex92Rsi) Process is out of control at Sample 16 on the x chart. 92 Chapter 9 Exercise Solutions 93. In a short production run situation, a standardized CUSUM could be used to detect smaller deviations from the target value. The chart would be designed so that δ , in standard deviation units, is the same for each part type. The standardized variable , 0, ( )/ i j j j y μ σ (where j represents the part type) would be used to calculate each plot statistic. 94. Note: In the textbook, the 4 th part on Day 246 should be “1385” not “1395”. Set up a standardized c chart for defect counts. The plot statistic is ( 29 i i Z c c c = , with CL = 0, UCL = +3, LCL =  3. Stat > Basic Statistics > Display Descriptive Statistics Descriptive Statistics: Rx94Def Rx94Def 1055 13.25 1130 64.00 1261 12.67 1385 26.63 4610 4.67 8611 50.13 1055 1130 1261 1385 4610 8611 13.25, 64.00, 12.67, 26.63, 4.67, 50.13 c c c c c c = = = = = = Stat > Control Charts > Variables Charts for Individuals > Individuals Observation Individual Value 40 36 32 28 24 20 16 12 8 4 3 2 1123 _ X=0 UCL=3 LCL=3 I Chart of Standardized Total # of Defects (Ex94Zi) Process is in control....
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This note was uploaded on 02/14/2012 for the course IE 530 taught by Professor Ravindran during the Spring '97 term at Purdue.
 Spring '97
 RAVINDRAN

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