Question

2. The fill volume of soft-drink beverage bottles is measured by placing a gauge over the crown and comparing the height of the liquid in the neck of the bottle against a coded scale. On this scale, a reading for zero corresponds to the correct fill height. Fifteen samples of size n 10 have been analyzed, and the fill heights are shown in Table 2. Table 2. Fill Height Data and Xbar, R. s Statistics Computed Sample x1 x4 x5 x6 x7 x8 x9 x10 X bar 5 1510 20 10 10 .5 05 0.s 25 0,500 40 1,333 1,0 0,0 1,5 0,0 0,4502,5 0,926 1,0 1-1,0一ㄧ一1,5 | 1,0 | 0,0 | -1,0 | -1,0 | 1,0 | 1,0 | 1,5-100 | 3,0-25 4 15 0 15 20 10 015 05 2.0 00 060035 1,174 0510 0.0 0,505 05 0,0 00 0.000 1.5 0471 1,0 0,5 ,0 1,0 0,000 3,0 0,972 0,0 1,0 1,5 1,0 0,0 1,0 0,0 1,0 0.0 10 0,050 2,5 0,896 1,5 o,s 0,0 0,1503,0 0,818 1,0 1,0 1,0 0,5 1,5 1,0 10 1.0 0,5 0 0 0.0 05 -10 0.0 -05 00 1.5 1,0 1 1,0 ļ 0,0 | 1,5 | 0,0 | 1,5 | 0.5 1-1,5 0,0 1-2,0 10,200 9 1,5 1,0 1,0 3,5 1,o ,0,150 5,0 1,528 10 5 15 0.0 20 0.0 05 15 20 0.0 0,300 3.5 1.206 1,0 -0,550 2,0 0,685 10 0,5 1,0 1,5 0,0 -05 050.0 1,5 20 0.5 0.0 0.000 1,0 0,5 -0,5 -1,0 10 00 20 12 13 14 15 10 1.5 05 05 0.0 0 10 20 0.5 15 10 15 05 0150 3.5 1.248 1,5 0,0 1.0 20 10 0.150 3.51,270 -0,0033,2001,066 Average a) Set up X and R control charts on this process. Does the process exhibit statistical control? If necessary construct revised control limits. b) Set up an s chart, and compare it with the R chart in part (a). c) Set up an s chart, and compare it with the s chart in part (b

Answer 1

51600122230622 05055050505005 4233132335342 33 01|23|45|67 1 2 3 4 5 67 8 9

Control Chart Calculations Control Chart Factors Table Subgroup size D3D4A2 Data 4 Sample/Subgroup Size 0 3.267 1.880 0 2.575 1.023 40 2.282 0.729 50 2.114 0.577 0 2.004 0.483 7 0.076 1.924 0.419 8 0.136 1.864 0.373 9 0.184 1.816 0.337 10 0.223 1777 0.308 110.256 1.7440.285 2 0.283 1.717 0.266 13 0.307 1.693 0.249 14 0.328 1.672 0.235 15 0.347 1.653 0.223 16 0.363 1.637 0.212 17 0.378 1.622 0.203 18 0.391 1.609 0.194 19 0.404 1.596 0.187 20 0.415 1.585 0.180 21 0.4251.575 0.173 22 0.435 1.565 0.167 23 0.443 1.557 0.162 24 0.452 1.548 0.157 25 0.459 1.541 0.153 15 R Chart Intermediate Calculations 8 D3 Factor 9 D4 Factor 10 3.2 0.347 1.653 R Chart Control Limits 12 Lower Control Limit 13 Center 14 Upper Control Limit 1.1104 3.2 5.2896 XBar Chart Intemediate Calculations 16 I 17 Average of Subgroup Averages 18 A2 Factor 19 A2 Factor RBar 200 21 22 Lower Control Limit 23 Center 24 Upper Control Limit 25 26 27 28 0.003333333 0.223 0.7136 XBar Chart Control Limits 0.716933333 0.003333333 0.710266667

0 1 Number XBar RangeLCL-R Center-R UCL-R LCL-X 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 3.25.2896 Center-X UCL-X 41.1104 2.5 1.1104 3 1.1104 3.5 1.1104 1.5 1.1104 3 1.1104 2.5 1.1104 3 1.1104 3.5 1.1104 5 1.1104 3.5 1.1104 41.1104 2 1.1104 3.5 1.1104 3.5 1.1104 0.5 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.00333 0.710267 0.45 -0.6 0.05 -0.15 0.2 -0.15 0.3 10 10 12 13 0.55 -0.15 0.15 14 16

Control Chart Calculations --UCL ーRBar LCL 10 12 16

X-bar Control Chart Calculations 0.8 0.6 04 0.2 2 10 14 16 0.2 0.4 0.6 -0.8