Question

TABLE S6.1 SAMPLE SIZE, n Omm Lecture Exercise #11 2 3 4 Factors for Computing Control Chart Limits (3 sigma) MEAN FACTOR, UPPER RANGE, LOWER RANGE, A₂ DA D 1.880 3.268 0 1.023 2.574 0 .729 2.282 0 .577 2.115 0 ,483 2.004 0 .419 1.924 0.076 .373 1.864 0.136 5 6 7 8 9 .337 1.816 0.184 We wish to determine if screw production is in statistical control. We have no prior information, other than the 5 samples (where each sample has 4 observations) 10 .308 1.777 0.223 12 .266 1.716 0.284 Number Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 0.5014 0.5021 0.5018 0.5008 0.5041 2 0.5022 0.5041 0.5026 0.5034 0.5056 3 0.5009 0.5032 0.5035 0.5024 0.5034 4 0.5027 0.5020 0.5023 0.5015 0.5039 1. Compute the sample range and mean for each of the 5 samples. 2. Compute , the average of the sample means, and R, the average of the sample ranges. 3. Construct the X-chart to check if the sample mean is in control 4. Construct the Range chart to check if process variation is in control.

Answer 1

2 Number Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 1 0.5014 0.5021 0.5018 0.5008 0.5041 0.5022 0.5041 0.5026 0.5034 0.5056 3 0.5009 0.5032 0.5035 0.5024 0.5034 4 Average Xbar Range Standard deviation X-Dbar UCL X-bar LCL x-bar R-bar LCL R 0.5027 0.5018 0.0018 0.000963457 0.502695 0.505585 0.497295 0.00208 0.502 0.50285 0.0021 0.502695 0.505585 0.497295 0.00208 0.5023 0.50255 0.0017 0.502695 0.505585 0.497295 0.00208 0.5015 0.502025 0.0026 0.502695 0.505585 0.497295 0.00208 0.5039 0.50425 0.0022 0.502695 0.505585 0.497295 0.00208 UCL R 0 0.004747 0 0.004747 0 0.004747 0 0.004747 0 0.004747 X-Bar chart R-chart 0.00474656 1104740474 TEU0474-01-00474656 0.505585372IL05585157055854 HIT 55855 IL505585372 L0.50425 1:502695 0.502695 0.501 BUMAS 0.0026 0.00208 TOGLIE 0.00208 0.0018 20020 0.00208 .001 0.497295 -0.497295 0.497295 0.497295 0.497295 0 0 0 0 3 1 2. 3 4 5 R-bar -LCL R UCL R Range Average Xbar X-Dbar UCL x-bar LCL x-bar

As from above chart all values of X-bar and R are within control limits hence process is under control.