Quality Management, PSC and Six Sigma

Week Mean(X-bar) 1 8.60 4.50 6.20 5.70 10.10 7.02 2 10.10 8.90 7.30 8.10 6.40 8.16 3 5.30 9.40 10.20 10.20 5.80 8.18 4 6.10 11.50 9.30 9.40 9.60 9.18 5 12.40 8.30 12.40 10.10 8.40 10.32 6 9.70 10.40 7.50 8.50 11.60 9.54 7 6.50 5.90 5.60 7.70 9.10 6.96 8 15.60 6.60 10.70 11.50 7.50 10.38 9 12.50 3.60 8.50 6.40 9.60 8.12 10 9.30 7.40 9.90 10.40 14.30 10.26 11 14.50 8.60 9.30 5.30 10.60 9.66 12 10.30 9.60 11.20 7.50 6.90 9.1 No. of samples 12 size of sample 5 A_2 0.58 D_3 0 D_4 2.11 Grandmean 8.906666667 Mean of range 5.80 UCL-mean 12.27066667 LCL-mean 5.542666667 UCL-R 12.238 LCL-R 0 a) Week UCL-mean X_db Mean(X-bar) LCL-mean 1 12.27 8.91 7.02 5.54 2 12.27 8.91 8.16 5.54 3 12.27 8.91 8.18 5.54 4 12.27 8.91 9.18 5.54 5 12.27 8.91 10.32 5.54 6 12.27 8.91 9.54 5.54 7 12.27 8.91 6.96 5.54 8 12.27 8.91 10.38 5.54 9 12.27 8.91 8.12 5.54 10 12.27 8.91 10.26 5.54 11 12.27 8.91 9.66 5.54 12 12.27 8.91 9.10 5.54 Response Times (min) 1 2 - 2.00 4.00 6.00 8.00 10.00 12.00 14.00 UC

Week UCL-R R-bar Range(R) LCL-R 1 12.238 5.80 5.60 0 2 12.238 5.80 3.70 0 3 12.238 5.80 4.90 0 4 12.238 5.80 5.40 0 5 12.238 5.80 4.10 0 6 12.238 5.80 4.10 0 7 12.238 5.80 3.50 0 8 12.238 5.80 9.00 0 9 12.238 5.80 8.90 0 10 12.238 5.80 6.90 0 11 12.238 5.80 9.20 0 12 12.238 5.80 4.30 0 The mean and the Range charts seem to be in control limits and nothing needs to be done b) Upper Specification 10 mins Lower Specification 0 mins 2.480627768 1.109370463 CP 1.502353562 Since, Cp >1, the tolerance range is greater than the process range and hence the process c) Upper specification 9 10.5 11 11.5 Lower Specification 0 0 0 0 CP 1.352118205 1.5774712397 1.6525889177 1.727707 Extra sigma 3 Standard Deviation of all times Est. Standard Deviation of X-BAR UC 1 2 3 0 2 4 6 8 10 12 14

st. dev 2.480627768 sigma_xbar 1.109370463 UCL-mean 12.23477806 LCL-mean 5.578555277 Week UCL-mean X_db Mean(X-bar) LCL-mean 1 12.23 8.91 7.02 5.58 2 12.23 8.91 8.16 5.58 3 12.23 8.91 8.18 5.58 4 12.23 8.91 9.18 5.58 5 12.23 8.91 10.32 5.58 6 12.23 8.91 9.54 5.58 7 12.23 8.91 6.96 5.58 8 12.23 8.91 10.38 5.58 9 12.23 8.91 8.12 5.58 10 12.23 8.91 10.26 5.58 11 12.23 8.91 9.66 5.58 12 12.23 8.91 9.10 5.58 1 2 - 2.00 4.00 6.00 8.00 10.00 12.00 14.00