Question

The data in the table below represent individual observations on molecular weight taken hourly from a chemical process. The target value of molecular weight is 1050 and the process standard deviation is thought to be about ? = 25. Please use software outputs to present your analysis. (a) Set up a tabular CUSUM for the mean of this process (choose appropriate ? and ℎ). (b) Set up an EWMA control chart with appropriate ? and ?.

Observation Number 1 2 Observation Number x 11 1.139 121,169 13 1.151 14 1,128 15 1.238 16 1,125 17 1,163 18 1,188 19 1,146 20 1,167 1,045 1,055 1.037 1.064 1,095 1,008 1.050 1.087 1.125 1,146 5 6 7 8 9 10

Answer 1

All the calculations are made using MS-Excel software.

page-4,5,6,7 is for CUSUM chart

page-8,9 is for EWMA chart.
For EWMA chart: target value =llo = Zo = 1050 X=0:1 =3 8= process standard deviation = 25 | Zie 1 xj + (1-1) Zi-

I Control limits for EWMA charti ICL = Elli) -L.S.E.(2) CL=E(2)=1050 UCL = E(Z;) + Lisie.Z;) where, Var(i) = . 2-1 02 [1-(1-x)2 ]

Xi Zi CL 1 1 6 7 Var(zi) S.e(zi) LCL UCL 1045 1049.5 6.25 2.5 1042.5 1057.5 1055 1050.05 11.3125 3.363406 1039.91 1060.09 1037 1048.745 15.41313 3.925955 1038.222 1061.778 1064 1050.271 18.73463 4.328352 1037.015 1062.985 1095 1054.743 21.42505 4.62872 1036.114 1063.886 1008 1050.069 23.60429 4.858425 1035.425 1064.575 1008 1050 1050 1050.062 25.36948 5.036812 1034.89 1065.11 1087 1053.756 26.79928 5.176802 1034.47 1065.53 1125 1060.88 27.95742 5.287477 1034.138 1065.862 1146 1069.392 28.89551 5.375454 1033.874 1066.126 1139 1076.353 29.65536 5.445674 1033.663 1066.337 1169 1085.618 30.27084 5.501895 1033.494 1066.506 1151 1092.156 30.76938 5.547016 1033.359 1066.641 1128 1095.74 31.1732 5.583297 1033.25 1066.75 1238 1109.966 31.50029 5.612512 1033.162 1066.838 1125 1111.47 31.76524 5.636066 1033.092 1066.908 1163 1116.623 31.97984 5.655072 1033.035 1066.965 1186 1123.56 32.15367 5.670421 1032.989 1067.011 1146 1125.804 32.29448 5.682823 1032.952 1067.048 1167 1129.924 32.40853 5.692849 1032.921 1067.079 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050 1050