Chapter 9
#’s 1,2, and 14

9.1 a.) μ0=1050 σ=25 δ=1σ K= δ2σ=1225=12.5 H=5σ= 525=125 Table of Tabular CUSUM Period | X | X - 1062.5 | C+ | N+ | 1037.5-X | C- | N- | 1 | 1045 | -17.5 | 0 | 0 | -7.5 | 0 | 0 | 2 | 1055 | -7.5 | 0 | 0 | -17.5 | 0 | 0 | 3 | 1037 | -25.5 | 0 | 0 | 0.5 | 0.5 | 1 | 4 | 1064 | 1.5 | 1.5 | 1 | -26.5 | 0 | 0 | 5 | 1095 | 32.5 | 34 | 2 | -57.5 | 0 | 0 | 6 | 1008 | -54.5 | 0 | 0 | 29.5 | 29.5 | 1 | 7 | 1050 | -12.5 | 0 | 0 | -12.5 | 17 | 2 | 8 | 1087 | 24.5 | 24.5 | 1 | -49.5 | 0 | 0 | 9 | 1125 | 62.5 | 87 | 2 | -87.5 | 0 | 0 | 10 | 1146 | 83.5 | 170.5 | 3 | -108.5 | 0 | 0 | 11 | 1139 | 76.5 | 247 | 4 | -101.5 | 0 | 0 | 12 | 1169 | 106.5 | 353.5 | 5 | -131.5 | 0 | 0 | 13 | 1151 | 88.5 | 442 | 6 | -113.5 | 0 | 0 | 14 | 1128 | 65.5 | 507.5 | 7 | -90.5 | 0 | 0 | 15 | 1238 | 175.5 | 683 | 8 | -200.5 | 0 | 0 | 16 | 1125 | 62.5 | 745.5 | 9 | -87.5 | 0 | 0 | 17 | 1163 | 100.5 | 846 | 10 | -125.5 | 0 | 0 | 18 | 1188 | 125.5 | 971.5 | 11 | -150.5 | 0 | 0 | 19 | 1146 | 83.5 | 1055 | 12 | -108.5 | 0 | 0 | 20 | 1167 | 104.5 | 1159.5 | 13 | -129.5 | 0 | 0 |

The CUSUM Chart

From the CUSM chart the process signal is out-of-control at period 10. Therefore, we can conclude that the process was last in control at period 10. At period 10 Ci+ =170.5 and Ci+ >H, we can say that the process is out of control at period 10. Since, N+=3 at the 10th period the assignable cause occurred after the 7th observation because 10 – 3 = 7. The shift may have occurred between 7 and 8.
b.)
σ=MR2/d2 σ=38.84211.128=34.4345 The estimate of σ is not reasonable since it is much smaller than that from the data.

9.2) K= δ2=12=0.5 H=5 We can conclude the same as before. 9.14) From the EWMA chart the process does seem to be in control.