Page 365 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

OTE/SPH
OTE/SPH
3:7
August 31, 2006
Char Count= 0
JWBK119-22
350 Simultaneous Monitoring of the Mean, Variance and Autocorrelation
Process Measurements
12
10
8
6
4
2
0
−2
−4
−6
0 100 200 300 400 500
Time (t)
Figure 22.5 The simulated process measurements.

The MH statistic at t = 200 must be based on the vector of observations x * =
200

(x 196 , x 197 ,..., x 200 ) . For the in-control state, the corresponding covariance matrix and
its inverse are as follows:

5.263 4.737 4.263 3.837 3.453
⎡ ⎤
4.737 5.263 4.737 4.263 3.837
⎢ ⎥
⎢ ⎥
Σ 0 = ⎢ 4.263 4.737 5.263 4.737 4.263 ⎥
⎢ ⎥
⎣ 3.837 4.263 4.737 5.263 4.737 ⎦
3.453 3.837 4.263 4.737 5.263
and

1.00 −0.90 0.00 0.00 0.00
⎡ ⎤
−0.90 1.81 −0.90 0.00 0.00
⎢ ⎥
Σ −1 = ⎢ 0.00 −0.90 1.81 −0.90 0.00 ⎥ .
0
⎥
⎢
⎥
⎢
⎣ 0.00 0.00 −0.90 1.81 −0.90 ⎦
0.00 0.00 0.00 −0.90 1.81
Table 22.1 Simulated process measurements, 196 ≤ t ≤ 205.
t x t MH statistic t x t MH statistic
196 −0.577 2.644* 201 1.666 1.383
197 1.934 7.311* 202 5.470 17.128
198 1.968 7.226* 203 5.315 16.546
199 1.234 6.426* 204 5.265 16.761
200 1.224 6.437 205 5.672 17.555
*Calculated using observations not shown in this table.