00206 s61d525289e95c98083ce52337cb095

208

Messina, Montgomery, Keats & Runger

1    51    101    151    201    251    301    351    401    451

Observation Number (t)

Figurę 12. CUSUM Chart with K = 2ct for a Trend of 1 Unit per Period at Obseryation 251, PM_EPC/spc = 89.973.

applying CUSUM schemes to control actions will be an ineffective method to remove them.

Simulation Studv of the Effects of Trends on Control Actions To further investigate the performance of this integrated EPC/SPC system for a trend in the process, a simulation study was performed. The trend magnitudes investigated were 0.05, 0.1, 0.25, 0.5, and 1.0 units per period. In each study, a trend of the appropriate magnitude was introduced in the process at observation 251 and is eliminated as soon as detected by the SPC rule. Weighted performance measures are used as described above. 2000 simulations were performed for each trend magnitude. These results show that the CUSUM is not an effective tool for monitoring the manipulated variable and hence is not recommended for use by the control engineer. Thus, our comments are confined to the predicted error EWMA and tracking signal scheme.

Table 3 presents the simulation results for the performance measure of the control actions for those trend magnitudes discussed above. The predicted error EWMA and tracking signal scheme provides a significant reduction in overall variability in the process when compared to the EPC scheme alone. The worst case occurs for a trend of 0.05 in which 3.5% of the simulations did not signal that a trend occurs in the process. Table 4 gives the average run lengths (ARLs) associated with the simulation conducted in Table 4. For large trends in