00200 ‰dd4c36466f230725aa367933239d12

202

Messina, Montgomery, Keats & Runger

1    51    101    151    201    251    301    351    401    451

Obssrva1ion Number (t)

FigurÄ™ 6. CUSUM Chart with K = 2ct for a Shift of 10 Units per Period at Observation 251, PMepc/spc = 3.23.

neither scheme signaled that an assignable cause has occurred. The performance measure for both schemes is 3.23 which is exactly that of the EPC scheme. This tends to indicate that applying CUSUM schemes to the correlated control actions might not improve the ability to determine that sustained shifts occurred in the process.

Simulation Results for Sustained Shifts

To further investigate the performance of this integrated EPC/SPC system for a sustained shift in the process, a simulation study was performed. The shift magnitudes investigated where 1, 2, 5, 7.5, and 10. In each study, a sustained shift of the appropriate magnitude was introduced in the process at observation 251 and is eliminated as soon as detected by the SPC rule. Performance measures are weighted due to the fact that only the number of observations after 251 to detect the sustained shift are included in the calculation. This weighted performance measure is used for each of the combined EPC/SPC schemes employed. For each scenario considered, the number of such simulations that did not signal are labeled with a star. The random variables e_t and a_t in equations (1) and (2) are assumed to be normally