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Applications of the EWMA

Figurę 6. Esample of Modified Shewhart Control with Delayed

Adjustment

model. Instead he uses a disturbance process, D_t in the context of Eąuation 1, which is the sum of a “noise” component, a NID(0,1) random variable, and a “signal” component madę up from a mixture of shifts, drifts, and cycles which is independent of the noise component and has a finite variance. He chooses the EWMA parameters X = .15 and L = 2.73 based on the Lucas and Saccucci recommendations, and his estimates of new process level for calculating the adjustment are Z_t for the EWMA algorithm and the average of the points involved with the rule violation for the modified Shewhart algorithm. For each type of adjustment algorithm, he makes a series of dififerent simulation runs by changing the variance of the signal component of the process disturbance, and then he compares the closed-Ioop variance (o\) with the

open-loop variance (g²d). If cr^> o¹, the control algorithm is said to be transmitting variability, and if cs\<cs¹D. the algorithm is said to be absorbing variability. Figurę 8 is adapted from Chatto’s simulation data, where each axis