00218 Œ3a14ee5828b6e6c53f84df808267d0

220

Baxley

Coefficient    Coefficicnt

of    of

k    k

FigurÄ™ 2. Forecast Weights for the IMA (0,1,1) Model.

E(K,₊ ||adjustment at t and S_t+ j = 0) = Target    (2)

Var(y^₊j|adjustnient at / and S_t+^ = 0) = a\    (3)

While the control error variance, Var(^ - Target) is u\ only on the samples immediately following an adjustment, the forecast errors, D_t - Z_t_j, always have a fixed mean of zero with constant standard deviation, a_a. As a result they conform to the assumptions of conventionaI control charting methods such as Shewhart charts. Therefore, conventional charting methods can be used on these forecast errors for the purpose of detecting special causes (S₍ * 0) in the form of unusual process behavior or laboratory errors not conforming to the IMA model. This leads to the Algorithmic SPC philosophy of making periodic adjustments to compensate for the normal drifting behavior and in addition using control charts on EWMA forecast errors to detect and fix upsets.