Page 195 - Special Topic Session (STS) - Volume 3

STS540 Zhi Song et al.
2
2
+ − 2

= .

2
2(1 − )

Note that ( |) = 1, ( |) = 1. Then the EC scheme is given by =

max{1, + (1 − ) −1 } , = 1,2, … and with the starting value = 1. Next,

0
we incorporate the similar FIR features as in Section 2.1 in the EC scheme for
quicker detection of an initial OOC situation.
1. EC scheme with FIR version of Lucas and Saccucci [1] [EC-fir] We
develop using the FIR feature with the fixed control limit EC scheme (denoted
as EC-fir) in the line of Lucas and Saccucci [1], which can be constructed in the
following way:
λ
= { ∈ ℕ| > 1 + √ }.

2 − λ
λ
We set the starting value 0ℎ = 1 + ℎ × √ 2−λ . When ℎ = 0 , the EC-fir
scheme is the fixed control limit EC scheme without FIR features.
2. EC scheme with FIR version of Rhoads et al. [6] [EC-fvacl] The FIR
feature with the EC scheme based on the variance-adjusted control limit,
denoted as EC-fvacl, is formulated as follows:

λ
2
= { ∈ ℕ| > 1 + √ ((1 − (1 − λ) )}.

2 − λ

λ
with the starting value 0ℎ = 1 + ℎ × √ 2−λ (λ(2 − λ)) (cf. Knoth [3]).

3. Optimization of EWMA schemes with FIR
In this section, we focus on optimally designing an FIR-EWMA scheme that
restricts early false alarm probabilities and facilitates quick detection. As
mentioned earlier, use of the FIR feature in a monitoring scheme has gained a
great deal of attention among the researchers over the years. Nevertheless,
the majority of the existing schemes with the FIR feature set the initial value
of the monitoring statistic at the halfway between the process target value and
the control limits. That is, they are based on a 50% advanced head start. The
OOC performance of such scheme is often better, specially for detecting shifts
at an early stage. Nevertheless, the probability of a few early false alarms also
increases. Therefore, we prefer to design an optimal FIR-based EWMA scheme
selecting the head start or starting value Z0h that ideally increases sensitivity
without compromising with the early false alarm probabilities.

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