Page 268 - Six Sigma Demystified

248 Six SigMa DemystifieD

includes several observations, so the central limit theorem provides that the
average of the points (or the moving average in this case) is normally distrib-
uted and the control limits clearly defined.
EWMA charts are also used to smooth the effect of known, uncontrollable
noise in the data. Many accounting, service, and chemical processes fit into this
categorization. For example, while day-to-day fluctuations in accounting pro-
cesses may be large, they are not purely indicative of process instability. The
choice of λ can be determined to make the chart more or less sensitive to these
daily fluctuations.
As with other control charts, EWMA charts are used to monitor processes
over time. The charts’ x axes are time-based so that the charts show a history
of the process. For this reason, you must have data that are time-ordered, that
is, entered in the sequence from which they were generated. If this is not the
case, then trends or shifts in the process may not be detected but instead attrib-
uted to random (common-cause) variation.

Methodology

When choosing the value of λ used for weighting, it is recommended to use
small values (such as 0.2) to detect small shifts and larger values (between 0.2
and 0.4) for larger shifts. An EWMA chart with λ = 1.0 is an X chart (for sub-
groups larger than 1) or an individual-X chart (when subgroup size equals 1).
Plotted statistic:

z = λ x + (1 – λ )z t–1
t
1
1
t
where λ is the value of the weighting factor, x is the subgroup average for the

t
current subgroup at time t, and the value of z at time zero (z ) is either a target
0
value or the overall average of the selected subgroups.
EWMA control limits:
 3 R  λ
−
t 2
CL = z ±   1 [ − 1 λ) ]
(
EWMA 0
 d 2 n  2 ( − λ)
where z is the starting value (either the target value or process mean value), n
0
is the subgroup size, d is a function of n, and m is the number of subgroups
2
selected for analysis.
The range chart (n > 1) or the moving-range chart (n = 1) is generally used
to monitor process variation.