Page 405 - Six Sigma Demystified

Part 3 S i x S i g m a To o l S 385

of a ±3 SD control limit is 0.27 percent if the process has not shifted. On
average, a false alarm is encountered with these limits once every 370
(1/0.0027) subgroups. Using ±2 SD control limits, the chance of being
outside the limits when the process has not shifted is 4.6 percent, corre-
sponding to false alarms every 22 subgroups! If we respond to these false
alarms, we tamper and increase variation.

Methodology

In an SPC analysis, we collect samples over a short period of time. Each of these
samples is referred to as a subgroup. Each subgroup tells us two things about
the process—its current location and its current amount of variation.
Once we’ve collected enough subgroups over a period of time, we can use
these short-term estimates to predict where the process will be (its location)
and how much the process is expected to vary over a longer time period.
Control charts take many forms depending on the process that is being ana-
lyzed and the data available from that process. All control charts have the fol-
lowing properties:

• The x axis is sequential, usually a unit denoting the evolution of time.
• The y axis is the statistic that is being charted for each point in time. Ex-
amples of plotted statistics include an observation, an average of two or
more observations, the median of two or more observations, a count of
items meeting a criterion of interest, or the percent of items meeting a
criterion of interest.
• Limits are defined for the statistic that is being plotted. These control
limits are determined statistically by observing process behavior, providing

an indication of the bounds of expected behavior for the plotted statistic.
They are never determined using customer specifications or goals.

The key to successful control charts is the formation of rational subgroups.
Control charts rely on rational subgroups to estimate the short-term variation
in the process. This short-term variation then is used to predict the longer-term
variation defined by the control limits.
Nelson (1988) describes a rational subgroup as simply “a sample in which all
of the items are produced under conditions in which only random effects are
responsible for the observed variation.” Another way of stating this is that the
causes of within-subgroup variation are equivalent to the causes of between-
subgroup variation.