Page 177 - The Handbook for Quality Management a Complete Guide to Operational Excellence

164 P r o c e s s C o n t r o l Q u a n t i f y i n g P r o c e s s Va r i a t i o n 165

Defining the control limits (i.e., the expected future variation in the
plotted statistic) using the within-subgroup variation implies that short-
term variation is used to predict the expected longer-term variation. This is
a perfect definition for process stability: if short-term variation can be used
to predict longer-term variation, then the process is stable (i.e., in statistical
control). Note the sharp contrast between this approach and the random
sampling approach used for enumerative statistical methods, where short-
term variation is pooled with longer-term variation to calculate a sample
standard deviation.
Rational subgroups have the following properties (Keller, 2011b):
1. The observations within the subgroup are independent, which implies
that none of the observations influences or results from any other. When
observations are dependent on one another, the process has auto-
correlation or serial correlation (these terms mean the same thing),
which can cause the within-subgroup variation to be small relative
to the between-subgroup variation. Examples of processes
influenced by autocorrelation include:
• Chemical processes. The temperature in a batch of beer is likely to
be dependent on the temperature 5 minutes earlier. The auto-
correlation diminishes over time, so the temperature an hour
later may be less dependent.
• Service processes. The wait time (i.e., time in queue) of a given
customer at the grocery store checkout is likely to be somewhat
dependent on the wait time of the customer immediately ahead,
and perhaps the customer two or three places ahead. The last
customer in line cannot be serviced until the others are completed,
so their wait times have dependence.
• Discrete part manufacturing. When feedback controls are used to
control an automated process, this causes dependence since the
process is adjusting based on these prior measurements.
2. The observations within a subgroup are from a single stable process. It has
been mentioned that subgroups are often formed over a small time
interval to limit the possibility for special causes to creep into the
subgroup. If the subgroup contains the output of multiple-stream
processes, the within-subgroup variation is likely to be larger than
the longer-term between-subgroup variation. Examples of this
include multiple cavity molding, multiple head filling stations, or
samples from the teller station and the loan officer at the bank.
3. The subgroups are formed from time-ordered data collection. The x-axis
of the control chart is time-ordered, so that the subgroups on the
right of the chart represent a time period later than the subgroups
to their left. Rational subgroups cannot be formed from a set of

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