Interpreting Standard Tests for Special Causes
Nelson (1984, 1985) makes the following comments concerning the
interpretation of the tests:
-
When a process is in statistical control, the
chance of a false signal for each test is less than
five in one thousand.
-
Test 1 is positive if there is a shift in the process
mean, if there is an increase in the process standard
deviation,
or if there is a
"single aberration in the process such as
a mistake in calculation, an error in measurement, bad
raw material, a breakdown of equipment, and so on"
(Nelson 1985).
-
Test 2 signals a shift in the process mean.
The use of nine points (rather than seven as in
Grant and Leavenworth 1988) for the pattern that
defines Test 2 makes the chance of a false signal
comparable to that of Test 1.
(To control the number of points for the pattern in test 2,
use the TEST2RUN= option in the chart statement.)
-
Test 3 signals a drift in the process mean.
Nelson (1985) states that causes can include
"tool wear, depletion of chemical baths,
deteriorating maintenance, improvement in skill, and so on."
-
Test 4 signals "a systematic effect such as produced
by two machines, spindles, operators or vendors used
alternately" (Nelson 1985).
-
Tests 1, 2, 3, and 4 should be applied routinely;
the combined chance of a false signal from one or more of these
tests is less than one in a hundred.
Nelson (1985) describes these tests as "a good set that
will react to many commonly occurring special causes."
-
In the case of charts for variables,
the first four tests should be augmented
by Tests 5 and 6 when earlier warning is desired.
The chance of a false signal increases to two in a hundred.
-
Tests 7 and 8 indicate stratification
(observations in a subgroup have multiple sources
with different means). Test 7 is positive when the observations in
the subgroup always have multiple sources.
Test 8 is positive when the subgroups are taken
from one source at a time.
Nelson (1985) also comments that
"the probabilities quoted for getting false signals
should not be considered to be very accurate"
since the probabilities are based
on assumptions of normality
and independence that may not be satisfied.
Consequently, he recommends that the tests
"should be viewed as simply practical rules for
action rather than tests having specific
probabilities associated with them."
Nelson cautions that "it is
possible, though unlikely, for a process to be out of
control yet not show any signals from these
eight tests."
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.
