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 Tests for Special Causes

## 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."

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