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A manufacturer is experiencing difficulty getting consistent readings of tensile strength between three machines located on the production floor, research lab, and quality control lab, respectively. There are also four possible technicians-Tom, Joe, Ken, and Carol-who operate at least one of the test machines regularly.

(a) How many operator-machine pairs must be included in a designed experiment where every operator tries every machine?

(b) If each operator-machine pair is required to test eight specimens, how many test specimens are required for the entire procedure? Note: A specimen is destroyed when its tensile strength is measured.
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(a) There are $n_{1}=4$ operators and $n_{2}=3$ machines, so $4 \cdot 3=12$ pairs are required.

(b) There are $n_{3}=8$ test specimens required for each operator-machine pair, so $8 \cdot 12=96$ test specimens are required for the designed experiment.
by Diamond (59.3k points)

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