A factory has four machines A, B, C, D. The quality control process
identifies defects from each machine. The iqd
dataset has four columns, one per machine; entries
correspond to the numbers of defects produced by each machine. The
NA
entries in a row indicate that a particular machine is
switched off.
The null hypothesis would be that there exist four non-negative
numbers $p_1,p_2,p_3,p_4$ with sum 1 such that the probability of
a defect arising from machine $i$ is proportional to $p_i$ if
it is switched on, and zero otherwise.
It is suspected that machine D is causing some sort of interference
with machine A; machine A produces very few defects when D is switched
off.
The shifts
dataset includes only three machines, A, B, C.
There are three columns, one per machine; and three rows, one per
operator (S1, S2, S3). On S1's shift, machine C was out of
commission.