Consider the problem of testing 4 machines to see if they differ significantly i

Question

Consider the problem of testing 4 machines to see if they differ significantly in their ability to produce a certain manufactured part. It is well known that different operators and different me periods in the work day will have an effect on production. Thus we set up 4 operators as columns" and 4 time periods as rows" and then assign at random the machines to the various cells in the square, subject to the restriction that each machine be used only once by each operator and in each time period. The following table represents the number of units produced by the four machines.

Explanation / Answer

Given the wording in the problem, we will assume that the variation in the # of parts manufactured at different time period by different operators is because of the differences in the operators' abilities at different time-periods.

So,overall, the total # of parts produced by all machines must be same.

So, Total # of parts produced by machine A=Total # of parts produced by machine B=Total # of parts produced by machine C=Total # of parts produced by machine D

Total # of parts produced by machine A=# of parts produced in time-period 1+# of parts produced in time-period 2+# of parts produced in time-period 3+# of parts produced in time-period 4

=67+54+44+55=220

220=Total # of parts produced by machine B=# of parts produced in time-period 1+# of parts produced in time-period 2+# of parts produced in time-period 3+# of parts produced in time-period 4

=36+59+37+M3

220=132+M3

M3=88

Similarly,M1=220-(50+43+65)=62

M2=220-(34+39+35)=112

# of parts produced by Operator1=181

# of parts produced by Operator2=34+54+43+M3=219

# of parts produced by Operator3=67+59+M2+65=303

# of parts produced by Operator4=36+M1+44+35=177

So best operator is Operator 3

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