Question $1$

I utorial Sheet $-$ Taguchi DoE

A production engineer is investigating the effect of four factors $($A$,$ B$,$ C and D$)$ on the amount of wear on the hammers of a shredder machine in a sugar milling factory. He is attempting to find the best set of conditions that would yield the longest life of the hammers by minimizing the amount of wear.

An L$8$ orthogonal array has been used with four factors each at two levels, and for each test, three $(3)$ measurements of the amount of wear $($in microns$)$ were taken. The results of the L$8$ OA are shown in Table Qu$1.$

Table Qu$1$: L$8$ Orthogonal Array and Results

$\backslash$table$[[\backslash$table$[[$Expt$],[$No$]],A,B,C,D,$Wear $($Microns$)],[1,1,,1,1,90,91,95],[2,1,1,1,2,120,118,119],[3,1,2,2,1,95,96,98],[4,1,2,2,2,125,126,128],[5,2,1,2,1,162,165,167],[6,2,1,2,2,180,182,183],[7,2,2,1,1,165,168,169],[8,2,2,1,2,189,190,191]]$

Using appropriate calculations find the optimum condition of each factor, and find the factors which have a dominant effect on the output result.

Show all calculations, and support your answer with relevant justifications.