QUESTION $1$a$]$

Requested daily quantity for a product is $500$ units $($defect free$).$ The production times $($given as normal time$)$ of the two operations respectively are as follows: Operation $a=2mi\frac{n}{?}$ unit; Operation $b=10mi\frac{n}{?}$ unit. The defect rates is given as $20\%$ for Operation a and $30\%$ for Operation b in serial. Workers assigned to these operations will accomplish the conversions. The performance of the individual employee are expected to be $90\%.$ There are two scenarios:

Scenario I: With Rework

Although the defect rates are given, no product is permitted to leave the plant with any quality defects. Accordingly, all of the defects must be corrected, and the average time to correct the defect is $150\%$ of the initial conversion time. The same work teams will accomplish this rework. The plant is run as a one$-$shift $8h\frac{r}{?}$ day $($meal break of $30$min $($unpaid$)$; Short Breaks $215$min; downtime$=45$min$)$ operation.

$\backslash$table$[[,\backslash$table$[[$With$],[$Repair$]],\backslash$table$[[$Without$],[$Repair$]]],[$Availability $\%,,],[$Flficiency $\%,,],[$Q$($Initial$-$starting amount of unit$)=$unit$/$shift$,,],[$Takt time$($min$/$unit$),,],[$WL $($min$/$shift$),,],[$Performance Level $(\%),,],[$Revized Cycle $($min$/$unit$),,],[$AT$=$Available time per person $($Performance considered$)=$min$/$person$,,],[$Revized Cycle $($Considering worker performance$)($min$/$unit$),,],[$Officiency of the line $($Performance of the line$)=\%,,],[$FY$/$TPY$,,],[$EO unit$/$shift$,,],[$PDF$1\%,,],[$PDF$2\%,,],[$NT min$/$unit$,,],[$Assignment of the operations to the stations:,,$],[$ST $($with PDF$1)$ min$/$unit$,,],[$ST $($with PDF$2)$ min$/$unit$,,],[$SO$=$ unit$/$shift per employee,,$],[$EO$=$ unit$/$shift$,,],[$If the cost per operator is $10$$$/$hr and the cost of defective unit $($material$),,],[$Under this conditions which Scenario is the best in respect to unit cost?,,$]]$

Draw a sketch showing the station$-$operator assignment $($With & Without Repair$)$

Prove the FY$/$TPY of your new redesigned station assignment $($With & Without Repair$)$

QUESTION $1$b$)$: If there is a $10\%$ of Efficiency Improvement $($not temporary it's permanent$)$ what will the effect on OEE? $($Hint: OEE; w; Assignment etc$)$

QUESTION $1$c$)$ If there is a $10\%$ of Efficiency of the line $(=$Performance of the line$)($by using an incentive system based on perfomance$)$ what will the effect on OEE? $($Hint: OEE; w; Assignment etc$)$

Prove the TPY of your new redesigned station assignment