Problem $1$: Breakdowns and defective products manufactured over the last $20$ days on a Thies Jet $($dyeing machine$)$ are presented in the following table:

Day $1234567891011121314151617181920$

Breakdown Code $--$ A A $--$ B C C D D $--$ E $----$ F $--$ G $--$ H H $--$

Breakdown Start Time $--12----1511--12----8----4--1--16----$

Breakdown End Time $----1--16--3--2--13----9--16----1--$

Setup Time $($minutes$)25--18--3--17--2--18----4--4----7--$

Defective products $2024020020240340310340350300250350140230290902027025030$

The breakdown code represents each recorded breakdown. If the same code appears on more than one day, it is because the repair did not take place or was not finished on the preceding day. Total production for the $20$ days is $10,700$ units. The company works two $8-$hour shifts per day $($Hours $116).$ The theoretical cycle time is $1\mathrm{.}5$ minutes per part.

$1.$ What are the quality, performance, and availability rates?

$2.$ What is the overall equipment efficiency $($OEE$)$ value?

$3.$ Which measure would you improve to improve the OEE? Why?