$(10$ pts$.)$ Breakdowns and defective products that were manufactured for the last $15$ days on a particular machining center, the $CNC-27$ machine, are presented in the following table:

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.

The machine's total setup time is $187$ minutes, and in the $15$ days that were investigated the machine produced $8280$ products. The company works $\frac{24}{7}.$ The theoretical cycle time is $2$ minutes per part.

$(1)$ What is the overall equipment efficiency $($OEE$)$ value?

$(2)$ What are the quality, performance, and availability rates?

$(3)$ Which measure would you apply first to improve the OEE indicator? Justify your answer.