Part$1$: Total productive maintenance, lean six sigma, SMED $(12$ points$)$

A company operates one $10$ hours shift every day to produce $20,000$ screws. Ideally, each screw takes $1$ second of operations. During a regular production day, it has been reported that the machines have unscheduled down time of $45$min and $500$ screws do not match the required specifications. Given that a scheduled break of $45$min and a setup time of $45$min are assigned for each machine during each shift.

a$)$ Calculate the Overall Equipment Effectiveness for the machines. $(3$ points$)$

b$)$ Calculate the OEE if the setup time is reduced to $10$min with no extra units produced. $(3$ points$)$