Q $3($a$)[10$ Marks$]$

The following costs and reliabilities have been calculated for a control mechanism.

What is the optimum redundancy to ensure the minimum overall cost?

p $($Reliability for unit of time.$)=0\mathrm{.}94$

Capital cost $=200$

Operating cost $=300$

Down time cost $($per unit time$)=120,000$

Q $3($b$)[10$ Marks$]$

A new machine is to contain seven identical systems each with a reliability of $80\%.$

The machine will continue to function as long as at least $4$ of the systems function.

What is the reliability of the machine?

Q $3($c$)[5$ Marks$]$

If the availability required for a plant is $0\mathrm{.}99,$ and the MTTF $500$ hours what will our

target for mean repair time be$?$