$($unit: mm $)$ A process is under statistical control and produces shafts with a basic size of $10$ mm $.$ The upper deviation of the shaft is $0\mathrm{.}015.$ The shaft tolerance is two times the shaft upper deviation. To meet the functional requirements, the allowance of the two mating parts is designed to be $-0\mathrm{.}035.$ The tolerance for the hole is $0\mathrm{.}006.$ The assembly requires that the two mating parts have an interference fit within $-0\mathrm{.}03,0.$ Given the process is capable of producing $96\mathrm{.}8\%$ of the holes and shafts that are within specified limits$.$

a$)$ Determine the maximum and minimum limits of hole sizes.

b$)$ What is the degree of interchangeability?