A six$-$station dial$-$indexing machine assembles components to a base part. The operations, element times, q and m values for components added are given in the table below $($NA means q and m are not applicable to the operation$).$ The repositioning time is $3$ sec$.$ When a jam occurs, it requires $1\mathrm{.}6$ min to release the jam and put the machine back in operation. Determine:

$($a$)$ Hourly production rate for the assembly machine,

$($b$)$ Yield of good product $($final assemblies containing no defective components$),$ and

$($c$)$ Proportion uptime of the system.

$(5)$

$(5)$

$(5)$

Station

Operation

Element Time$($s$)$

$9$

m

$1$

Add part A

$5$

$0\mathrm{.}025$

$0\mathrm{.}7$

$2$

Fasten part A

$4$

NA

NA

$3$

Assemble part B

$6$

$0\mathrm{.}02$

$0\mathrm{.}9$

$4$

Add part C

$5$

$0\mathrm{.}03$

$1\mathrm{.}0$

$5$

Fasten part C

$4$

NA

NA

$6$

Assemble part D

$7$

$0\mathrm{.}02$

$0\mathrm{.}6$