A six$-$station automatic assembly line has an ideal cycle time of $12$ sec$.$ defective components result in downtime. The fraction defect rate of each of the six components added to the base part at the six stations is $2\%.$ The probability that a defective component will cause a station jam is $0\mathrm{.}5$ for all stations. Downtime per occurrence for defective parts is $2$min$.$ Determine $($a$)$ yield of assemblies that are free of defective components $($b$)$ proportion of assemblies that contain at least one defective component $($c$)$ average production rate of good product $($d$)$ uptime efficiency.