A six-station automatic assembly line has an ideal cycle time of 12 sec. Downtime occurs for two reasons. First, mechanical and electrical failures cause the line to stop that occur with a frequency of once per 50 cycles. The average downtime for these causes is 3 min. Second, defective components also result in downtime. The fraction defect rate for each of the six components added to the base parts at the six stations is 2%. The probability that a defective component will cause a station jam is 0.5 for all stations. Downtime per occurrence for defective parts is 2 min. Determine a) Yield of assemblies that are free of defective components? (5 marks) b) proportion of assemblies that contain at least one defective component? (2 marks) c) Average production rate of the good products? (10 marks) d) Uptime efficiency