Which of the following is NOT a condition for Hardy-Weinberg Equilibrium?

What is the raw material for evolutionary change?

A small manufacturing system produces parts for sea kayaks in La Jolla, San Diego. The parts arrive from an upstream Poisson process with an arrival rate of 1 part every 5 minutes. All the parts that enter the system must go through a station which houses 2 prefabrication machines. A part, though, only requires to be processed by 1 of the 2 machines during prefab. The prefab time is exponentially distributed with the same mean for each of 8 minutes. If all the machines at the prefab station are busy, then the part will wait for the next available machine. [HINT: The machines do NOT break down and thus do not need to be repaired]. a. What is the probability that both machines are idle? Please round your answer to 3 decimal places (e.g. #.###). [PartA]  (4pts) b. What is the overall system utilization? [PartB] (2pts) c. What is the average number of parts waiting for prefab? [PartC] (2pts) d. A floor technician suggests that the system utilization rate should be lower (less than 30%) if the company wants to maintain the life of the machines and avoid machine failures. Do you think adding a third machine with the same processing rate will achieve that goal? Please show the new utilization rate to support your answer. Please express your answer to 3 decimal places and your asnwer (e.g., #.###, yes or #.###, no) and explain why on your scratch paper. [PartD] (2pts)

TRUE or FALSE: Implicit Enumeration is a procedure for estimating the variance of throughput time in queuing networks.

TRUE or FALSE: Implicit Enumeration is a method for solving problems by asking experts for their best estimate of what to do.

TRUE or FALSE: Lot Streaming reduces batch throughput time by running machines at a faster speed.

TRUE or FALSE: Little’s Law is valid for all systems and provides estimate of mean and variance of queue lengths.

For a paced transfer line with 3 machines and without buffer, if each machine fails on average every 10 cycles and average repair time is two cycles. What is the availability of the line? (Assume that the failure and repair time follows a geometric distribution).   

A serial production line will have ten stages. Each stage will fail on average once every 200 cycles with average repair time of 4 cycles. Desired availability is 92%. Which of the following is true of buffers applied to this system?

The Daytona 500 racetrack in Florida has some of the best pit-crews in the world to service cars as they race for NASCAR. Each pit crew in NASCAR can contain up to 8 crew members, but only 5 are allowed in the pit at any time. In this scenario, the cars, as they stop, line up and have a crew member assigned. The crew members do not have the same service speed (see table below), but you should assume that all crew members can service a car in full regardless of title (meaning cars do not need to visit all crew members, they are serviced by 1 as they are assigned). Crew Member Pit Speed Jackman 4 cars per hour Tire Changer 6 cars per half hour Gasman 5 cars per 15 min Utility Man 7 cars per hour Tire Carrier 1 car per 10 min The pit-stop area (nicknamed Tartarus) is where each car is assigned a crew member and are serviced from right to left (meaning the last car is serviced first, then the 19th car and so on). 5a. How many cars can the entire crew serve in 1 hour? (5pts) [PartA] 5b. Identify the order of which the crew members should be placed in the pit (1st, 2nd, 3rd, 4th, 5th). (5pts) [PartB1st] , [PartB2nd] , [PartB3rd] , [PartB4th] , [PartB5th] 5c. Identify which crew member is the bottleneck for the whole pit. (3pts) [PartC]5d. Identify each range of cars the crew members will work when the pit-stop system reaches steady state (REMEMBER: Cars arrive right to left). Please show all work on scrap paper. (10pts) [PartD]