Consider the following manufacturing system where two distinct types of parts are processed. Parts of Type I arrive with interarrival times following a Lognormal Distribution with a mean of 11.5 hours and standard deviation of 0.2 hours. These parts then go under a process which is designated for only Type 1 parts, and an operator named Alfred processes the parts. The processing times follow a Triangular Distribution with parameters 5. 6, and 8 hours. Parts of Type 2 arrive with interarrival times following an Exponential Distribution with mean of 15.1 hours. These parts go under a different process that is designated for only Type 2 parts, and an operator named James processes the parts. The processing times follow a Triangular Distribution with parameters 3. 7, and 8 hours. After being processed by the human operators, all parts are sent to be processed by an automatic machine which has a single queue for both parts and processing times following a Triangular Distribution with parameters 4, 6, and 8 hours. Finally, completed parts exit the system. Using ARENA, simulate the system for 5000 hours and collect output data for 5 replications (20 points). a) It is observed that the real system has an average waiting time of 30.74 hours at the automatic machine queue. Evaluate whether the model output is consistent with system behavior by conducting a t-test using a 0.05 (8 points). b) Find the power of the test. If a power of at least 50% is assumed to be sufficient, what is your comment on the minimum required number of replications for this system? Is the initial replication size enough (8 points)? e) In order to reduce the waiting time at the automatic machine queue, the management came up with an alternative. The alternative is to modify the automatic process such that the process time follows a Normal Distribution with a mean of 6 hours and standard deviation of 0.5 hours. Make a comparison between the current and the alternative system, using a 0.05 significance level. Which system gives better results for the waiting time at the automatic machine queue (9 points)? d) The management is discussing another alternative to the original system that might have an effect on the waiting time at the automatic machine queue. In this alternative system, Type I parts have priority over Type 2 parts in the automatic machine queue. Additionally, the operator Alfred can also process the parts at the automatic machine process. However, it is preferred that the automatic machine processes the parts if it is idle. If not, Alfred can process the parts. It is assumed that the process time of automatic machine process follows a Normal Distribution with a mean of 8 hours and standard deviation of 2 hours after this modification. Considering the original system and the alternative model developed in part (c) together with this suggested system, make all pairwise comparisons using an overall significance level of a = 0.15. Which system gives better results for the waiting time at the automatic machine queue (55 points)?