Question: Below is a case study: A manager of an electrical chip's production company would like to assess the performance of the production system of the

Below is a case study:

A manager of an electrical chip's production company would like to assess the performance of the production system of the main product line of his company. This line manufactures four different circuits that are used for biomedical applications, named Part A, Part B, Part C and Part D respectively. The four parts do not follow the same sequence of operations in their manufacturing process. The process is as follows (in sequence): - Dedicated Preparation for each part (Preparation Area A for Part A, Preparation Area B for Part B,) - Quality control 1 (the same for all parts) - Welding process (for both Part A and Part B) - Electronic components assembly for all parts (A, B, C, and D) - Sealing (for Parts C and D) - Packaging (for all parts) - Quality control 2 (only for parts A and D) - Road shipping (for parts A, B and C) - Air Shipping (for part D) We assume that there are enough raw materials for all the process. The manufacturing process for any part is triggered by an ordering process from the customers. In other words, when a customer order is received for a given part, its processing starts immediately if the resources are available. Otherwise, the order is put in a queue and following 2 a FIFO process, it will be processed when the resources become available. The orders arrive as follows: - Exponential interarrival time with: a mean of 4 minutes for A a mean of 10 minutes for B a mean of 8 minutes for C - Unknown probability distribution for D Upon reception of the orders, they are transmitted immediately to their corresponding preparation area. In the preparation areas, the raw materials are prepared and the preparation process takes the same times for all the parts, which are random, and follow a triangular distribution (15, 30, 40) minutes for all the four parts. After the preparation process, the parts are transferred to a quality control center (Quality control 1) with a transit time of 5 minutes. The quality control test is instantaneous. After the quality control 5% of the order raw materials are returned to the corresponding preparation area with a transfer time of 5 minutes. Moreover, the following times apply: - Welding process: normal distribution with mean of 5 min and standard deviation of 3 min (for both Part A and Part B) - Electronic components assembly for all parts: exponential time with a mean of 6 minutes for A and B and 12 minutes for C and D - Sealing: exponential time with a mean of 10 minutes for Parts C and D - Packaging: unknown time for all parts - Quality control 2: instantaneous and results in 10% of the parts (A and D) being considered as scrap and 90% shipped. - Road shipping: instantaneous (for parts A, B and C) - Air Shipping: instantaneous (for part D) There are some transfer times between these workstations.

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