Before completing production, a product must pass through three stages of produc

Question

Before completing production, a product must pass through three stages of production. On the average, a new product begins at stage 1 every 6 minutes. The average time it takes to process the product at each stage is as follows: stage 1, 3 minutes; stage 2, 2 minutes; stage 3, 1 minute. After finishing at stage 3, the product is inspected (assume this takes no time). Ten percent of the final products are found to have a defective nd must return to stage 1 and go through the entire system again. After completing stage 3. 20% of the final products are found to be defective. They must return to stage 2 and pass through 2 and 3 again. On the average, how many jobs are in the system? Assume that all interarrival times and service times are exponential and that each stage consists of a single server.

Explanation / Answer

Stages # 1 2 3 processing time 3 2 1 mins Time between arrivals 6 mins Mean arrival rate 10 per hour 10% of final products 1 prooduct / hour 20% of final products 2 prooducts / hour 70% of final products 7 prooducts / hour 70% products Total service time 6 mins 10% products Total service time 12 mins 20% products Total service time 9 mins total service time for 10 products 72 mins (= 1*12+2*9+7*6) Avg. Service time for 1 product 7.2 mins Mean service rate 8.33 per hour Since the arrival rate is higher than the service rate, the system will be blocked or is not in a steady state. For a steady system (where arrival rate

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