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 part and 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

Interarrival rate: 10 products/hr

Service rate: Without considering defects: Cycle time = 20 products/hr - 2 prod/hr - 8/3 products/hr = 15.33 products/hr

Jobs in the system: 10/(15.33-10) = 1.87 or approx 2

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