1. A factory line has three lathe processing stations 1, 2, and 3, with reliabilities of 0.99, 0.96, and 0.93, respectively. The lathe stations are arranged so that if one breaks down, the others will stop working as well. To increase the reliability of the production line managers are experimenting two different plans. Plan A involves adding an identical backup line in series layout, and plan B is to provide backup in parallel layout for each machine. In either case, three additional machines (1, 2, and 3) would be used with reliabilities equal to the original three.

1. Which plan will provide higher reliability? Show your reasoning and calculations.

2. Explain why the two reliabilities are not the same.

3. What other factors might enter into the decision of which plan to adopt?