Nitin's  production line has three machines A, B, and C, with Reliabilities of 0.99. 0.96, and 0.93, respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineers are weighing 2 two alternative designs for increasing the lines, reliability.  Plan one involves adding an identical back up line, and plan two involves providing a backup for each machine. In either case, three machines (A, B, C ) would be used with reliabilities equal to the original three.

a) Which plan will provide the higher reliability? Show all your calculations.
                                 
b) Describe why the two reliabilities are the same.
                      

c) What other factors may enter into the decision in which plan to adapt?
                                           
(d) Suppose that the single switch used in plan on98% reliable, while readabilities of the machine remain the same. Recalculate the ratability of plan one. Compare the reliability of this plan with the ratability of plan one calculated in solving the original problem. How much did the ratability of plan one decrease as a result of a 98% reliable switch?
                                       

e)  Suppose that the three switches used in plan two are all 98% reliable, while reliabilities of the machines remain the same. Recalculate the reliability of plan two. Compare the reliability of this plan with the reliability of plan two calculated in solving the original problem. How much did the reliability of plan two decreases?