Rick Wing is looking at improving the temperature control on one of his machines. This system currently has four integrated controllers in series:

A B C D

The reliability of these four controllers are 0.90 (A), 0.92 (B), 0.94 (C), and 0.96 (D).

Rick is looking at installing a back-up for each of the controllers. The back-up controllers all have a reliability of 0.90

a) What is the reliability of the new system which provides a back-up for each of the controllers and what is the percent improvement compared to the current design?

b) Suppose that Rick is considering another back-up design. Here he would create a back-up system in parallel to the current system. This is shown below. The reliability of all four back-ups, A1, B1, C1, and D1, are each 0.90.

A B C D A1 B1 C1 D1

What is the reliability of this back-up design?