Question

A production line has three machines A, B, and C, with reliabilities of .92, .97, and .87, respectively. The machines are arranged so that if one breaks down, the others must shut down. Engineers are weighing two alternative designs for increasing the line’s reliability. Plan 1 involves adding an identical backup line, and plan 2 involves providing a backup for each machine. In either case, three machines (A, B, and C) would be used with reliabilities equal to the original three.

A. Compute overall system reliability under Plan 1.
B. Compute overall system reliability under Plan 2.
C. Which plan will provide the higher reliability?1. Plan 2.2. Plan 1.

Answer 1

The answer is below

Step-by-step explanation:

If one machine breaks, the others breaks, this means that the are connected in series, hence the reliability of the line is:

Reliability of line = 0.92 * 0.97 * 0.87 = 0.7764

A) Plan 1: Plan A involves connecting a backup line in parallel, therefore the overall reliability would be:

Overall reliability = 1 - (1 - 0.7764)² = 0.95

B) Plan 2: In plan B, each machine has a backup.

Hence:

For machine A: Reliability = 1 - (1 - 0.92)² = 0.9936

For machine B: Reliability = 1 - (1 - 0.97)² = 0.9991

For machine C: Reliability = 1 - (1 - 0.97)² = 0.9831

Overall system reliability = 0.9936*0.9991*0.9831 = 0.9759

C) Since plan 2 has a higher reliability hence plan 2 is the better plan