A production line has three machines A, B, and C, with reliabilities of .98, .93

Question

A production line has three machines A, B, and C, with reliabilities of .98, .93, 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. (Round your intermediate calculations and final answer to 4 decimal places.)

Reliability             

b. Compute overall system reliability under Plan 2. (Round your intermediate calculations and final answer to 4 decimal places.)

Reliability             

c. Which plan will provide the higher reliability?

Plan1

Plan2

Explanation / Answer

a) The production line is a series system of three machines (A, B and C)

Reliability of each line = 0.98*0.93*0.87 = 0.7929

Overall system reliability under plan 1 = 1 - probability of both lines failure simultaneously = 1 - (1-0.7929)^2 = 0.9571

b) Overall system reliability under plan 2 = (1-(1-0.98)^2)*(1-(1-0.93)^2)*(1-(1-0.87)^2) = 0.9779

c) Plan 2 provides higher reliability.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.