(a) A system consists of five identical pumps. The pumps are set in such a way t

Question

(a) A system consists of five identical pumps. The pumps are set in such a way that if one fails the whole system fails. Each having a reliability of 0.97 and The average failure is 0.1 failure/hour. Find the MTBF, failure rate and reliability of the system. (b) A system consists of 3 pumps, A, B and C with reliability of 0.9, 0.8 and 0.7 respectively. Each pump can supply the desired amount and system fails when all the pumps fail. The average failure rate for each component is 0.1, 0.2 and 0.3 failure/hour respectively. Find the system reliability and MTBF of the system.

Explanation / Answer

Answer to part a)

Failure rate of system = 0.1

MTBF = 1 / 0.1 = 10

The reliability of the system = 1 - (1-0.97)^5 = 0.9999

.

Answer to part b)

Reliability of system = 0.9*0.8*0.7 = 0.4328

Failure of entire system = 0.1*0.2*0.3 = 0.006

MTBF = 1 / failure rate

MTBF = 1 / 0.006

MTBF = 166.67

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