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

ID: 3260553 • Letter: #

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

MTBF = mean time between failures (hours per failure)
Lambda = failures per hour
F = failure rate or probability of failure in one hour
R = reliability rate (probability of working in one hour)

Lambda = 1 / MTBF
MTBF = 1 / Lambda
and assuming a constant failure rate
F = Lambda / 1 or 1 / MTBF
R = 1-F


1.
This is an example of serial fail (failure of one pump will stop the whole system). Sample illustration below

Pump1 -> Pump2-> Pump3-> Pump4->Pump5

MTBF of system = 5*1 hour/0.1 = 50 hour MTBF

Failure rate of system = 1/MTBF=1/50=0.02


2.
This is an example of redundant pumps since failure of all 3 pumps is needed to halt the system
MTBf(Pump1)=1/0.1=10
MTBf(Pump2)=1/0.2=5
MTBf(Pump3)=1/0.3=3.33

The failure rate(F) of systm that all pumps faile at the same time is:
F = 0.1*0.2*0.3
F = 0.006

MTBF = 166.67 hours

Hence there is substantial improvement in reliability when using redundant or parallel pumps (i.e system fails when all pumps fail)