Question

a) Three identical pumps are connected in parallel and are statistically independent. The system operates if at least one pump is working. The age specific failure rate of this type of pump is of constant value, \lambda of 0.01 per hour. Calculate the probability of survival after 100 hour of a single pump? b) These process components are related in series. Thus, if any one of the components fails, the entire system fails. Calculate the reliability and probability of each component is given, calculate the overall reliability, overall probability, overall failure rate and MTBF of the system. Component Failure rate $\mu$ (faults/yr) Reliability $R = e^{-\mu t}$ Failure probability $P = 1 - R$ Control valve 0.60 0.55 0.45 Controller 0.29 0.75 0.25 DP cell 1.41 0.24 0.76

          a) Three identical pumps are connected in parallel and are statistically independent. The system operates if at least one pump is working. The age specific failure rate of this type of pump is of constant value, \lambda of 0.01 per hour. Calculate the probability of survival after 100 hour of a single pump?
b) These process components are related in series. Thus, if any one of the components fails, the entire system fails. Calculate the reliability and probability of each component is given, calculate the overall reliability, overall probability, overall failure rate and MTBF of the system.
Component	Failure rate $\mu$ (faults/yr)	Reliability $R = e^{-\mu t}$ 	Failure probability $P = 1 - R$
Control valve	0.60	0.55	0.45
Controller	0.29	0.75	0.25
DP cell	1.41	0.24	0.76

a) Three identical pumps are connected in parallel and are statistically independent. The system operates if at least one pump is working. The age specific failure rate of this type of pump is of constant value, λof 0.01 per hour. Calculate the probability of survival after 100 hour of a single pump?
b) These process components are related in series. Thus, if any one of the components fails, the entire system fails. Calculate the reliability and probability of each component is given, calculate the overall reliability, overall probability, overall failure rate and MTBF of the system.
Component Failure rate μ (faults/yr) Reliability R = e^-μ t Failure probability P = 1 - R
Control valve 0.60 0.55 0.45
Controller 0.29 0.75 0.25
DP cell 1.41 0.24 0.76

Added by Michael D.

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