Consider a thermal power plant composed of four subsystems, namely, feed water p

Question

Consider a thermal power plant composed of four subsystems, namely, feed water pumps, boilers, turbines, and generators, and connected as shown in figures below.

a. Each subsystem consists of two identical units connected in parallel to increase its reliability. The power plant functions and generates power only when at least one unit of each subsystem between the points 1 and 2 functions. The probability that each unit functions is given in the figure. Assuming that the probability of the functioning of a unit does not depend on whether or not the other units (and other subsystems as well) are functional, determine the probability that the power plant generates the power

b. What if the configuration of the units changes as below?

c. What is the conclusion?

Explanation / Answer

a) probability that power plant generates the power

=P( at least one feed water pump works)*P(at least one Boilers work)*P(at least one turbines work)*P(at least one generator work)

=(1-P( none of feed water pump works)*(1-P(none of  Boilers work))*(1-P(none of  turbines work))*(1-P(none of  generator work))

=(1-0.1*0.1)*(1-0.05*0.05)*(1-0.15*0.15)*(1-0.01*0.01)=0.965209

b) probability that power plant generates the power =P(at least one of line work)

=1-P( none of line work) =1-(1-0.9*0.95*0.85*0.99)*(1-0.9*0.95*0.85*0.99)

=0.9231

c)from above we can see that configuration in part A is better.

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