Determine the overall oneyear system reliability for the wat

Determine the overall one-year system reliability for the water-supply pump system shown below, if the probability of failure for each pump within a year is 3%, and individual pump failures are independent events.

Solution

In order to calculate the reliability of the entire system, let us first evaluate the reliability of the parallel combination of pumps 2 and 3, and then consider this parallel system in series with pump 1.

Let relaibility of pumps 1,2 and 3 be denoted by R1, R2 and R3.

R1 = R2 = R3 = (100-3)% = 1 - 0.03 = 0.97

Relaibility of parallel system of pumps 2 and 3 = 1 - (1-R2)(1-R3) = 1 - 0.03*0.03

= 0.9991

Reliability of series system of 1 and combo of 2 and 3 = (1-R1)*0.9991 = 0.97*0.9991 = 0.9691

Answer: 96.91%