Question

The corrosion rate in a piping system is modelled as an exponential random variable, Y, with a mean of 5% wall thickness loss per year. A percentage value of the wall thickness means the percentage of the original wall thickness of the pipe. The original wall thickness of pipe is The pipe must be replaced as soon as the wall thickness loss exceeds 60% of the original thickness. (1) What is the probability that a pipe section will survive a 5 year operating interval? (2) In a population of 100 pipes, how many are expected to be replaced after 6 years of operation?

Answer 1

: Answer: corrosion rate per year 5%. Given mean => 0.05 D what is the section will interval ? probability survive a 5 that year a pipe operating The mean corrosion rate per 5 year -0.05 x 5 = 0.25 25.1. now we have fcy) = cos 0,25 fly) = 48 49

To find PC y< 60:l.) - PCy<0.6) = 5 819) dy oob -44 - Fenyora [C1042") (.04.2- -[-***-e-co] =(-2** - C-1)] = (-+**+13 Inė 2.4

1 0.091 -10.909) 2) In a population of 100 pipes, how many are expected to be replaced after 6 years of operation ? Mean rate per 6 year will be = 6x0.05 - 0.30 frescoes Now we have , PCys0.6 fligdy 0.6

fets I - Screening ote? = 01135 i probability that one pipe replaced after 6 years is 0.135 then in 100 pipes we can expect 100X0.135 - 13.5 pipes to be replaced in 6 years. -- 0 -