Question

Suppose that the time to failure (in hours) of hard drives in a personal computer can be modelled by an exponential distribution with λ = 0.002.

Use Monte Carlo simulation, or otherwise, to approximate the following: Assume a computer now has three independent hard-drives and the failure of the computer occurs once all three hard drives have died. What is the mean life of the computer?

Answer 1

Here he time to failure (in hours) of hard drives in a personal computer can be modelled by an exponential distribution with λ = 0.002. Let the 3 failure times be

We Assume a computer now has three independent hard-drives and the failure of the computer occurs once all three hard drives have died. So the life time of the computer is . Using simulation 10,000 times life times of the computer is generated using R. The R code below.

n <- 10000
X1 <- rexp(n,rate=0.002)
X2 <- rexp(n,rate=0.002)
X3 <- rexp(n,rate=0.002)
X <- pmax(X1,X2,X3)
mean(X)

The simulated mean life time of the computer is . The theoretical mean life time is

We can see that the simulated life time is close to theoretical life time.