
9 Reliability
Section 9.2: First Excursion Failure
9.1. Consider a car that is being hit by hail. The number of times that hail hits the car is modeled as
a Poisson process with the arrival rate of ν = 1 hail/s. Find the probability that the car will be hit
more than 100 times in 20 min. It is estimated that only one tenth of the hail is big enough to cause
permanent damage to the car. What is the probability that the car will have more than 5 such dents in
20 min.
Solution: The Poisson probability density is given by
p
N
(n, t) =
(νt)
n
e
−νt
n!
,
where p
N
(n, t) is the probability of exactly n arrivals in time t. The probability that the car will be hit more ...