Question

What is the probability of mission success if there are 16 trucks scheduled for a 20-hour mission and at least 10 trucks must operate for the entire duration of the mission if each truck has a failure rate of 1 failure per 100 hours?

Answer 1

Let the random variable X

X : Failure time of truck.

Since truck has a failure rate of 1 failure per 100 hours.

X ~ Exp (mean = 100)

The probability distribution of random variable X is

and cumulative distribution function is given by

Since truck scheduled for a 20 hour mission.

probability of truck will be operate after 20 hours is

n = number of truck shceduled for a mission = 16

p = probability of success = 0.8187

Let Y : Number of trucks will be operate after 20 hours.

Hence the random variable Y follows binomial distrbution with n = 16 and p = 0.8187.

The mission will be success if atleast 10 truck must operate.

P (Mission success) = P ( Y >= 10)

By using excel function

P ( Y < =9) = BINOMDIST(9,16,0.8187,1) = 0.01590

P (Mission success) = 1- 0.01590 = 0.98410