The brake A Bac Trucking company requires 2 workers to unload a truck in 5 hr. W

Question

The brake A Bac Trucking company requires 2 workers to unload a truck in 5 hr. Working together, the workerrs have a mortality rate ( due to heart failure) of 0.05 per hour. However if one experiences a heart attack and dies, the other's mortality rate increases to 0.2 per hr as a result of the increase in the unloading rate neccessary in order to complete the task on time. Compute the probability (reliability) that a truck will be successfully unloaded by a 2 person crew.

What is the expected time to failure( in working hours) of the two person crew?

Explanation / Answer

Here we are given that

The Thomas Brake Trucking Company requires two workers to unload a truck in 5 hr. Working together, the two workers have a mortality rate (due to heart failure) of 0.05 per hour.

However, if one experiences a heart attack and dies while unloading a truck, the others mortality rate increases to 0.2 per hour as a result of the increase in the unloading rate necessary in order to complete the task on time.

Let X be a number of persons working together to unload the truck.

Here X ~ Poison ( = 0.05)

The p.m.f. of X is,

P(X =x) = ( e- * x ) / x!

Compute the probability (reliability) that a truck will be successfully unloaded by a two-person crew in five hours.

That is we have to calculate here P(X = 2).

P(X = 2) = (e-0.05 * 0.052) / 2!

= (0.9512 * 0.0025) / 2

= 0.001189

The expected time is  to failure (in working hours) of the two person crew () = parameter of the distribution = 0.05

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