The Thomas Brake Trucking Company requires two workers to un

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. Compute the probability (reliability) that a truck will be successfully unloaded by a two-person crew in five hours. What is the expected time to failure (in working hours) of the two person crew?

Solution

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