Question

a product is designed to operate at a constant failure rate of 5 failures per hour for the engineer to realize a reliability of 60% what must the operation time (in hours) be?

a. 0.500 hrs b. 0.050 hrs c. 0.120 d. 0.102 hrs

Answer 1

Here the failure rate is constant which is 5 failures per hour

or time taken for one failure (Expected) = 1/5 hour = 0.20 hour

so here we want a reliability of 60%

that means we want the time for there is 60% chance that the product will work.

so here as the failure rate is constant the distribution of failure time would have negative exponential distribution function

f(t) = (1/0.2) e^-t/0.2 ; t > 0

so here

cumulative probability distribution is

F(t) = 1 - e^-5 ; t > 0

so here we want a reliability of 60%. so we have to find t for that value

so here

F(t) = 1 - 0.6 = 0.4

0.4 = 1 - e^-5t

0.6 = e^-5t

ln(0.6) = -5t

t = 0.102 hours

Option d is correct here.