In the course of subjecting 100 components to 5000 hours of

In the course of subjecting 100 components to 5,000 hours of operation, five of the components had failed as of 2, 500 hours but the remainder survived the entire time. What is the failure rate in terms of Percent failure? Number of failures per hour per component? If each component is utilized 1, 750 hours per year, what is the average number of failures per year per component? If 500 of this kind of component are to be installed in machines in a plant, how many can be expected to fail during the next year?

Solution

Back-up Theory

Average Failure Rate = 1/Average Life. i.e., if m = average life in, say hours, average failure rate per hour () = 1/m

Now, to calculate m, out of 100, five had a life of 2500 and 95 had a life of 5000. So, m = {(5 x 2500) + (95 x 5000)}/100 = 12500 + 475000)/100 = 487500/100 = 4875 hrs = m

Answer for Part (a)

m = 4875 hours => as against 5000 hours, the average life is only 4875 hours => survival % = 97.5 => failure % = 100 – 97.5 = 2.5% ANSWER

Answer for Part (b)

This is same as average failure rate () = 1/m = 1/4875 = 0.0002 ANSWER

Answer for Part (c)

With a failure rate of 0.0002 per component per hour, (as obtained in (b) above), failure rate per year of 1750 hours of utilization = 1750 x 0.0002 = 0.35 ANSWER

Answer for Part (d)

Expected number of failures of 500 components over one year (next year) = 500 x failure percentage = 500 x 2.5% = 12.5 ANSWER