Question

Suppose that device has a failure rate of: λ(t)=(0.015+0.02t)yr

−1
, where t is in years.
a) Calculate the reliability for a five-year design life assuming no maintenance is performed.

Answer 1

The reliability of the device over a five-year period with a given failure rate and no maintenance is approximately 72.3%.

Step-by-step explanation:

The question asks to calculate the reliability of a device with a failure rate given by λ(t) = (0.015 + 0.02t)yr-1 over a five-year period without maintenance. Reliability is the probability that a system will perform its intended function for a specified time period under stated conditions. To calculate reliability, we use the formula R(t) = e-∫ λ(t)dt. Here, we integrate the failure rate from 0 to 5 years and then exponentiate the negative of that value.

First, we integrate the failure rate:

∫05 (0.015 + 0.02t) dt = [0.015t + 0.01t2]05 = 0.075 + 0.25 = 0.325

Then we calculate the reliability:

R(5) = e-0.325

Using a calculator, we find:

R(5) ≈ 0.723

So, the reliability of the device over a five-year period assuming no maintenance is performed is approximately 72.3%.