Question

7 - 22 (page 365). Spacescope Inc. has an electronic component that has a failure rate of 0.0000165 units/hour. Find the mean time to failure (MTTF). What is the probability (assume an exponential distribution) that the component wil not have failed after 15,000 hours of operation? Calculate your answer using the appropriate mathematical formula, and verify your results using Excel.

Answer 1

MTTF is given by the below formula

$\small MTTF = \frac{1}{\lambda}$

where $\small \lambda$ is the failure rate of the component which equals 0.0000165 units/hour. Hence MTTF equals

$\small MTTF = \frac{1}{0.0000165} = 60606.06 \textup{ hours}$

Hence MTTF is 60606.06 hours

Assuming exponential distribution, the probability that the component will not have failed after t hours of operation is given by below formula

$\small R(t) = e^{-\lambda*t}$

For given case $\small \lambda$ = 0.0000165 and t = 15000,hence we get

$\small R(t) = e^{-0.0000165*15000} = 0.7807 = 78.07 \%$

Hence probability that the component will not have failed after 15000 hours of operation is 78.07%