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# Reliability, failure analysis and problem solving

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1. A Porsche GT3 Cup car's engine has a mean time between failures of 250 hours, where the failure rate is constant. Suppose that a certain race requires failure-free operation of the engine for 20 hours. What is the probability that the engine will complete the race without failure? Please round your answer to 2 decimals.

2. The hazard function of a product is given by λ = λt where λ > 0. Suppose we subject the product to the burn-in period T0. Will the conditional reliability R (t|T0 ) increase or decrease as the burn-in period T0 increase?

3. The failure distribution is given by the function below. What is the MTTF (in hours).
f(t)=(3t²/(10⁹))^ ,for 0 ≤t≤1000hr

4. The time to failure of a typical household refrigerator has the following pdf: What is the reliability of the refrigerator for the first year? Please round your answer to 2 decimals
f(t)= {█(0.003t^2-0.06t+0.3 for 0≤t≤10 years@0 elsewhere)┤

5. Pick three contributing factors for observing an IFR hazard.
Hint: These factors can typically be addressed using preventative maintenance.

https://brainmass.com/engineering/aerospace-engineering/reliability-failure-analysis-problem-solving-624940

#### Solution Preview

Hello as attached, thanks John

A Porsche GT3 Cup car's engine has a mean time between failures of 250 hours, where the failure rate is constant. Suppose that a certain race requires failure-free operation of the engine for 20 hours. What is the probability that the engine will complete the race without failure? Please round your answer to 2 decimals.

For a constant failure rate the reliability (probability of no failure) up to a time t is given by

R(t)=e^(-t⁄MTBF)

Where Mean Time Between Failures MTBF=250 hrs

Thus probability of no engine failure up to including 20hrs is

R(20)=e^(-20⁄250)=e^(-0.08)=0.92

The hazard function of a product is given by λ = λt where λ > 0. Suppose we ...

#### Solution Summary

Various problems and solutions addressing failure, failure rate, hazard and reliability

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