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I dont know how to approach this problem. Suppose that a machine has a probability of failure of 43% at 90 hours of operation. How can you calculate the failure rate and the probability of surviving x hours without having failures?

Jesus Oropeza Maray
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  • Recommended: the RIAC toolkit, https://www.quanterion.com/projects/system-reliability-toolkit/ . Quanterion charges for hardcopy, but somewhere on their site you should be able to find a PDF downloadable for free. – Carl Witthoft Oct 08 '18 at 18:16
  • Another source: https://reliabilityanalytics.com/Rome_Laboratory_Reliability_Engineers_Toolkit.pdf – Carl Witthoft Oct 08 '18 at 18:24

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$$ \large{R(t)=e^{\lambda t}}\\ \begin{align} R&=\text{Reliability}\\ t&=\text{time}\\ \lambda&=\text{failure rate} \end{align}$$

At $t=0$

$$ R(t=0)=1\\ \implies100\% $$

I think, if the reliability follows exponential distribution, you can use the formula given above. Reliability is the probability that a machine will function normally during a period of time under proper working conditions. So, $$\text{reliability}=1-\text{probability of failure}$$

grg
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