The lifetime of a component has

WeibullDistribution with

and

given in

. Find the probability that the component survives 300 hours:

Find the probability that the component is still working after 500 hours, after it has survived 300 hours:

Find the mean time to failure:

Simulate the failure times for 30 independent components like this:

The lifetime of a device has

WeibullDistribution. Find the reliability of the device:

The hazard function is increasing in time for

>1 and any value of

:

Find the reliability of two such devices in a series:

Find the reliability of two such devices in parallel:

Compare the reliability of both systems for

and

:

A component is manufactured in two factories. The products coming from factory A have a lifespan following Weibull distribution with

,

, while the time to failure for products coming from factory B follows Weibull distribution with

and

. Find the probability that a component from factory A fails before a component from factory B:

Assume 60% of components are being manufactured in factory A. Find the distribution of the time to failure of a randomly selected component:

Find the mean time to failure:

Compare the mean time to failure for each factory origin:

In the theory of fading channels,

WeibullDistribution is used to model fading amplitude for mobile radio systems operating in the 800-900 MHz frequency range. Find the distribution of instantaneous signal-to-noise ratio where

,

is the energy per symbol, and

is the spectral density of white noise:

Find the mean:

Find the amount of fading:

Limiting values:

WeibullDistribution can be used to approximate wind speeds:

Find the estimated distribution:

Compare the PDF to the histogram of the wind data:

Find the probability of a day with wind speed greater than 30 km/h:

Find the mean wind speed:

Simulate daily average wind speeds for a month:

A site has mean wind speed 7 m/s and Weibull distribution with shape parameter 2:

The resulting wind speed distribution over a whole year:

The power curve for a GE 1.5 MW wind turbine:

The total mean energy produced over the course of a year is then 4.3 MWh:

The magnitude of the annual maximum earthquake can be modeled using

WeibullDistribution. Consider earthquakes in the United States in the past 200 years:

Find the annual maximum:

Create a sample, eliminating the missing data:

Fit a Weibull distribution into the sample:

Compare the histogram of the sample with the PDF of the estimated distribution:

Using the model, find the probability of the annual maximum earthquake of magnitude at least 6:

Find the average magnitude of the annual maximum earthquake:

Simulate the magnitudes of the annual maximum earthquake for 30 years: