Extreme-Value Parameter Estimates

[#1]

Not sure how Extreme-Value Parameter Estimates compare to  alpha/beta estimates used in the Weibull Parameter Estimates for days to failure plots.

charles_revelle_1-1668625318021.png

Understand beta of >1 means in Weibull indicates the device will continue to failure over-time, is the Extreme-Value Estimates just a transform of the Weibull Analysis?

Thanks, 

Charles

JMP 17

[#2]

The Weibull distribution cumulative distribution function is related to the Smallest Extreme Value distribution CDF:

weibull 1.PNG

(JMP Training course)

The SEV distribution:

small.PNG

(JMP Training course)

The Weibull CDF above can be transformed from a location-scale parameterization to a scale-shape parameterization:

weibull 2.PNG

(JMP Training course)

The interpretation of the shape parameter is specifically:

hazard.PNG

(JMP Training course)

I am not sure if this information is helpful. Continue to ask questions if it is still not clear.

[#3 · Accepted solution]

Mark,

Thanks for the info..  Went back and re-read Bill Meeker book. Think I will stick with Weibull and LogNormal for a device that "gracefully" degrades over time.  Appears Extreme Value is better for early life failures with increasing hf.

Thanks,

Charles