Weibull Distribution - HxGN EAM - 11.07.01 - Feature Briefs - Hexagon

HxGN EAM Reliability Analysis

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HxGN EAM
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Feature Briefs
HxGN EAM Version
11.7.1

Wallodi Weibull (1887-1979) was a Swedish engineer, scientist, and mathematician. In 1939, he published his paper on Weibull distribution probability theory and statistics. This distribution is now by far the world's most popular statistical model for life data. Not in the least because it can be used with smaller sample sizes than any other statistical distribution. Normally you would want sample sizes to represent the population, however in reliability engineering you often do not have the luxury to wait for that sample size. Just think of the space shuttle program. There have been two catastrophic failures out of 135 missions. Would you be willing to use the Weibull distribution to prevent the third one, or would you rather wait until ten shuttles failed before drawing conclusions? Clearly, using the Weibull distribution to prevent catastrophic failures is the best option.

Weibull distributions are based on three parameters:

  • β (Beta), is called the shape parameter or slope

  • η (Eta) is called the scale parameter or characteristic life

  • Location parameter

For our purposes, the ‘three parameter Weibull’ is not used. The location parameter is useful in scenarios where life does not start immediately. Think of shipping televisions to a distributor and then to the retailer. The real life of the TV starts only after installation by the consumer. The location parameter would represent this transport delay in the age to failure. For our purposes the ‘two parameter Weibull’, using Beta and Eta only, is sufficient.