WEBVTT

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One formula. Almost any shape of risk.

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Watch what happens to all three panels as

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one number changes: beta.

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Below beta equals 1, the hazard falls with

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age. Early failures, then a levelling risk.

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At beta equals 1, risk stops depending on

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age at all. This is the exponential distribution,

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and it is nothing more than this one

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setting. Above beta equals 1, risk climbs with

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age, and the higher beta climbs, the faster

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that risk accelerates. The peak of the density

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moves later and gets sharper.

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The line on the plot gets steeper.

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Same pivot point, every time, because eta hasn't

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changed. By beta of 8, failures cluster tightly

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around one age. That is a batch problem,

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or a single, very well-defined wear mechanism, not

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a spread of random risk.

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One point never moves on that third panel:

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eta, the 63.2% life.

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Whatever beta does to the shape, eta always

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marks the same place.