WEBVTT

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Every Weibull probability plot starts with ages and status,

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not beta and eta.

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This synthetic fleet has eleven bushings:

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eight target-mode failures and three right-censored suspensions.

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Suspensions are not assigned failure-probability points,

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but, assuming independent censoring,

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their survived exposure changes the adjusted ranks of later failures.

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Convert those adjusted ranks with Benard's approximation.

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These are estimated plotting positions,

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not observed failure fractions.

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On ordinary axes, the fitted two-parameter Weibull cumulative distribution

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is a curve.

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First, transform age with x equals the natural logarithm of t.

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Then transform probability with y equals the natural logarithm

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of the natural logarithm of one over one minus F.

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The theoretical Weibull curve becomes a straight line.

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The eight empirical points remain slightly offset,

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as real sample data should.

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Fit the line and two parameters become visible.

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On standard Weibull axes,

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the positive slope is beta.

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Here, beta is about 2.84,

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indicating increasing hazard under this model,

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not proving a physical cause.

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Where the line crosses about 63.2 percent cumulative failure,

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read eta: about 109,800 hours.

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Eta is characteristic life,

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not mean life or a replacement interval.

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One population.

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One target failure mode.

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One declared life measure.

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A transparent path from observations to the fitted parameters.