WEBVTT

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A gearbox seal, replaced every twenty weeks.

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The task has been in the plan for years,

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and nobody on site can tell you where the interval came from.

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Over a hundred weeks there are thirteen events.

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Five are planned seal replacements,

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and the seal was serviceable every time.

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Eight are corrective failures.

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A work order records work.

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It does not record a failure.

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Those eight failures happen at gearbox ages of

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thirty, fifty, sixty-five, seventy-five,

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eighty-three, ninety, ninety-six and ninety-nine weeks.

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Cumulative age. Not the gap between them.

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And the gaps are closing.

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Crow-AMSAA models that as a power law.

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Beta is the trend.

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Sum the natural log of T over each age,

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and divide n by it.

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Beta above one means failures are arriving faster.

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But eight events is not many, so test it.

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The ninety per cent interval runs from

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one point three five to four point four four.

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It never touches one.

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Correct for small-sample bias

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and beta is still two point three seven.

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Across the whole record, failures arrive at

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nought point zero eight a week.

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Right now, nought point two two.

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They differ by exactly beta.

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Over the next six months this model expects seven failures.

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A constant rate assumption expects two.

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Beta tells you the system is getting worse.

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It does not tell you where.

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So drill in.

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Half of all failures are one bearing failure mode,

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and every one of them is lubrication.

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And the seal? Five removals, zero failures.

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That is not nothing.

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Five censored lives put characteristic life at

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twenty-nine and a half weeks or more,

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against a twenty-week interval.

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The only component on a fixed interval

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is the only one that never failed.

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Change the lubrication, mark the date,

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and fit the trend again.