If I have 210 widgets with an E(lifespan) of 1 week, and uniform age distribution [0,7] days, with instant replacement, is it reasonable to assume 210/7=30 widgets will need to be replaced daily? What other assumptions are lurking here? Does the shape of lifespan distro matter?
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Replying to @vgr
what is the variance in lifespan estimate? over a long time period you probably do converge on 30 widgets/day but any given week might diverge from that significantly.
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Replying to @danlistensto
yeah, I want to avoid modeling the stochastic process at the fine-grained level and just do a deterministic substitute... it is a longer time horizon model where week to week doesn't matter much
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Replying to @vgr
makes sense. if that's how you're modeling it then I think you've answered your own question already: no, the shape of the distro doesn't matter.
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Replying to @danlistensto @vgr
Except if failure probability depends on day of the week. Extreme case is widgets guaranteed to break on Mondays (regardless of age).
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ah, so it's an Apple product then
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