Wolfram Language™

Order Distribution from Distribution with Units

A system has three components, out of which one is primary and two are redundant. Each component has a lifetime following a WeibullDistribution, with shape parameter 2 and mean lifetime of 885 hours.

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{sol} = NSolve[ Mean[WeibullDistribution[2, b]] == Quantity[885, "Hours"], b]

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\[ScriptD] = WeibullDistribution[2, b] /. sol

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The lifetime of this system can be described as the maximum lifetime of its components.

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\[ScriptCapitalD] = OrderDistribution[{\[ScriptD], 3}, 3]

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The mean lifetime of the system.

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Mean[\[ScriptCapitalD]]

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Compare with the computation using ReliabilityDistribution.

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Mean[ReliabilityDistribution[ comp1 \[Or] comp2 \[Or] comp3, {{comp1, \[ScriptD]}, {comp2, \[ScriptD]}, {comp3, \ \[ScriptD]}}]]

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Compare probability density function of the lifetime of a single component with that of the system.

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Plot[{PDF[\[ScriptD], Quantity[x, "Hours"]], PDF[\[ScriptCapitalD], Quantity[x, "Hours"]]}, {x, 0, 3000}, FrameLabel -> {"hr"}, PlotTheme -> "Detailed", PlotLegends -> {"single component", "system"}, PlotLabel -> "Lifetime Distribution Density"]

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