Reliability of a Space Launch

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ground = guidance1 \[And] guidance2 \[And] ignition1A \[And] 
   ignition1B \[And] ignition2A \[And] ignition2B \[And] 
   separation1 \[And] separation2 \[And] powerA \[And] powerB \[And] 
   comA \[And] comB \[And] instrumentA \[And] instrumentB \[And] 
   structure;
Subscript[\[ScriptCapitalR], ground] = 
  ReliabilityDistribution[
   ground, {{guidance1, Subscript[\[ScriptCapitalD], 
      iGuidance]}, {guidance2, Subscript[\[ScriptCapitalD], 
      iGuidance]}, {ignition1A, Subscript[\[ScriptCapitalD], 
      iIgnition]}, {ignition1B, Subscript[\[ScriptCapitalD], 
      iIgnition]}, {ignition2A, Subscript[\[ScriptCapitalD], 
      iIgnition]}, {ignition2B, Subscript[\[ScriptCapitalD], 
      iIgnition]}, {separation1, Subscript[\[ScriptCapitalD], 
      iSeparation]}, {separation2, Subscript[\[ScriptCapitalD], 
      iSeparation]}, {powerA, Subscript[\[ScriptCapitalD], 
      oPower]}, {powerB, Subscript[\[ScriptCapitalD], oPower]}, {comA,
       Subscript[\[ScriptCapitalD], iCom]}, {comB, 
      Subscript[\[ScriptCapitalD], iCom]}, {instrumentA, 
      Subscript[\[ScriptCapitalD], iInstrument]}, {instrumentB, 
      Subscript[\[ScriptCapitalD], oInstrument]}, {structure, 
      Subscript[\[ScriptCapitalD], structure]}} /. k -> 5];

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launch = guidance1 \[And] 
   guidance2 \[And] (ignition1A \[Or] ignition1B) \[And] 
   propulsion1 \[And] 
   separation1 \[And] (ignition2A \[Or] ignition2B) \[And] 
   propulsion2 \[And] 
   separation2 \[And] (powerA \[Or] powerB) \[And] (comA \[Or] 
     comB) \[And] instrumentA \[And] instrumentB \[And] structure;
Subscript[\[ScriptCapitalR], launch] = 
  ReliabilityDistribution[
   launch, {{guidance1, Subscript[\[ScriptCapitalD], 
      oGuidance]}, {guidance2, Subscript[\[ScriptCapitalD], 
      iGuidance]}, {ignition1A, Subscript[\[ScriptCapitalD], 
      oIgnition]}, {ignition1B, Subscript[\[ScriptCapitalD], 
      oIgnition]}, {ignition2A, Subscript[\[ScriptCapitalD], 
      oIgnition]}, {ignition2B, Subscript[\[ScriptCapitalD], 
      oIgnition]}, {separation1, Subscript[\[ScriptCapitalD], 
      oSeparation]}, {separation2, Subscript[\[ScriptCapitalD], 
      oSeparation]}, {powerA, Subscript[\[ScriptCapitalD], 
      oPower]}, {powerB, Subscript[\[ScriptCapitalD], oPower]}, {comA,
       Subscript[\[ScriptCapitalD], oCom]}, {comB, 
      Subscript[\[ScriptCapitalD], oCom]}, {instrumentA, 
      Subscript[\[ScriptCapitalD], oInstrument]}, {instrumentB, 
      Subscript[\[ScriptCapitalD], iInstrument]}, {structure, 
      Subscript[\[ScriptCapitalD], structure]}, {propulsion1, 
      Subscript[\[ScriptCapitalD], oPropulsion]}, {propulsion2, 
      Subscript[\[ScriptCapitalD], oPropulsion]}} /. k -> 400];

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plotOpts = {PlotRange -> {0, 1}, Filling -> Axis, Ticks -> None, 
   ImageSize -> 150, PlotRangePadding -> 0};
Grid[{{"", "Ground", "Launch", 
   "Orbit"}, {Rotate["SurvivalFunction", \[Pi]/2], 
   Plot[SurvivalFunction[Subscript[\[ScriptCapitalR], ground], t], {t,
      0, 15000}, Evaluate@plotOpts, 
    FillingStyle -> ColorData["Crayola"]["Mahogany"]], 
   Plot[SurvivalFunction[Subscript[\[ScriptCapitalR], launch], t], {t,
      0, 40}, Evaluate@plotOpts, FillingStyle -> Orange], 
   Plot[SurvivalFunction[Subscript[\[ScriptCapitalR], orbit], t], {t, 
     0, 50000}, Evaluate@plotOpts, 
    FillingStyle -> ColorData["Crayola"]["Inchworm"]]}, {Rotate[
    "MTTF", \[Pi]/2], Mean[Subscript[\[ScriptCapitalR], ground]], 
   Mean[Subscript[\[ScriptCapitalR], launch]], 
   Mean[Subscript[\[ScriptCapitalR], orbit]]}, {Rotate[
    "Mission time", \[Pi]/2], 24, 0.1, 
   100*24}, {Rotate["Reliability", \[Pi]/2], 
   SurvivalFunction[Subscript[\[ScriptCapitalR], ground], 24], 
   SurvivalFunction[Subscript[\[ScriptCapitalR], launch], 0.1], 
   SurvivalFunction[Subscript[\[ScriptCapitalR], orbit], 
    100*24]}, {Item["Mission reliability:", Background -> LightBlue], 
   SpanFromLeft, Item[rel, Background -> LightBlue], SpanFromLeft}}, 
 Frame -> All, Spacings -> {1, 2}, 
 BaseStyle -> {FontFamily -> "Verdana", FontSize -> 12}]

Model a launch into space in three phases: a ground check, a launch phase, and in orbit. The three phases have environmental harshness factors of 5400 and 1.

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