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Reliability
Data Center Reliability
A data center needs 20 servers to work, one power supply, one cooling system, and one network connection. The power supply has a standby component. The network connection consists of two parallel connections.
In[1]:=
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\[ScriptCapitalR]hdd = ReliabilityDistribution[ BooleanCountingFunction[{2, 3}, {x, y, z}], {{x, WeibullDistribution[4, 1.25 10^6]}, {y, WeibullDistribution[4, 1.25 10^6]}, {z, WeibullDistribution[4, 1.25 10^6]}}];
In[2]:=
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\[ScriptCapitalD]cpu = ExponentialDistribution[1/30000]; \[ScriptCapitalD]ram = WeibullDistribution[.82, 2500];
In[3]:=
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\[ScriptCapitalR]Server = ReliabilityDistribution[ hdd \[And] cpu \[And] ram, {{hdd, \[ScriptCapitalR]hdd}, {cpu, \[ScriptCapitalD]cpu}, \ {ram, \[ScriptCapitalD]ram}}];
In[4]:=
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\[ScriptCapitalS]PowerSupply = StandbyDistribution[ ExponentialDistribution[ 1/5000], {ExponentialDistribution[1/2000]}];
In[5]:=
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\[ScriptCapitalD]Network = ParetoDistribution[1500, 10]; \[ScriptCapitalD]Cooling = ExponentialDistribution[1/5000];
In[6]:=
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servervars = Table[Subscript[s, i], {i, 20}]; serverdists = Table[{i, \[ScriptCapitalR]Server}, {i, servervars}]; \[ScriptCapitalR]Datacenter = ReliabilityDistribution[(And @@ servervars) \[And] power \[And] (net1 \[Or] net2) \[And] cooling, Join[serverdists, {{power, \[ScriptCapitalS]PowerSupply}, {net1, \ \[ScriptCapitalD]Network}, {net2, \[ScriptCapitalD]Network}, \ {cooling, \[ScriptCapitalD]Cooling}}]];
In[7]:=
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mttf = NExpectation[t, t \[Distributed] \[ScriptCapitalR]Datacenter];
In[8]:=
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failures = RandomVariate[\[ScriptCapitalR]Datacenter, 100];
In[9]:=
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Grid[{{"MTTF", "SurvivalFunction", "Simulation"}, {mttf, Plot[Evaluate@SurvivalFunction[\[ScriptCapitalR]Datacenter, t], {t, 0, 100}, Filling > Axis, PlotRange > {0, 1}, Mesh > {{mttf}}, MeshShading > {Automatic, ColorData["Crayola"]["Mahogany"]}, MeshStyle > PointSize[Medium]], ListPlot[{failures, {{0, mttf}, {100, mttf}}}, Joined > {False, True}, Filling > Axis, AxesOrigin > {0, 0}]}}, Frame > All, FrameStyle > Gray, Spacings > {2, 2}, Background > {None, {LightBlue}}, BaseStyle > {FontFamily > "Verdana", FontSize > 12}]
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