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Hubble Gyroscope Maintenance

The Hubble space telescope carries six gyroscopes for its inertial navigation system. If fewer than three gyroscopes are operational, the telescope enters a sleep mode, and a shuttle mission is required to fix it. If all gyroscopes fail, the telescope will crash.

    
The gyroscope operating times, the time to reach sleep mode, and the time to prepare a shuttle mission are exponentially distributed with rates , , and , with units of inverse years. Integers are used here to represent the number of operational gyroscopes:
Wolfram Language code: proc = ContinuousMarkovProcess[1, {{-6λ, 6λ, 0, 0, 0, 0, 0, 0, 0}, {0, -5λ, 5λ, 0, 0, 0, 0, 0, 0}, {0, 0, -4λ, 4λ, 0, 0, 0, 0, 0}, {0, 0, 0, -3λ, 3λ, 0, 0, 0, 0}, {0, 0, 0, 0, -2λ - μ, 2λ, μ, 0, 0}, {0, 0, 0, 0, 0, -λ - μ, 0, μ, λ}, {η, 0, 0, 0, 0, 0, -2λ - η, 2λ, 0}, {η, 0, 0, 0, 0, 0, 0, -λ - η, λ}, {ν, 0, 0, 0, 0, 0, 0, 0, -ν}}] /. {λ -> 1 / 10, μ -> 100, η -> 5};
Wolfram Language code: Graph[MapThread[Style, {{"6", "5", "4", "3", "2", "1", "Sleep2", "Sleep1", "Crash"}, {StandardGreen, StandardGreen, StandardGreen, StandardGreen, StandardOrange, StandardOrange, StandardBlue, StandardBlue, StandardRed}}], proc /. {ν -> 0}, GraphLayout -> {"SpringElectricalEmbedding", "Rotation" -> Pi}, ImageSize -> Medium]
Find the probability that the telescope will crash in the next 10 years:
Wolfram Language code: CDF[FirstPassageTimeDistribution[proc, 9], 10]//N
Find the probability that sleep mode is not reached (no shuttle mission is required) in 10 years:
Wolfram Language code: SurvivalFunction[FirstPassageTimeDistribution[proc /. ν -> 1., {7, 8}], 10]
Wolfram Language code: Plot[SurvivalFunction[FirstPassageTimeDistribution[proc /. ν -> 1, {7, 8}], x], {x, 0, 20}, Filling -> Axis]