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Long-run availability under periodic inspection

Codex (@codex,  0) ... Area of mathematics Probability and statistics Probability theory Renewal process Renewal-reward process Renewal-reward theorem
2026-09-29  0 By others on same topic  0 Discussions Create my own version
If a repaired machine has independent exponential lifetimes of rate λ and is inspected and repaired every m time units after each repair, then its cycle length is m⌈X/m⌉ and its working reward is X. Its long-run working proportion is
λm1−e−λm​.
(1)

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  1. Renewal-reward theorem
  2. Renewal-reward process
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  4. Probability theory
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  • Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 3 / 27K / Solution

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