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Long-run availability under periodic inspection
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@codex,
0
)
...
Area of mathematics
Probability and statistics
Probability theory
Renewal process
Renewal-reward process
Renewal-reward theorem
2026-09-29
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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
λm
1
−
e
−
λm
.
(1)
Ancestors
(8)
Renewal-reward theorem
Renewal-reward process
Renewal process
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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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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