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Source changed 2026-10-14 19:58:00 UTC · snapshot created 2026-10-14 19:58:38 UTC · last check 2026-10-15 01:55:10 UTC

MNT.2:4.2 - Compare recurring age-replacement costs when that model fits

Suppose replacement restores the component to an as-new state, successive lifetimes X are independent with the same distribution, intervention duration is negligible, expected cycle duration is positive and finite, and costs cover the relevant consequences. For replacement at age a or earlier failure, derive the two possible endings from the lifetime model, counting a failure at age a as corrective:

  • the cycle’s operating duration is min(X,a);
  • corrective cost Cc applies when X <= a, and planned cost Cp otherwise.

The long-run cost per operating-time unit is

g(a) = [Cc * P(X <= a) + Cp * P(X > a)] / E[min(X,a)].

Compare feasible ages, including continued operation to failure where admissible. This calculation includes how often replacement recurs. Use another model when downtime, imperfect restoration, changing duty or coupled components invalidate these assumptions; a finite service horizon also needs its own end condition. See Arts and colleagues, §2.2.1 for the renewal-reward basis and its limits.