The Age Replacement Optimization Model
Under the classical age replacement policy, equipment is replaced preventively at operating age T_p or upon failure, whichever comes first. By balancing the low cost of planned replacement against the high cost of emergency downtime, this model computes the exact inflection point that minimizes total life-cycle cost rate.
Formulas
Expected Cost Rate: C(T_p) = [ C_p · R(T_p) + C_f · (1 - R(T_p)) ] / ∫₀T_p R(t) dt
Run-to-Failure Rate: CRTF = C_f / MTTF
Cost Savings: [ (CRTF - C(T_p^*)) / CRTF ] × 100%
Frequently Asked Questions
What happens if failure cost equals planned cost (Cf = Cp)?
If Cf = Cp, the optimal policy is run-to-failure (Tp* = ∞). There is no financial penalty for failing in service, so replacing components before they fail prematurely discards remaining useful life.