Observable gradual failure progression

Many mathematical models exist where the faiulre progression starts at time t = 0, and continues gradually until a failure occurs unless a hard maintenance action is conducted

The standard cost equation to minimize is:

$ \color{blue}{ C(\tau,l) = C_\mathrm{I}/\tau + (C_\mathrm{F} + C_\mathrm{CM}) \lambda_\mathrm{E}(\tau,l) + C_\mathrm{RC}·\rho_\mathrm{E}(\tau,l) }$

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• l is the maintenance limit
• C_I is the cost of one inspection
• C_F is the cost related to a system failure (= C_EP + C_ES + C_EM)
• C_CM is the corrective maintenance cost of repairing the failed component
• C_R is renewal cost, i.e., the cost of repairing or replacing a component reaching the maintenance limit
• λ_E(τ,l ) is the effective failure rate, various numerical methods exist
• ρ_E(τ,l ) is the effective renewal rate, various numerical methods exist