PF-model - Fast failure progression

• The PF-model for fast failure progression is used if there is a relative long period where failure progression is not observable, and then there is a period where the failure proression is rahter fast.
• The point of time where failure progression is observable depends on available inspection methods, and is denoted a potential failure P)
• The point of time when a failure occurs is denoted (F)
• The PF-interval is the time between the potential failure and the point of time of the faiulre
• The PF interval is a stochastic variable

Model quantities

• MTTF = Mean time to failure if PM is not conducted, often denoted MTTF_N where "N" means "naked"
• E_PF = Expected length of the PF-interval
• SD_PF = The standard deviation of the PF-interval
• q = Probabiity that an inspection does not reveal a potential failure
• f = 1/(MTTF - E_PF) = the rate of potential failures (approximation)
• The effective failure rate in the PF-model is given by: λ_E(τ) = f⋅Q₀(τ; E_PF, SD_PF,q)
  • where Q₀(τ; E_PF, SD_PF,q) is the probability that the inspection regime fails to reval potentail failures in due time, and requires numerical methods (see course compendium)
• The cost equation to minimize: C(τ) = C_I/τ + (C_F+C_CM) λ_E(τ) + C_PM⋅f⋅[1- Q₀(τ; E_PF, SD_PF,q)]
  • C_I is the cos tof one inspection
  • C_F is the cost of 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 with a potential failure