Renewal Theory

age-specific failure rate alternating renewal process applies argument asymptotic normality Chapter coefficient of variation consider cumulative distribution function cumulative process defined distri distribution of failure-time distribution of recurrence-time equation equilibrium renewal process example exponential distribution failure occurs follows formulae forward recurrence-time given Hence Ho(t integral interval inversion Laplace transform large number limiting distribution log-normal distribution mathematical mean and variance mean failure-time modified renewal process N₁ number of renewals obtained ordinary renewal process p.d.f. of failure-time parameter particle pe¯px planned replacement Poisson distribution Poisson process ponent pooled output prob probability generating function problems properties rational function renewal density renewal function renewal occurs renewal theory rth renewal section 1.3 semi-invariant sequence service replacement simple Smith special Erlangian distribution stages stochastic processes Strategy Suppose survivor function Type I component type of failure U₁ wear Weibull distribution X₁ Y₁ zero μι σχ