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This report outlines a theoretical solution for the estimation of rainflow range density functions using statistics computed directly from power spectral density data. The rainflow range mechanism is broken down into a set of events which can be analyzed using Markov process theory. The dependence between extremes in this instance is modelled using an approximation of the joint distribution of peaks and troughs first proposed by Kowalewski. NOMENCLATURE dh = interval width used to discretise the stress range f., = long run transition probability f; = absorption probability in state i from originating level j h = stress range pk = transition probability of going from state i to state k P =transition probability matrix p ( i p ) = probability of a peak being at level ip PSD = power spectral density function tp = twice the mean signal value y ( t ) = signal as a function of time ps,, ( h ) = rainflow range probability density function Y , , Y,, Y, = events as described in Section 3

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