CONDITIONAL PROBABILITIES OF FAILURES IN RESERVOIR OPERATION FOR MORAN-GOULD MODEL

The distribution of the number of failures n in N years of reservoir operation is examined via the Moran‐Gould model of seasonal inflows. This distribution is conditional on the initial state of the system. It is derived from the m‐step transition matrices (m = 1, 2, … N) and the vector of probabilities of intrayear failure corresponding to all states of the system Ei (i = 0, 1, 2,… k). Introduction of probability generating functions simplifies the presentation of the material. These functions are briefly discussed. A simple numerical example illustrates the theory. Copyright 1969 by the American Geophysical Union.