Conditional probabilities of failures in reservoir operation for the 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.