The number of failed components in a consecutive-k-of-n:F system

For a consecutive-k-out-of-n:F system an exact formula and a recursive relation are presented for the distribution of the number of components, X, that fail at the moment the system fails. X estimates how many cold spares are needed to replace all failed components upon system failure. The exact formula expresses the dependence of the distribution of X upon parameters k, n. The recursive formula is suitable for efficient numerical computation of the distribution of X.<
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