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This note considers an inventory model for repairable stock items for which S. G. Allen and D. A. D'Esopo had previously derived an approximate expression for backorder rate, derives an exact expression for the stationary distribution of stock on hand and backordered under considerably more general assumptions, and shows that the backorder rate can be calculated exactly from this. The stationary expected number of backorders per unit time can also be calculated from this distribution.
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Simon et al. (1971) studied this question.
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