Allocating for Acceptable Risk Instead of Expected Value

Allocation of inventory, spares, or redundancy in reliable systems often seeks to maximize expected orders filled or hours until failure (assuming known distributions). Often there is no opportunity for an averaging process to permit this expectation to materialize. Each operation of the system may be critical, instead of the average of many, or the first shortage may terminate the whole operation. Predictable adequacy of each operation is attained by considering the full distribution, e.g., of operating hours before failure, instead of just the mean (expected) value. Distributions with small standard deviations permit more precise prediction of probable time before failure (shortage). Plans based on marginal utility concepts tend to avoid the expected-value trap but do not necessarily minimize the appropriate risk of shortage. Operating characteristic curves, like those used in quality control, allow intelligent consideration of the risks involved in choosing among alternate allocation plans. Allocation of a small number of stock items is used to illustrate the criterion.