Distribution-Free Approximations for Chance Constraints

This paper concerns developing methods for approximating a chance-constrained set when any information concerning the random variables must be derived from actual samples. Such a situation has not been presented in the literature. When existing chance-constrained programming techniques are used, it is not possible to relate the accuracy of sample-based assumptions to actual constraint satisfaction. The methods presented here employ the concept of a distribution-free tolerance region to construct various sets whose elements have the common property of satisfying the chance constraint with a preassigned level of confidence. The sample size required to meet the desired confidence is readily available in tabular or graphical form.