Distribution-Free Approximations for Chance Constraints

F. M. Allen, R. N. Braswell and P. V. Rao
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F. M. Allen: Western Electric Engineering Research Center, Princeton, New Jersey
R. N. Braswell: Armament Development and Test Center, Air Force Systems Command, Eglin Air Force Base, Florida
P. V. Rao: University of Florida, Gainesville, Florida

Operations Research, 1974, vol. 22, issue 3, 610-621

Abstract: 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.

Date: 1974
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