We use the generalized two-sided Chebyshev inequality to reformulate a certain nonlinear, chance-constrained new product risk model. The problem has a linear cost objective and a constraint set featuring a probabilistic lower bound on an event which depends on a collection of mutually-independent, uniform random parameters. Our reformulation permits a reduction of the problem to a sequence of second-order cone programs. We, therefore, identify a new family of non-convex programs whose members are amenable to convex programming solution techniques.