The problem of designing mechanical systems or components under uncertainty is considered. The basic idea is to ensure quality control at the design stage by minimizing sensitivity of the response to uncertain variables by proper selection of design variables. This formulation is applied to the design of a brass sleeve which is press fitted over a steel shaft in an uncertain thermal environment. The contact pressure is determined using finite element analysis. By optimizing the shape of the sleeve, the sensitivity of contact pressure with respect to operating temperature is reduced. The minimum sensitivity approach offers a straightforward procedure for robust design and can be implemented in a general manner. It is shown that reduction in sensitivity leads to increase in probability of safety.