The sensitivity analysis of engineering designs has been performed following Taguchi’s methodology. The technique is reliable and computationally inexpensive, thus suitable for real life problems. The design problem involves a mathematical model of a gas turbine blade cooling hole system. The model includes twelve input variables and three non linear constraints. The orthogonal matrix as suggested by Taguchi and the tolerances on the input design variables are used to define a neighbourhood of a design solution. Three different categories of sensitivity are defined, such as, design solution sensitivity, design variable sensitivity and constraint sensitivity. The sensitivities are defined within the neighbourhood of a design solution. The use of the orthogonal matrix allows an approximate sensitivity analysis without resorting to exhaustive local search. Taguchi’s signal to noise ratio is used to define the design solution sensitivity. Methodology involved in the estimation of factor effects in an experiment is used to calculate the design variable sensitivity. The extents of constraint satisfaction within the neighbourhood of a design solution defines different categories of constraint sensitivity, such as, constraint satisfied, statistically active constraint, quasi-active constraint, peak-active constraint and constraint not satisfied. The paper briefly discusses Taguchi’s methodology and then defines the different sensitivities. Results from the sensitivity analysis of the real life turbine blade cooling hole system are presented and discussed.