The expanding use of experimental design techniques for statistical tolerancing is primarily due to their simplicity. They can be understood easily and implemented by engineers and scientists having only a limited knowledge of statistics and experimental design. The method is generally attributed to Taguchi (1978). In this article. we describe Taguchi's method and why it works. both intuitively and mathematically. Our results show that Taguchi's method, although giving good results for many applications, is not optimal. We propose alternative tolerancing procedures that are uniformly better than Taguchi's method with little sacrifice in simplicity. We illustrate the use of these methods. first with some simple examples and then with a partial-differential-equation model.