AbstractBased on the principles introduced by TUKEYand FRASER, a method is proposed to construct non‐parametric multivariate tolerance regions of irregular multiplanar shape. Contrary to the regions of corresponding shape as constructed by Tukey and Fraser, the tolerance regions constructed according to the proposed method can be shown to be invariant to linear scale transformations. In medical applications, where the concept of multivariate tolerance regions can be used to define “normal” regions forp≦ 2 variables with measuring units generally differing from each other, the quality of scale‐independency of the regions is essential. With reference to the method proposed, sample size determination and some important aspects of the use of multivariate tolerance regions are