In some manufacturing processes, the quality characteristic is represented by a two-
dimensional (2-D) surface. Surface data can generally be treated as a special profile with
one response variable and two explanatory variables, for which spatial correlations are
commonly observed. Existing parametric charts for profile monitoring are unable to
adequately describe the spatial correlations among variables in 2-D surface data, and
nonparametric charts cannot be applied to a 2-D data structure directly. In this study, we …