A modelling approach has been useful for the analysis of data from robust designs for quality improvement. Recently, Robinson et al. (J. Qual. Technol. 2006; 38:65–38) proposed the use of generalized linear mixed models (GLMMs) and they used the marginal quasi-likelihood (MQL) method of Breslow and Clayton (J. Am. Statist. Ass. 1983; 88:9–25). Hierarchical generalized linear models (HGLMs) extend GLMMs by allowing structured dispersions and conjugate distributions of arbitrary GLM families for random effects. In this paper we use two examples to illustrate how these additional features in HGLMs can be used for the analysis of data from quality-improvement experiments. We also show that the hierarchical likelihood (HL, or h-likelihood) estimators have better statistical properties than the MQL estimators. Copyright © 2010 John Wiley & Sons, Ltd.