Abstract: A unbalanced one-way random model is considered for assessing the proportion of workers whose mean exposure exceed the occupational exposure limit (OEL) based on exposure measurements to the worker. Hypothesis testing for the relevant parameter of interest is proposed when the exposure data are unbalanced. The method is based on the generalize inference. A simulation study is conducted to compare it with that of Krishnamoorthy and Guo (2005). Simulation results suggest that the proposed method appears to be better, especially in very unbalanced design.