Optimal inspection and maintenance of complex systems in modern industry is important for safety and economic reasons. With appropriate statistical modelling, the utilization of inspection resources and quality of inferences can be greatly improved. Modelling and inspection of a full-scale industrial furnace subject to corrosion will be considered. A suitable Bayesian spatio-temporal dynamic linear model is developed for wall thickness, by eliciting the beliefs of experts and incorporating other relevant data for related systems. The model may be used to derive efficient inspection schedules for corrosion detection and we demonstrate the considerable reduction in the inspection burden which the model allows. Copyright © 2004 John Wiley & Sons, Ltd.