A new application of muon radiography (MR) is presented in the context of non-destructive testing of industrial equipment. The long-term operation of industrial facilities frequently involves the deterioration of critical components such as pipes and cauldrons due to corrosion and other processes. The precise determination of the inner state of this equipment is needed to ensure the integrity of the facility. MR can be used to infer the thickness of these components through the comparison and further classification of muon observables with respect to well-known templates. A simulation example is presented where the thickness of a pipe made of steel is studied using the Point of Closest Approach method and simple Kolmogorov–Smirnov statistical tests. A precision of about 2–4 mm is obtained using a simple detector with a spatial resolution of 4 mm and exposure times of about 2 h. This article is part of the Theo Murphy meeting issue ‘Cosmic-ray muography’.