This paper presents an approach to optimise condition-based maintenance (CBM) of multi-component systems where the state of certain components could affect the rate of degradation of other components, i.e., state-rate degradation interactions. We present a real example of an industrial cold box in a petrochemical plant, where data collected on fouling of its tubes show that the extent of fouling of one tube affects the rate of fouling of other tubes due to overloading. A regression model is used to characterise the state-rate degradation interactions for this example. Further, we optimise the condition-based maintenance policy for this system using simulated annealing. The outcomes of the case study demonstrate that modelling degradation interactions between components in the system can have significant positive impact on CBM policy of the system. The paper therefore tackles a problem that has not been addressed in the literature, paving way for further developments in this important area of research with practical applications.