In reliability engineering, time on performing preventive maintenance (PM) on a component in a system may affect system availability if system operation needs stopping for PM. To avoid such an availability reduction, one may adopt the following method: if a component fails, PM is carried out on a number of the other components while the failed component is being repaired. This ensures PM does not take system׳s operating time. However, this raises a question: which components should be selected for PM? This paper introduces an importance measure, called component maintenance priority (CMP), that is used to select components for PM. The paper then compares the CMP with other importance measures and studies the properties of the CMP. Numerical examples are given to show the validity of the CMP. •Introduced an importance measure for prioritising units for preventive maintenance.•Investigated the relationships between the new measure with other existing measures.•Derived the lower and upper bounds of the number of failures for a set of units.