Modelling a flexible two-phase inspection-maintenance policy for safety-critical systems considering revised and non-revised inspections

•Failures of safety-critical systems may have drastic consequences.•We propose a flexible two-phase inspection-maintenance policy.•The model performs well in terms of cost-rate and rate of operational failures.•An effective maintenance plan is essential for safety-critical system.•A new delay-time-base model with a fixed and flexible inspection time is presented. This paper presents a flexible two-phase inspection and maintenance policy that has been designed for safety-critical systems to prevent failures that can have serious consequences. The proposed policy comprises two phases: the first guides inspections with a constant frequency and the second guides inspections with varying time intervals. Two delay-time-based mathematical models are presented. Model 1 concerns a case where an in-house inspection team has autonomy to perform the component replacement, and Model 2 concerns a case where a specialized team (often outsourced) is responsible for the replacements. A numerical application is presented, and the results showed that the proposed policy, when compared to its simpler variability: (i) always performs better in terms of cost-rate; (ii) has an even greater impact on reducing the rate of operational failures; (iii) is less sensitive to variations in the parameters of inspection, quality; (iv) tends to respond better to uncertainties in the estimation of the model parameters. Furthermore, a comparison between the results obtained applying the two models shows that the inspection-revised policy with maintenance outsourcing is advantageous when in-house team interventions can result in installation errors with a negative impact on the system's reliability.