Optimal inspection intervals for safety systems with partial inspections

The introduction of International Standard IEC 61508 and its industry-specific derivatives sets demanding requirements for the definition and implementation of life-cycle strategies for safety systems. Compliance with the Standard is important for human safety and environmental perspectives as well as for potential adverse economic effects (eg, damage to critical downstream equipment or a clause for an insurance or warranty contract). This situation encourages the use of reliability models to attain the recommended safety integrity levels using credible assumptions. During the operation phase of the safety system life cycle, a key decision is the definition of an inspection programme, namely its frequency and the maintenance activities to be performed. These may vary from minimal checks to complete renewals. This work presents a model (which we called ρβ model) to find optimal inspection intervals for a safety system, considering that it degrades in time, even when it is inspected at regular intervals. Such situation occurs because most inspections are partial, that is, not all potential failure modes are observable through inspections. Possible reasons for this are the nature and the extent of the inspection, or potential risks generated by the inspection itself. The optimization criterion considered here is the mean overall availability Ao. We consider several conditions that ensure coherent modelling for these systems: sub-systems decomposition, k-out-of-n architectures, diagnostics coverage (observable/total amount of failure modes), dependent and independent failures, and non-negligible inspection times. The model requires an estimation for the coverage and dependent-failure ratios for each component, global failure rates, and inspection times. We illustrate its use through case studies and compare results with those obtained by applying previously published methodologies.