Reducing maintenance costs by including imperfect inspections J. Driessen*, Eindhoven University of Technology February, 2014 / School of Industrial Engineering Introduction As minimisation of maintenance costs remains an important pillar in the industry, inspections are included in maintenance to further reduce costs. However, most scenarios consider inspections to be perfect, when in practice they are not. In addition, the reliability aspect is gaining priority on the industrial and political agenda. This yields the research question, initiating this research: How does the imperfectness of inspections affect cost optimal maintenance schedules under a reliability constraint? Methods We consider a Delay Time Model type of model distinguishing three asset states: normal, defective and failed. The asset is subject to a maintenance schedule consisting of an inspection interval length (T) and an inspection instance of preventive replacement (M). We differentiate between two inspection errors: false positives and false negatives, occurring with probabilities α and β, respectively. We propose three behaviours for α and β: A1, A2 and A3, corresponding to Figures 1, 2 and 3. Figure 1: First modelling approach (A1): constant probabilities Figure 3: Third modelling approach (A3): non-constant probabilities Figure 2: Second modelling approach (A2): non-constant probabilities We derive an optimisation model, minimising the average costs per time unit subject to a reliability constraint. Hence, three optimisation models are developed, relating to Figures 1, 2 and 3. Results We differentiate the results for the unconstrained problems and constrained problems. The results present different optimal maintenance schedules for the three models. Conclusions The conclusions underlie the premises of Weibull distributed state durations. The different model approaches yield different results for the maintenance schedules and costs. The model approach for the non-constant probabilities of α and β determines the effects on the optimal maintenance schedules and costs. Higher inspection quality yields a schedule with a high inspection frequency and low costs. Low inspection quality yields the opposite results. The work illustrates the importance of having a good understanding of inspection behaviour, especially when this behaviour is non-constant over time. Recommendations Compare the models’ results to the results from practice. Investigate and estimate the probabilities of false positives (α) and false negatives (β). Derive additional model approaches to further investigate the non-constant probabilities’ effects. Model approachMTC(M,T)ΔC(M,T) A12162,185,21 A2688,374,84-7,10% A32169,325,23+0,39% Table 1: Numerical results for unconstrained problems Table 2: Numerical results for constrained problems Model approachMTC(M,T)ΔC(M,T) A1320,2325,20 A22211,6119,25-23,61% A3222,2924,77-1,70% Supervisors: Dr. H. Peng, TU/e, OPAC Prof. Dr. Ir. G.J. van Houtum, TU/e, OPAC Ir. B. Huisman, NedTrain