Condition Based Maintenance (CBM) Policy

2.1 The Strategy

The deterioration along a specific sample path is deterministic in the RV model, whereas it varies probabilistically in the GP model. In a linear RV model, one inspection determines the deterioration rate and it fixes the future deterioration path. An inspection in GP model reveals only its current state from which we can infer only the probability distribution of future deterioration. This distinction has profound implications to the optimization of condition-based maintenance strategies.

The condition based maintenance (CBM) strategy involves the periodic inspection of a structure at a fixed time interval tI and cost Ci. We assume that the inspection is accurate such that the deteriorationX(t) can be measured with negligible error. The threshold for the preventive maintenance, cp (0 < c <1), is a fraction of the failure threshold. The preventive maintenance (PM) results in complete renewal (as good as new) of the component. If X(ti) < cp, no action is taken until the next inspection. A component is renewed with cost CP when cp < X(ti) < p. The structure would be immediately replaced upon failure at any time whenX(t) > p, incurring a failure cost, CF. Typically PM cost is much lower than the failure cost (Cp < CP).

The optimization of the condition-based maintenance means finding the inspection interval (tI) and the PM ratio (c) that would minimize the mean cost rate. This in principle involves a two-dimensional optimization problem. In practical situations, however, the PM threshold cp is known from experience or prescribed by operation standards or regulation. In such cases, the inspection interval is the only optimization variable. For illustration purpose, we fix the PM ratio as c = 0.8 and determine the optimal inspection interval and the associated mean cost rate for the RV and GP models.