Maintenance models

There are three types of maintenance model: reactive, preventive, predictive.

It is important to realize the difference between the action of inspection and maintenance. Inspection lead to preventive maintenance only when the observed state is about a threshold (r from the plot).

Inspection happens at t = \tau_0 + k * \tau, where \tau_0 is first inspection time and \tau is the interval between the inspection (the two could be decision variables). PM happens when the observed state is from r to s-1 and CM happens when state is above s. Otherwise, no maintenance happens, even though there could be accumulated failure (for example if state is r-1).

Fig 3 plots the probability based maintenance (PBM) count and period fixed maintenance (PFM) count in Fig 2 (from ref2). In the dynamic simulation in Fig3, it is assumed that the stock variable, PFM failure probability is reset to 0 right after every inspection. This may not be true considering no maintenance happens when observed state is from 1 to r-1.

The purpose of ref1 was to suggest interval optimization maintenance that balances the convenience from period-period maintenance and efficiency from probability-based maintenance maintenance. Out of three maintenance, reactive, preventive, predictive, PFM are preventive (=planned) while PBM are predictive maintenance.

To analyze the cost structure, realizing the difference between inspection and PM is crucial; PM is an action conditional on the action inspection which is completely controllable by the designer. PM is a random variable that depends on the failure function (probability at each age or time). The following table shows the incurred cost for each observed state.

state	cost
functional	C_I
marginal	C_I + C_pm
failure	i) C_cm + C_underage ii) C_I + C_cm

references