Modeling and Analysis of a Scheduled Maintenance System: a DSPN Approach

Abstract

Maintenance is the main instrument to assure system quality service over time, despite of ageing and wearing of its components. The entire set of the maintenance actions (inspections, replacements, repair, refuelling etc.) carried out on a system during its operational life can be classified into preventive and corrective actions. The former are all those actions performed on the system according to a previously settled time scheduled program and represent the scheduled maintenance program. The latter represent the part of maintenance devoted to the emergency repair and restoration of the system (or just a part of it) each time a failure occurred. It is good practice to minimize corrective maintenance by optimally tuning the scheduled maintenance program. Usually it means to find the proper set of actions and their timed sequence that best satisfy dependability requirements subject to budget constraints. In most cases this is a very though task involving a multi-parametric optimum problem whose solution needs an accurate knowledge of the system behaviour, usually represented by some model of the system and of its behaviour. From the modelling point of view, a system under scheduled maintenance program (SMS) can be seen as a multiple phased system (MPS). Each phase is associated to the configuration of the system during some time interval (the part of the system being actually maintained or operational [1]), while the scheduled maintenance program drives phase changes. The behaviour of the system in each time period (phase) is governed by a complex stochastic process accounting for the simultaneous presence of the individual components failure processes and of maintenance actions, which depend on the phase performed. Under reasonable assumptions (constant failure rates and constant duration of the phases) we have a Markov process, in each phase, and a Markov regenerative process for the phase sequence. The state space modelling approach gives us the basis for the analytical solution of such a problem (Markov renewal theorem), nevertheless there remain computational obstacles due to the well know state-explosion problem that limits drastically the size of problem to be solved. Starting from these considerations our work is directed towards the proposal of a new modelling approach and its experimentation for checking whether it can bring some advantages. This methodology relies upon Deterministic and Stochastic Petri Nets (DSPN) as a modelling formalism and on Markov Regenerative Processes (MRGP) for the model solution. Due to their high expressiveness, DSPN models are able to cope with the dynamic structure of MPS and allow defining very complex model in a concise way. These models are solved with a simple and computationally efficient analytical solution technique based on the divisibility of the MRPS underlying the DSPN of the MPS [2]. This approach is fully integrated in the DEEM tool [3], specifically tailored for the dependability modelling and evaluation of MPS. Using DEEM the model of a MPS is split into tw...

Optimal Aggregation of Components for the Solution of Markov Regenerative Processes

“…We consider 5 models: the last two have been artificially created to investigate cases in which acyclicity is non-trivial (cases in which Rule 8 plays a significant role in constraining the solution), while the first three are variations of Phased Mission Systems (PMS). In particular they are cases of a Scheduled Maintenance System (SMS), inspired by [9], in which a system alternates between two phases: Work and Maintenance, and behaves differently depending on the phase (as typical in PMS). The model is studied for its transient behaviour, the stopping condition for model A is determined by the number N P of phases, while models B and C cycle over the two phases, and the stopping condition is triggered when the system reaches a failure state.…”

Use of Petri Nets to Model the Maintenance of Wind Turbines

“…Simeu‐Abazi and Sassine adopted PNs to implement various maintenance strategies into a manufacturing system. Bondavalli and Filippini modelled scheduled maintenance systems. Lei et al .…”

Optimal Maintenance of Semi-Markov Missions

“…We refer the reader to Burdick et al [3], Veatch [15], Kim and Park [9] and references cited in these papers for phased-mission systems with deterministic sequence of phases. There are also some papers on phased-mission systems with random sequence of phases such as Mura and Bondavalli [10], Mura and Bondavalli [11] and Bondavalli and Filippini [2].…”