Reliability Engineering and System Safety Supporting group maintenance through prognostics-enhanced dynamic dependability prediction

Condition-based maintenance strategies adapt maintenance planning through the integration of online condition monitoring of assets. The accuracy and cost-e ﬀ ectiveness of these strategies can be improved by integrating prognostics predictions and grouping maintenance actions respectively. In complex industrial systems, however, e ﬀ ective condition-based maintenance is intricate. Such systems are comprised of repairable assets which can fail in di ﬀ erent ways, with various e ﬀ ects, and typically governed by dynamics which include time-dependent and conditional events. In this context, system reliability prediction is complex and e ﬀ ective maintenance planning is virtually impossible prior to system deployment and hard even in the case of condition- based maintenance. Addressing these issues, this paper presents an online system maintenance method that takes into account the system dynamics. The method employs an online predictive diagnosis algorithm to distinguish between critical and non-critical assets. A prognostics-updated method for predicting the system health is then employed to yield well-informed, more accurate, condition-based suggestions for the maintenance of critical assets and for the group-based reactive repair of non-critical assets. The cost-e ﬀ ectiveness of the approach is discussed in a case study from the power industry.


Introduction
The main goal of maintenance is to achieve desirable system dependability whilst minimising cost [1]. Dependability is a term that encompasses a range of attributes which include safety, reliability, availability, and maintainability [2]. Some industries are moving away from traditional time-based or reactive maintenance regimes towards condition-based maintenance (CBM), where intervention is scheduled when monitoring data indicates asset deterioration [1].
CBM applications have explored different areas for cost-effective maintenance planning such as grouping maintenance strategies or updating maintenance models with prognostics information. Grouping maintenance actions together can reduce downtime and personnel costs through considering functionally or spatially related assets within the system [3][4][5][6][7][8][9][10][11][12]. Prognostics and health management (PHM) is an integral aspect of CBM which focuses on system degradation management with the following main groups of activities [13]: • Anomaly detection: monitoring and detection of abnormal conditions in the system operation.
• Diagnostics: if an anomaly is detected, diagnose the cause of the fault.
• Prognostics: predict the likely future degradation of the asset and estimate its remaining useful life.
• Operation and maintenance planning: mitigate the effects of failure and reduce unnecessary planned maintenance.
The RUL denotes the time distance from the current prediction time, t p , to the end of the useful life (or failure time) of the system denoted EOL: Given that remaining time after t p is random, uncertainty representation mechanisms are needed to model RUL [19,20]. Fig. 1  • probability density function (PDF) of the RUL (e.g. derived using particle filters [14,24]).
So as to use prognostics results within CBM planning, one possibility is to parametrize prognostics prediction results [25]. For deterministic prediction results, the RUL value can be used directly assuming a constant degradation rate and confidence bounds can be used to estimate maximum and minimum boundary values [26]. As for the PDF of the RUL, the PDF can be parametrized through regression methods (e.g., Weibull regression [27,28]), or alternatively mean, maximum and minimum RUL values can be calculated [25].
Despite these advances, cost-effective CBM planning is far from trivial in complex industrial systems. Such systems are comprised of many potentially repairable assets, which can fail in different ways and with various effects. The operation of assets and the system is typically governed by dynamics which include time-dependent and conditional events and they cause complexities in the system reliability prediction and maintenance planning [29]. The use of combinatorial failure models (fault trees, reliability block diagrams) to model the failure logic of complex systems has disadvantages for maintenance planning. For instance, in a fault-tolerant system, the criticality of assets can change substantially over time [30]: in a system with two parallel redundant channels, when one fails the criticality of assets within the single remaining channel increases. Combinatorial failure models have limited ability to represent these situations. Therefore, system maintenance strategies based combinatorial failure models may also miscalculate dependability and maintenance costs.
Several dynamic dependability techniques have emerged to enable a more accurate analysis of dynamic scenarios that include state changes and sequencing of failures [31]. The application of these techniques for CBM planning would enable a more accurate health assessment estimation compared with maintenance planning methods based on combinatorial failure models. In this paper, we argue that the increasing capabilities for prognostics and maintenance strategies along with dynamic dependability models create opportunities for improved dependability estimations and system maintenance planning.
In that context, optimization of system maintenance remains an open research problem. Making progress in this area, in our view, requires incorporating accurate prognostic-enhanced dynamic dependability models into maintenance planning. Preliminary work on incorporating prognostics in a dynamic dependability model and informing asset-level maintenance planning has been done in [32,25,33], but this solves only part of the problem. Moving from asset to system level maintenance requires incorporating grouping criteria suited for dynamic failure logic systems. Dynamic dependability models can be used for clustering tasks based on the criticality analysis of assets. However, the connection between dynamic dependability models and potential maintenance strategies is complex because unforeseen events have effects on dependability which are hard to foresee a priori and cause effects on the dependability profile of the assets and system making further maintenance decisions harder. In particular, the specification of different groups of assets for maintenance at different intervals becomes hard because grouping criteria and clusters should change dynamically to optimise dependability and cost. In this paper, our aim is to address some of the above challenges in the dynamic planning of maintenance. The main contribution of this paper is the proposal of an advanced system-level dynamic maintenance planning method building on our earlier work on prognosticsenhanced dynamic dependability models for maintenance [25,33]. The core of the proposed approach is a system-level maintenance planning algorithm which coordinates predictive diagnostics activities and assetlevel prognostics information, and interacts with the dynamic dependability model.
The online predictive diagnosis algorithm classifies assets as critical or non-critical according to their importance at the system level. The system maintenance planning algorithm takes this information and interacts with the dynamic dependability model to implement grouping maintenance strategies and predict the consequence on the system health. The dynamic dependability model is updated with prognostics information, so as to yield well-informed, more accurate, conditionbased suggestions for the maintenance of assets that have been identified as critical and for the group-based reactive repair of assets that have been identified as non-critical. This paper is organized as follows. Section 2 presents related work. Section 3 introduces the prognostics-updated system maintenance approach for dynamic systems. Section 4 presents the implementation of the proposed approach for asset and system level maintenance strategies. Section 5 applies the proposed approach to a power transmission substation case study. Section 6 discusses the applicability and limitations of the method and Section 7 presents conclusions and future prospects.

Related work
Condition-based maintenance planning has recently gained interest as a possible method of cost-effective maintenance planning for stochastically deteriorating assets and systems [34]. Different costeffective maintenance strategies have been proposed for asset-level condition-based maintenance focusing on specific failure modes such as fatigue crack growth [14] or pitting corrosion [35].
When designing maintenance strategies for complex systems with multiple assets, engineers need to consider stochastic, structural, and economic dependencies between assets [36]. Stochastic dependency implies that asset degradation impacts the performance of other assets, structural dependency means that maintaining an asset implies the maintenance of other assets, and economic dependency addresses the difference between group and independent maintenance actions.
For efficiency, maintenance strategies with economic dependencies must allow for the grouping of assets in different periods of maintenance. This grouping can be static or dynamic to reflect changes in operational circumstances [37]. Dynamic maintenance grouping methods can be divided into finite horizon planning (no online re-planning) and rolling horizon planning (long term plan revised as new informa- . We will use the term RUL to denote deterministic RUL values and we will explicitly refer to the PDF of the RUL when needed.

J.I. Aizpurua et al.
Reliability Engineering and System Safety xxx (xxxx) xxx-xxx