Leaf it to renewal: Improved predictive maintenance policies via renewal theory and decision trees

TL;DR

The paper addresses prognostics-based predictive maintenance by marrying renewal theory with prognostic RUL distributions to derive simple, interpretable policies. It introduces a one-step discrete-option assessment (DOA) framework that generates heuristic policies for two settings: preventive replacement and preventive ordering, using the long-run cost rate ECTR as the optimization criterion. The DOA policies, including a replacement rule and an ordering rule, rely on the RUL-PDF input and plug-in initial estimates of ECTR to balance immediate costs against the value of waiting for more information. Numerical studies on a virtual RUL simulator and a C-MAPSS turbofan case show that DOA policies achieve lower cost rates and greater robustness to data limitations than standard benchmarks, offering practical, data-efficient tools for PHM deployment.

Abstract

We propose a general method for deriving prognostics-based predictive maintenance policies. The method takes into account the available decision options at hand, the information on the future state of the system provided by a prognostic model, as well as the costs of the underlying renewal-reward process. It results in heuristic policies with only a few parameters, which can be determined based on theoretical considerations or by optimization from run-to-failure data. We show the potential of the method on two separate predictive maintenance decision settings, namely preventive replacement and preventive ordering. Numerical investigations show that the derived heuristic policies achieve significantly lower cost ratios than other benchmark heuristic policies, while at the same time being more robust against overfitting.

Figures (15)

• Figure 1: Workflow of maintenance decision policies. At every time step $k$, the latest RUL-PDF is fed into a heuristic policy ($\Pi$), which outputs a decision to either do nothing or to perform a maintenance action, e.g., replacement or ordering a spare component.
• Figure 2: Decision tree for a deteriorating component that can be preventively replaced. Component states are represented by round nodes, and maintenance decisions ($a_k$) as square nodes. The action taken (PR/DN) as well as the condition of the component (Failed/Safe) with the corresponding event probabilities are included in the respective paths, where $p_F=\Pr(RUL\leq\Delta t)$. The component's end of life (filled black circle) is shown together with the associated expected costs. The Figure is adapted from bismut2021optimal.
• Figure 3: Exemplary incurred costs for each of the considered branches (a) to (c) of the decision tree in \ref{['fig:rep_decision_tree']}.
• Figure 4: Decision tree for a deteriorating component, where a spare can be preventively ordered. Component states are represented by round nodes and the ordering decision ($a_k$) as a square node. The action taken, as well as the condition of the component (Failed/Safe) with the corresponding event probabilities are included in the respective paths, where $p_{F}^{(1)} = \Pr(RUL\leq l)$ and $p_{F}^{(2)}=\Pr(RUL\leq l+\Delta t)$. Here, filled black circles indicate the component's eventual end of life (the ordering decision has no influence on that). The costs for each branch are not shown in the graph to avoid cluttering; instead, they are listed in \ref{['eq:h_ord_tk_fail', 'eq:h_ord_tk_surv', 'eq:h_ord_tk+1_fail', 'eq:h_ord_tk+1_surv']}.
• Figure 5: Exemplary incurred costs for each of the considered branches of the decision tree in \ref{['fig:order_decision_tree']}. The dotted black line indicates interruption of the component's function; hence, no costs are accumulated due to the continuation of the renewal-reward process.