Dynamic reliability decision-making frameworks: trends and opportunities

1. INTRODUCTION

Reliability engineering and management are crucial for product quality and market competitiveness. Demand for high performance and reliability has made decision-making a key research focus in this field.

Traditional static models assume constant conditions, failing to capture dynamic factors such as production, usage, and environment^[1-3]. For instance, lithium-ion battery (LiB) reliability in electric vehicles depends on manufacturing, usage, and maintenance^[4,5]. Therefore, dynamic reliability decision-making provides more adaptive solutions across three main stages: reliability testing and optimization, modeling and evaluation, and post-service design.

Reliability testing and optimization face challenges due to complex, long-lasting products^[6]. Standard life tests under normal conditions are impractical for highly reliable consumer durables^[7]. Accelerated reliability testing (ART) uses stresses such as higher temperatures or humidity to expedite failure^[8]. Reliability optimization, once limited to the design phase, now requires ongoing adjustments due to dynamic usage and environments^[9,10], involving complex programming and algorithm development^[11].

Traditional lifetime prediction methods lack today’s needed precision, driving data-driven model growth^[12]. The complexity of dynamic environments and varied usage further complicates model development. Peng et al. highlight the role of dynamic conditions in reliability modeling^[13].

Reliability engineering includes testing, modeling, optimization, and post-service design, linked to degradation and operational environments^[14]. For example, Gan et al. propose a maintenance optimization strategy for multi-state systems in dynamic environments^[15].

The shift towards dynamic decision-making frameworks is driven by the practical needs of industries such as aerospace, automotive, and energy, where systems operate under highly variable conditions. This paper explores trends in dynamic reliability decision-making, addressing challenges and highlighting future research directions for adaptive and responsive management.

2. RELIABILITY TESTING AND OPTIMIZATION

Reliability testing and optimization are typically conducted during product design. However, modern systems' complexity makes system-level testing challenging^[16]. Reliability is often assessed by testing the basic units, sometimes performed by suppliers rather than manufacturers. A key challenge in reliability testing is the extrapolation needed for predictions. Long-lasting consumer durables render traditional life tests impractical, making accelerated tests (ARTs) a preferred framework^[17,18].

ARTs are typically categorized into accelerated life tests (ALTs) and accelerated degradation tests (ADTs), with some studies combining these methods^[19]. Both methods shorten testing time and yield valuable reliability data. ALTs apply higher stress levels to accelerate failure^[20], while ADTs track performance degradation over time^[21,22]. In ALTs, unit failures and failure times are recorded, whereas ADTs measure periodic degradation. Planning is the first crucial step in ART for reliability assessment. Most existing studies follow a scheme that hinges on large-sample approximation to design ARTs, in which the optimality criteria are established via a function of the Fisher information and other selected variables. Figure 1 shows some key elements to be considered during the planning phase. The scheme is statistically sound, flexible, and adaptable to various scenarios.

Figure 1. Important aspects in ART plan optimization.

Recent literature regarding related topics has implied several possible future directions. First, there are numerous research gaps in formulating new optimality criteria. Classical criteria such as D-, A-, and V-optimality, while statistically robust, often lack practical relevance. Bayesian optimization has been effectively applied to reliability-based design optimization, particularly in estimating design points with high accuracy^[23]. Song et al. employ the constrained Bayesian optimization method and its variant to adaptively learn design points^[24]. Emerging studies have increasingly concentrated on the connections between statistical criteria and the decision-maker’s objectives^[25,26]. Etemadi and Fotuhi-Firuzabad^[27] propose optimizing protection system design by balancing costs and relay failure losses, integrating economic aspects into reliability. Incorporating maintenance and warranty perspectives into these criteria is promising. Second, the enrichment of the ART model and reliability model is always an outlet. Specifically, enhancing the interpretability of such models presents a significant challenge^[28]. Last but not least, dynamic methods in ART planning are limited. Most extant works treat the test planning as a static design of experiment problem, yet in practice, tests can be planned and conducted in a dynamic, sequential manner^[29,30]. Dynamic decision-making methods such as the Markov decision process (MDP) and reinforcement learning (RL) can be promising tools to tackle such planning problems^[31].

Adding redundancy is a traditional yet effective way to boost system reliability, commonly seen in high-safety engineering systems such as airliners and automobiles. Reliability optimization covers various design problems, such as the redundancy allocation problem (RAP)^[32], the reliability allocation problem and the reliability RAP (RRAP)^[11]. Simply speaking, the problem is selecting the optimal components and quantities to ensure system operation. The uncertainty embedded in the reliability of units can make the problem quite onerous to solve. Risk-aware decision-makers often seek worst-case reliability solutions^[33,34], leveraging distributionally robust methods. Nevertheless, the problem usually falls into the category of hard-to-solve mixed integer linear or nonlinear programs. Efficient algorithms remain a research priority, with specific system structures guiding algorithm improvements. Reihaneh et al. propose an exact branch-and-price (BP) algorithm for RAP with heterogeneous components under a mixed redundancy strategy^[35].

Traditionally, reliability optimization was viewed as a static design-phase problem. However, with modern systems experiencing diverse usage and dynamic environments, system design now spans the entire lifecycle. Peiravi et al. introduced a novel Universal Redundancy Strategy (URS) aimed at improving system reliability by dynamically adjusting the configuration of redundant components during system operation^[36]. Planning for redundancy upgrades and maintenance interactions is a time-dependent problem that classic methods may not handle effectively. Sequential decision models present a promising approach for tackling such dynamic challenges.

3. RELIABILITY MODELING AND EVALUATION

Data-driven reliability modeling methods have significantly evolved^[37], but conventional lifetime-based methods, such as Weibull and Poisson models, remain popular in both research and applications^[38]. Meanwhile, degradation modeling that utilizes the health characteristics of products for reliability analysis plays an increasingly important part in related fields^[39]. This approach has been used to study reliability through performance loss in batteries, wear in machine tools, and crack growth in turbine blades. Reliability modeling and evaluation is not inherently a decision-making problem, but it provides crucial input for reliability-focused decision-making frameworks.

Dynamic factors can significantly affect system reliability during operation, as most systems function in time-varying environments. Changes in external conditions, such as higher temperatures, can negatively impact electronic products such as batteries and chipsets. Singpurwalla^[40] and Eryilmaz and Rıza Bozbulut^[41] have explored these effects on reliability modeling. Luo et al. propose a statistical model that accounts for both correlated component lifetimes and lifetime ordering constraints under dynamic conditions to show direct impacts on reliability^[42]. Dynamic environments are generally modeled as time-varying covariates linked to reliability parameters^[1,43]. Zhang et al. use a Wiener process for system degradation, treating the dynamic environment as a covariate^[44].

Hybrid models have emerged as a transformative approach by integrating the strengths of physics-based models and data-driven techniques to address key challenges in reliability modeling. One such challenge is managing the heterogeneous usage patterns of products, which introduce complex operational variances and significantly affect system reliability. Accurately managing high-dimensional, often correlated, covariates is crucial. Machine learning-based methods can be a resort, yet incorporating the physical principles of reliability into these models can be complex. For a comprehensive review, refer to the study by Xu and Saleh^[45]. Physics-informed machine learning methods need more in-depth investigation.

Dependent and Competing Failure Processes (DCFP) are increasingly important in reliability modeling, especially for systems facing multiple, interacting failure mechanisms such as wear, corrosion, and fatigue^[46]. In DCFP, one failure process can influence the likelihood of others. This is particularly relevant for industrial applications such as LiB systems^[47] and micro-electro-mechanical systems (MEMS)^[48]. Additionally, Wu and Ding^[49] explore how Markov environments influence systems with DCFP, highlighting dynamic environmental factors. Zhou and Li^[50] study interactions between minor and major failures. Future research could integrate DCFP into dynamic decision-making frameworks for a deeper understanding of system reliability in changing conditions.

Reliability modeling for complex multi-component systems is another challenging task especially with component dependencies. Complex systems can be onerous to characterize using classical block diagrams. Network or graph-based characterizations are far more flexible and informative^[51]. Combining stochastic models with regression-based methods can enhance the efficiency and accuracy of reliability models.

4. POST-SALE SERVICE DESIGN VIA RELIABILITY MODELS

Maintenance modeling and optimization are crucial post-sale strategies for manufacturers and consumers, with dynamic methods widely studied. MDP-based maintenance optimization dates back to the 1950s when reliability engineering first emerged. Early research discussed system deterioration without explicitly mentioning “condition-based maintenance”, favoring the term “preventive maintenance”. In recent decades, condition-based maintenance (CBM) has garnered huge attention^[52]. As shown in Figure 2, maintenance schemes often rely on different key state thresholds, which may lead to over-maintenance or unexpected failures. CBM dynamically adjusts maintenance decisions by continuously monitoring the system’s degradation state.

Figure 2. Different maintenance planning schemes.

Maintenance optimization via MDP and its variants has been studied intensely^[53-55]. MDP is a framework for decision-making under uncertainty, representing a system where an agent chooses actions that lead to different states with specific rewards^[56,57].

Unlike traditional CBM methods that set a constant threshold, MDP-based approaches use dynamic criteria linked to long-term utility for optimal policies. Semi-MDP (SMDP) and partially observed MDP (POMDP) are among the most commonly used variants of MDP in such problems^[58,59]. The decisions are planned as illustrated in Figure 3. Under the MDP framework, system states (S₁ to S₅) are fully observable, while the POMDP framework addresses situations where system states are not directly observable. Instead, the decision-maker relies on observations to update belief states, which serve as probabilistic representations of the system's underlying condition. Mahmoodi et al. explore SMDP-based maintenance for parallel unit systems in dynamic environments^[60], while Arcieri et al. propose a framework for inferring POMDP parameters using Markov Chain Monte Carlo (MCMC) to and address model uncertainty through domain randomization in RL training^[61].

Figure 3. MDP and POMDP in maintenance planning.

Warranty management stands at the interfaces of various engineering and management perspectives, including reliability, quality, marketing, design, etc.^[62]. Maintenance and warranty policies for sold systems can be optimized jointly using MDP. Developing adaptive, tailored strategies in this context shows great potential.

Maintenance modeling can be expanded by incorporating system dynamics and varied maintenance actions to suit different scenarios. One intriguing direction is to incorporate time-varying dynamic covariates into degradation models, enabling decisions based on both system state and external factors. For example, Zheng et al. use an SMDP integrated with lot sizing and maintenance scheduling^[63], while Luo et al. model the dynamic environment as a time-varying covariate affecting the degradation drift via a Markov process^[64]. Joint policies combining maintenance with other decisions, such as production planning and inventory management^[65,66], offer significant benefits. Paraschos et al. study a stochastic production and inventory system that accounts for multiple deterioration failures and product quality^[67]. Zheng et al. consider the quality of spare parts supplied by vendors as a critical factor in their model^[68]. MDP can facilitate the joint optimization of maintenance and warranty policies, particularly by exploring adaptive and customized strategies, incorporating adaptive approaches and risk-aware criteria, as shown by Xu et al.^[69].

To tackle sequential decision problems, especially in larger-scale scenarios, algorithms can leverage system reliability characteristics. For example, modern electricity distribution systems consist of intricate networks with interdependent subsystems, presenting significant maintenance challenges due to their scale. RL-driven CBM policies are increasingly popular for their adaptability to dynamic, uncertain systems^[70]. However, the dependencies among these subsystems can be limited, allowing for factored MDP modeling to simplify the problem and make the computation of optimal policies more feasible. Furthermore, current RL methodologies applied in CBM optimization primarily focus on determining optimal policies through numerical approaches. There is a notable gap in research regarding the convergence of regrets, a promising area for exploring CBM policy structures within the RL framework.

5. CONCLUSIONS

The paper highlights progress and future directions in dynamic decision-making for reliability. Advancements in operations research, computer science, and statistics offer valuable tools for modeling and solving dynamic optimization problems. Integrating domain expertise from mechanical and systems engineering enhances applicability. Future research should prioritize physics-informed machine learning to merge physical principles with data-driven reliability models. Transitioning to dynamic ART can yield more realistic simulations, while ensuring model interpretability and computational efficiency is critical as complexity rises. Tailored algorithms for specific systems will enable real-time applications. In CBM, RL can improve policy decisions, addressing challenges such as regret convergence. Developing adaptive maintenance and warranty strategies and new optimality criteria that balance statistical and practical aspects will be essential for practical deployment. The focus on these dynamic approaches signals a promising path for future research across system life cycles.