The Industrial Internet of Things (IIoT) enables interoperability among networked machines, driving the need for Remaining Useful Life (RUL) prediction to ensure operational safety. However, substantial variations in machine specifications introduce severe data distribution discrepancies. Existing research predominantly handles intra-machine operating conditions, while variations across machines remain largely underexplored. To address this challenge, a novel domain generalized framework is proposed for RUL prediction across machines in IIoT. The core idea is to leverage a renovated large language model, acting as an advisor, to generalize a temporal diffusion model through mutual information optimization. Specifically, the temporal diffusion model is first designed to capture degradation dynamics by forward simulating degradation with stochastic noises and then backward eliminating noises via conditioned denoising over time. Then, the renovated large language model is constructed to provide domain-agnostic knowledge by encoding engineered textual prompts and temporal sensor embeddings via the multimodal knowledge fusion. Finally, a mutual information optimization objective is proposed to integrate individual models by seamlessly amalgamating temporal degradation dynamics with domain-agnostic knowledge, offering theoretical guarantees and enabling generalization to unseen machines. Extensive experiments on four bearing datasets validate the superiority, demonstrating its ability to deliver accurate RUL predictions across machines in IIoT.

The real-time and reliable transmission of data packets is a critical foundation for ensuring Internet of Things applications. Therefore, how to ensure the timely reliability of wireless sensor networks has become a hotspot. However, existing timely reliability models often overlook the impacts of energy depletion and channel capacity randomness on wireless transmission. Additionally, most evaluations focus on single-hop, single-path scenarios, while practical data transmission typically requires multi-hop and multi-path strategies. To overcome the above shortcomings, this study conducts the timely reliability evaluation and optimization of wireless sensor networks considering channel capacity randomness and energy depletion. First, focusing on data transmission delay modeling, this study emphasizes the effects of energy depletion and channel capacity randomness on wireless data transmission, and further proposes a timely reliability evaluation model based on the G/G/1 queuing model. Secondly, to tackle the computational challenges of multi-hop and multi-path data transmission, this study proposes a timely reliability solving algorithm that integrates the binary decision diagrams with Monte Carlo simulation.. Building on these foundations, this study develops a periodic optimization model for signal transmission power, balancing sensor lifetime and network transmission performance. Finally, taking the military Internet as an example, the effectiveness of the proposed method is verified.

Assessing the lifetime of products or materials effectively is essential for formulating maintenance strategies and warranty policies. With advancements in engineering technology, high-reliability, long-lifetime products are becoming increasingly common. To quickly obtain lifetime data for such products, constant-stress accelerated life tests (CSALT) have been widely employed. The failure-free life (FFL) characterizes the early stage during which these products experience no failures, and the three-parameter Weibull distribution (TPWD) models FFL through its threshold parameter. However, the effect of acceleration on the threshold parameter has not been adequately investigated, particularly in terms of modeling and estimation. To solve the above problem, firstly, we introduce a modeling approach based on the linear cumulative exposure model and fatigue theory, which accounts for the acceleration of the threshold parameter in CSALT. Applied to TPWD, the resulting model is referred to as CSALT-TPWD. Then, we examine the non-regular problem in the maximum likelihood estimation of CSALT-TPWD. Next, generalized fiducial inference is employed to provide both point and interval estimates. Furthermore, to enhance the sampling efficiency of the posterior distribution, a Hadamard-based$\ell ^{2}$norm prior is proposed. Theoretical analysis confirms that this prior accelerates computation compared to other commonly used norms, while preserving the value of the traditional$\ell ^{2}$norm prior. Finally, numerical simulations and real case analysis demonstrate that the proposed method captures the characteristics of FFL effectively.

Satellite-terrestrial networks (STNs) are a promising paradigm for providing Internet services for users globally. Since the dynamics of service resources and the uncertainty of computational requests, how the service resources in STNs can be efficiently exploited to execute differentiated computational tasks is an essential challenge. In this work, we investigate the dynamic task scheduling in the integrated cloud-edge STNs. First, we propose a cloud-edge collaborative computing framework in STNs, where the computational tasks of users can be processed collaboratively by satellite edge servers, terrestrial edge servers, and cloud servers. Based on this framework, a dynamic task scheduling problem is formulated with the objective of maximizing the task success rate. Second, to make effective real-time decisions at decision points in the dynamic scheduling process, we develop a scheduling heuristic with the routing rule and queuing rule, which incorporates dynamic features related to servers, computational tasks, and network environments. Third, to automatically learn the scheduling heuristic, we propose a multitree genetic programming with rule reconstruction (MTGPRR), which introduces a selective reconstruction operator. This operator increases the chance of matching good rules with other rules by recombining common individuals and elites. Experimental results demonstrate that the proposed MTGPRR performs significantly better than the state-of-the-art methods in improving the task success rate. Moreover, the evolved scheduling heuristic has good interpretability, which is important for practical applications.

In the realm of pairwise lifetime model discrimination, it is a customary practice to frame it as a hypothesis test. In literature, generalized pivotal quantity (GPQ) emerges as an effective tool with complete observations, primarily owing to its advantages in addressing challenges posed by intricate parameter functions and limited sample size. In practical lifetime tests, the occurrence of censoring observations is not uncommon. Under this circumstance, the GPQ-based discrimination is infrequently employed primarily due to the inherent challenge of directly constructing the requisite GPQ. To tackle it, the present study first introduces an algorithm directly integrating data filling with GPQ. Then to mitigate the impact of data filling to GPQ, the generated samples from fiducial distribution also emulate the censoring and filling processes. This novel algorithm is thus designated as the “Mimic filling Algorithm.” For application purposes, this algorithm is applied to Type I censoring data, with the simulation study centered around widely encountered discrimination scenarios for Lognormal, Gamma, and Weibull distributions. In terms of two types errors, simulation results unequivocally demonstrate its superior performance compared to the direct integration of data filling with bootstrap, asymptotic normal approximation, and GPQ. Finally, this study applies the mimic-filling algorithm to discriminate two lithium-ion battery lifetime models with close-fitting results.

There has been increasing attention to the maintenance optimization of balanced systems in recent years. However, existing studies mostly neglect state-dependent inspection intervals and group maintenance, which inadequately addresses the maintenance challenges of balanced systems. Thus, we propose an availability evaluation and maintenance optimization method for balanced systems considering state-dependent inspection intervals. First, multiple maintenance thresholds are introduced to characterize the maintenance strategy considering preventive maintenance and state-dependent inspection intervals, where the next inspection interval is determined based on the post-maintenance system state. Then, the system availability is evaluated by combining semi-regenerative theory and universal generating functions, where calculations are simplified by merging the same system states. Meanwhile, this study also explores the system availability under group maintenance to better reflect reality. Second, the average maintenance cost per unit of time is calculated using the renewal theory. The optimal maintenance thresholds are given by minimizing the maintenance cost under the constraint of minimum system availability. To improve the optimization efficiency, a tabu list-based two-stage iterative partial optimization algorithm is proposed. Finally, the effectiveness of the proposed method is demonstrated through a numerical example involving a lithium-ion battery pack.

The Tweedie exponential dispersion (TED) process provides a flexible framework for degradation process modeling. To obtain degradation information quickly and realistically, we focus on the design of accelerated degradation tests (ADTs) under the TED process with random effects (TEDRE), commonly encountered in practice. Traditional ADT designs primarily rely on the historical data, which may not consider the differences between historical batches and current products. Therefore, we propose an adaptive ADT design method for TEDRE incorporating the historical and online degradation data. First, optimize major decision variables for ADT design using the historical data; subsequently, update measurement intervals and times based on real-time remaining useful life (RUL) predictions from the online degradation data. In addition, a three-stage D-optimality criterion is proposed to simplify the Fisher information matrix computation. To better predict RUL and optimize ADT design, we propose a novel approach to organically combine maximum likelihood estimation and generalized pivotal quantity for small samples and model complexity, and an improved EM algorithm utilizing analytical solutions of model parameters to resolve the slow convergence and accuracy issues; then, simulation studies provide detailed application recommendations. Finally, we illustrate the effectiveness of the proposed method through the stress relaxation and spiral springs data.

Degradation is an important phenomenon for industrial products, which manifests as the gradually deterioration of some performance characteristics. The degradation process is often relevant to both time and usage, and indexing the degradation process merely by the time or usage cannot characterize the process accurately. Considering a stochastic usage process, this study proposes a degradation process model indexed by two scales, i.e., the time and the usage, where the degradation along the two scales are modeled as correlated nonlinear Wiener processes. We develop two simulation-based algorithms for reliability evaluation and study the model inference problems for the proposed model. The estimation procedure and the reliability assessment algorithms are validated by simulations. The performance of the proposed model is justified with an application to a real degradation dataset of outdoor coating materials, which shows that indexing the degradation process by two scales can considerably improve the degradation modeling performance.

Studies on maintenance and inventory optimization have been frequently combined to cut the total operation and maintenance costs of multicomponent systems. Most existing studies assume that components are stochastically independent and only collaborate on inventory management-related resources. In practice, stochastic dependencies exist in most complex systems, and limited maintenance time becomes a crucial resource shared by all components during multimission selective maintenance (SM). Neglecting these features reduces the practicality of policies. To address this limitation, we investigate joint multimission SM and inventory optimization for systems considering stochastic dependency among components. First, an extended factor analysis model incorporating the effects of working conditions is proposed, based on which diverse and dependent degradation processes of components under multiple missions can be well characterized. Then, the sequential optimization of joint multimission SM and inventory policies, which consider information about component degradation states, available resources, and mission profiles simultaneously, is developed using a continuous-state Markov decision process. Decision variables are optimized by an efficient reinforcement learning algorithm. Conclusively, the superiority of the proposed method is illustrated using a numerical example of a photovoltaic system.

In many real situations, because of the lack or inaccuracy of data, it is difficult to evaluate the performance levels and state probabilities of multistate components with precise values. Thus, the reliability evaluation of systems is always affected by the epistemic uncertainty. Existing research on epistemic uncertainty just focuses on simple multistate systems, without considering the phased mission and performance sharing characteristics of systems. Besides, the impact of transmission loss and performance storage on reliability needs to be considered in the modeling of performance sharing systems. In this article, considering the epistemic uncertainty, transmission loss, and performance storage simultaneously, an efficient reliability evaluation method for multi-state phased mission systems with common bus performance sharing is proposed. The transmission loss during the processes thatperformance sharing between subsystems and transferring between phases is considered in the system model. A modified Markov model combined with the mass function is adopted to measure the precise belief degree of component states at any given moment. Then, the belief universal generating function (UGF) method based on the Dempster—Shafer evidence theory is utilized to evaluate the uncertainty of the system instantaneous availability. Finally, two case studies are carried out to demonstrate the effectiveness of the proposed method and explore the dynamic system availability under epistemic uncertainty.

The ad hoc network is an emerging wireless communication technology. Recently, the reliability of ad hoc networks has attracted increasing attention in the literature. In this paper, the reliability of such networks is analyzed by incorporating the impacts of node failures and interference, because node failures usually obstruct the achievement of the intended function of a network, and interference is a key factor that degenerates the communication quality. We consider a general case that an ad hoc network is functional if at least k arbitrary nodes are operational and connected. Accordingly, two novel reliability indices, the generalized k-terminal reliability and the average generalized k-terminal reliability, are proposed, and their calculation methods are provided based on the Laplace transformation technique and the graph theory. For optimizing the design of an ad hoc network, a multiobjective optimization problem is investigated to maximize the reliability level and minimize the cost. The optimization problem is handled by the weighted sum method, and the most suitable solution is selected by the fuzzy satisfying approach. Finally, a numerical example is given to demonstrate the application of the proposed methods.

The continuous glucose monitoring system is an effective tool, which enables the users to monitor their blood glucose (BG) levels. Based on the continuous glucose monitoring (CGM) data, we aim at predicting future BG levels so that appropriate actions can be taken in advance to prevent hyperglycemia or hypoglycemia. Due to the time-varying nonstationarity of CGM data, verified by Augmented Dickey-Fuller test and analysis of variance, an autoregressive integrated moving average (ARIMA) model with an adaptive identification algorithm of model orders is proposed in the prediction framework. Such identification algorithm adaptively determines the model orders and simultaneously estimates the corresponding parameters using Akaike Information Criterion and least square estimation. A case study is conducted with the CGM data of diabetics under daily living conditions to analyze the prediction performance of the proposed model together with the early hypoglycemic alarms. Results show that the proposed model outperforms the adaptive univariate model and ARIMA model.

Confronted with the ever-growing demand for electricity delivery over long distances, the gas insulated transmission line (GIL), as an advanced underground technology, has been under rapid development recently. Physics-of-failure analysis for the GIL indicates that it experiences two competing failure modes: 1) Once the amount of air leakage is greater than a predetermined threshold level, a deterioration-based soft failure happens. 2) The arrival of a partial discharge with overlarge voltage will result in a shock-based hard failure. Furthermore, statistical analysis of some engineering projects shows that the beginning of the GIL degradation, i.e., the inner air begins to leak, occurs after an initiation time. In addition, the flashover voltage decreases considerably as the SF6 in the GIL leaks outside and the moisture penetrates inside, which reflects that the hard failure threshold level is related to the degradation process. Confronted with these problems, a new dependent competing failure model is presented for the GIL, with the consideration of degradation initiation time. The GIL reliability assessment is obtained through theoretical derivation, and the numerical calculation method with controllable approximation accuracy. Finally, a case study is carried out to show the implementation of the proposed model.

To improve the system reliability while conserving the limited system resources, cold standby sparing is often used. In computing tasks, because active components fail randomly, and the standby component has to pick up the mission task whenever required, scheduled backups are often implemented to save the completed portions of the task. The backups can facilitate an effective system recovery where the standby component can take over the mission task from the last backup point instead of resuming the mission task from the very beginning. This paper considers a k-out-of- n cold standby system subject to scheduled backups, where k components are online and operating, with the remaining components waiting in the unpowered, cold standby mode. Whenever an online component fails, a cold standby component is activated to take over the mission task from the last backup point. The backup intervals are deterministic, but can be even or uneven. As the component may fail due to an imperfect switching from the standby state to the fully powered up state, the switching failure is also considered in the system model. A multi-valued decision diagram (MDD)-based analytical approach is proposed to evaluate the reliability of the considered system, and its complexity is analyzed. The proposed method is applicable to systems with non-identical components following arbitrary lifetime distributions. Examples are given to illustrate the MDD-based method. The correctness and efficiency of the proposed method are verified using Monte Carlo simulations.