Connection reliability, which describes the capability that paths exist between specified nodes in a network, has been widely studied. However, the states of both the network and its nodes/edges have epistemic uncertainty owing to the lack of data and information, which makes existing connection reliability assessment methods unacceptable. To solve this problem, this article proposes a new connection reliability based on uncertainty theory: Belief connection reliability. Considering different node connection requirements, we define two belief connection reliability metrics as single-node-pair belief connection reliability (SBCR) and multi-node-pair belief connection reliability (MBCR). Based on the uncertain graph, an extended uncertain graph is built to model networks whose nodes and edges' existence has epistemic uncertainty, and two algorithms are proposed to compute SBCR and MBCR based on finding the most reliable connection path. Finally, a comparison study on a small network is used to illustrate the correctness of the proposed method, and the Belgian telephone interzonal network is used as a case to indicate the effectiveness of our network model and algorithms.

The reliability of complex electronic systems is paramount due to their widespread application and critical functions. The existence of uncertainty and dependency increases the difficulty of reliability analysis. Current research cannot effectively solve this problem. This article proposes a reliability modeling analysis and uncertainty quantification method for electronic systems with multireliability dependency. The structure-related reliability, the overload-related reliability, and the performance reliability are utilized to evaluate the multidimensional capacities of an electronic system. The degradation-aware model and arithmetic Liu process are employed for uncertainty model construction of the structure-related reliability, while the uncertain random renewal reward process is utilized for uncertainty modeling of the overload-related reliability. Performance reliability is influenced by them, and it is modeled with margin-based reliable principle. The dependencies among the three reliabilities are categorized as O-S (overload-structure) dependency, S-O (structure-overload) dependency, and S/O-P (structure/overload-performance) dependency to analyze the effect of the multireliability dependency on the reliability analysis result. Accordingly, the comprehensive reliability analysis algorithm is developed. Finally, the proposed method is implemented to the numerical case of the microcontroller unit as a specific illustration, demonstrating its effectiveness and rationality.

Component signal seriously affects the loose particle detection results. The existing research focused on pure loose particle and component signals, training suitable classifiers to classify the data of two labels from two signals. However, in real application scenarios, pure signals rarely appear, and the data classification results are not the required signal recognition or loose particle detection results. The feasibility and practicality of the existing research are limited. In this article, the authors proposed a loose particle detection method based on the recognition of overlapping signals. By obtaining the optimal recognition model and standard confidence probability, the pure and overlapping signals can be accurately recognized, and the loose particle detection can be realized in a comprehensive manner. Multiple detection results in real application scenarios indicated that the obtained overlapping signal recognition and loose particle detection results were stable and reliable. Compared with the existing research, the loose particle detection sensitivity has been significantly improved.

When evaluating the reliability of a complex system, epistemic uncertainty exists due to the lack of data and knowledge. The control system's feedback compensation mechanism propagates the uncertainty throughout the system. In addition, the real-time performance compensation causes the system to exhibit implicit degradation, which brings new challenges to reliability evaluation. This article proposes a method to solve the problems of complex feedback control system epistemic uncertainty propagation and reliability evaluation. The arithmetic Liu process is used to model the uncertain performance degradation process of the components in the feedback control system. The feedback behavior of the system and the propagation of uncertainty are described by the uncertain degradation state space model. The Laplace transform is then used to deduce the reliability expression of the system. Afterward, the epistemic uncertainty of the components is transmitted to the uncertainty of the system output. Taking the wind turbine pitch control system as a case, the proposed reliability evaluation method is compared with the method based on probability theory. When there is a lack of degradation data, the results suggest that the proposed strategy is more conservative.

While a number of network systems are running under certain stress with a limited lifetime, it is still unknown how to predict the lifetime–stress relation of complex systems. We develop a percolation-based approach to build an operational lifetime–stress model for complex networks, which captures the spatial and temporal reliability characteristics of the system. In this article, the general analytical expression for the entire operational lifetime–stress relation has been presented, which suggests that the load stress and the number of nodes in the network impact the operational lifetime in the same manner. The size effect found here in the lifetime–stress relation is observed for the first time, to our best knowledge. For 2-D lattices, we show that the lifetime–stress relation can be regarded as the combination of two parts—an approximately linear region for small stress, and nonlinear region for large stress. We also analyze the lifetime–stress function of Beijing road network and the western United States power grid. Our article might help to develop acceleration testing methods, which will facilitate better design of reliable complex systems.

Due to the increased dependency of the modern system on software-based system, software reliability has become the primary concern during the software development. To track and measure the software reliability, various software reliability growth models under the framework of probability theory have been proposed. Note that software failures involve lots of epistemic uncertainty, which cannot be depicted well by the probability theory, and debugging processes are usually imperfect due to the complexity and incomplete understanding of software systems. This article deduces an imperfect debugging software belief reliability growth model using the uncertain differential equation under the framework of uncertainty theory, and investigates properties of essential software belief reliability metrics, namely belief reliability, belief reliable time, and mean time between failures based on the belief reliability theory. Estimations for unknown parameters in this model are derived. Real data analyses validate our model and show that it performs better than previous models from the perspective of the sum of square error. A theoretical analysis for these results is presented.

Software reliability plays an important role in modern society. To evaluate software reliability, software reliability growth models (SRGMs) investigate the number of software faults in the testing phase. Obviously, testing progresses are inevitably influenced by dynamic indeterministic fluctuations such as the testing effort expenditure, testing efficiency and skill, testing method, and strategy. To model these dynamic fluctuations, several probability theory-based SRGMs are proposed. However, probability theory is suitable for dealing with aleatory uncertainty, but fails to deal with epistemic uncertainty widely existing in software faults. Therefore, this article considers software reliability from a new perspective under the framework of uncertainty theory, which is a new mathematical system different from probability theory, and proposes a software belief reliability growth model (SBRGM) based on uncertain differential equations for the first time. Based on this SBRGM, properties of essential software reliability metrics are investigated under belief reliability theory, which is a brand-new reliability theory. Parameter estimations for unknown parameters in SBRGM are presented. Furthermore, some numerical examples and real data analyses illustrate our methodology in detail, and show that it performs better than several famous probability-based SRGMs in terms of fitting ability and prediction ability. Finally, an optimal software release policy is discussed.

The high dependence on software in today's society has increased the demand of reliable software immediately. Many researchers have proposed various software reliability growth models (SRGMs) to forecast software reliability by analyzing failure data throughout the testing process. Unfortunately, since software is an intellectual artifact obeying cognitive informatics, its failures involve lots of epistemic uncertainty that can not be handled well by existing methods. Furthermore, different software errors have different implications and thus need different handling. In order to deal with these problems, this paper deduce a novel multiple error types software belief reliability growth model (MESBRGM) under the framework of uncertainty theory. Reliability evaluation is conducted by investigating several reliability indexes namely belief reliability and belief reliable time based on belief reliability theory. Parameter estimations for unknown parameters in MESBRGM are also derived. Real data analysis illustrates our proposed model in detail, and demonstrate its capability compared with several popular models.

Epistemic uncertainty exists in system availability evaluation due to the lack of data and information. To address it, this article proposes a series of definitions of the uncertainty theory-based availability, called belief availability, expanding the scope of belief reliability by introducing uncertainty-measured logistics and maintenance into belief reliability. Based on an uncertain alternating renewal process, we construct a belief availability model for repairable systems subject to the epistemic uncertainty. From the model, we derive formulas of several belief availability metrics, including belief availability (inherent, achieved, and operational), delay time ratio, maintenance time ratio, and belief failure frequency. We find an interesting property that the states order or the initial state in the model will not influence these metrics. A case study about the oxygen generation system (OGS) on the international space station was conducted to analyze the impact of its working, logistics, and maintenance time on the OGS belief operational availability. The results show a potential application in belief availability tradeoff between the OGS's availability-related parameters. In addition, we compared the proposed availability with probability one based on the time distributions of the OGS states, illustrating our method can effectively reduce the deviation of availability evaluation with insufficient data.

Accelerated degradation testing (ADT) aids the reliability and lifetime evaluations for highly reliable products. In engineering applications, the number of test items is generally small due to finance or testing resource constraints, which leads to the rare knowledge to evaluate reliability and lifetime. Consequently, the epistemic uncertainty is embedded in ADT data and the large-sample based probability theory is no longer appropriate. In this paper, we introduce the uncertainty theory, which is a theory different from the probability theory, to account for such uncertainty due to small samples and build up a framework of ADT modeling. In this framework, an uncertain accelerated degradation model is first proposed based on the arithmetic Liu process. Then, the uncertain statistics for parameter estimations are presented correspondingly, which is completely constructed on objectively observed ADT data. An application case and a simulation case are used to illustrate the proposed methodology. With further comparisons to the Wiener process based accelerated degradation model (WADM) and the Bayesian-WADM, the sensitivities of these models to sample sizes are explored and the results show that the proposed model is superior to the other two probability-based models under the small sample size.

Condition-based maintenance has been developed as a very efficient strategy for guaranteeing multicomponent system performance and preventing unexpected failures. However, there are shortcomings in the existing condition-based maintenance optimization models. First, the existing models do not utilize the accelerated degradation testing (accelerated degradation testing) data obtained at the stage of component development. Second, most of these models assume perfect repair instead of imperfect repair. Third, the degradation models used in these condition-based maintenance models cannot consider the epistemic uncertainty. Motivated by these problems, this paper presents a new condition-based maintenance optimization model for multicomponent systems with imperfect repair. An integrated degradation prediction framework utilizing both ADT data and field data is presented to timely update the parameters in the proposed model. In order to solve the proposed multivariable, nonlinear programming model, a novel genetic algorithm with self-crossover operation and shift-mutation operation is developed. Numerical examples and comparisons are conducted to evaluate the performance of the proposed model. Results show that the proposed model can evaluate the degradation process of components accurately and achieve lower total maintenance cost.

A sequential Bayesian approach is presented for remaining useful life (RUL) prediction of dependent competing failure processes (DCFP). The DCFP considered comprises of soft failure processes due to degradation and hard failure processes due to random shocks, where dependency arises due to the abrupt changes to the degradation processes brought by the random shocks. In practice, random shock processes are often unobservable, which makes it difficult to accurately estimate the shock intensities and predict the RUL. In the proposed method, the problem is solved recursively in a two-stage framework: in the first stage, parameters related to the degradation processes are updated using particle filtering, based on the degradation data observed through condition monitoring; in the second stage, the intensities of the random shock processes are updated using the Metropolis-Hastings algorithm, considering the dependency between the degradation and shock processes, and the fact that no hard failure has occurred. The updated parameters are, then, used to predict the RUL of the system. Two numerical examples are considered for demonstration purposes and a real dataset from milling machines is used for application purposes. Results show that the proposed method can be used to accurately predict the RUL in DCFP conditions.

This brief develops a degradation-based imperfect maintenance policy considering both positive effect and negative effect for a deteriorating system with variations of operating conditions. The proposed method improves the positive effect on the imperfect maintenance, which further considers the impact of resource on the distribution function of the positive effect after each maintenance process. The positive effect induces the system state into a random interval which is related to maintenance resource applied into each preventive maintenance action and actual maintenance times. Meanwhile, a new negative deteriorating effect model for describing the impacts of imperfect maintenance actions is established. The new model considers that the degradation rate increases after each imperfect maintenance process; meanwhile, it includes the impacts of variations of operating condition bringing to the degradation rate which is described as a distribution subjected to stress as well. Therefore, a condition-based adaptive maintenance policy is applied for a deteriorating system. The optimal maintenance cost allocation and maintenance threshold are determined by maximizing an availability function. Finally, a numerical example is illustrated to demonstrate the application of our maintenance model and policy.

By elevating stress levels, accelerated degradation testing (ADT) can obtain sufficient degradation data within limited time to predict the reliability and lifetime for highly reliable and long life products. In general, the degradation data collected in ADT have three kinds of characteristics: the time-stress-dependent structure, the random uncertainties caused by random effects in time dimension, and unit-to-unit variations, and the epistemic uncertainty caused by the small sample problem. However, existing acceleration degradation models based on Brownian motion with drift can successfully consider the time-stress-dependent structure and the random uncertainty, while failing to take the epistemic uncertainty into account. In this paper, based on the random fuzzy theory, a new random fuzzy accelerated degradation model and its corresponding statistical analysis method are proposed. The proposed model can take the above three kinds of characteristics into consideration simultaneously. The application case indicates that the proposed methodology is applicable for modeling the ADT data under small sample size. The simulation results show that the proposed methodology is more stable and slightly more conservative than the ADT model considering unit-to-unit variations. In addition, under small sample size (from 3 to 10), the proposed methodology is more stable and more accurate than the ADT model considering unit-to-unit variations.

Measuring system reliability by a reasonable metric is a common problem in reliability engineering. Since real systems are usually uncertain random systems affected by both aleatory and epistemic uncertainties, existing reliability metrics are unreliable. This paper proposes a general reliability metric, called belief reliability metric, to cope with the problem. In this paper, the belief reliability is defined as the chance that a system state is within a feasible domain. Mathematically, the metric can degenerate to either probability theory-based reliability, which copes with aleatory uncertainty, or uncertainty theory-based reliability, which considers the effect of epistemic uncertainty. Based on the proposed metric, some commonly used belief reliability indexes, such as belief reliability distribution, mean time to failure, and belief reliable life, are introduced. We also develop system belief reliability formulas for different systems configurations. To further illustrate the formulas, a real case study is performed.

Standby techniques of different types have been applied in a wide range of industries to improve system reliability. Since the reliabilities of the operating components are generally high in the initial period of the mission and the standby components are hardly needed, it is more reasonable to set a standby component into cold standby state at the beginning and switch it into the warm standby state after certain period. In this paper, we consider 1-out-of-N: G standby systems with components whose lifetimes can follow general distributions and investigate the optimal state transfer scheduling problem with the objective of maximizing system reliability at mission time. For system reliability evaluation, the system reliability functions are derived in a recursive way and the numerical methods based on the closed Newton-Cotes quadrature rules are proposed without using derivatives. The optimal state transfer scheduling is derived by using the meta-heuristic differential evolution algorithm. By identifying the optimal state transfer scheduling, the state transfer order of standby components can also be determined. Two numerical examples are provided to illustrate the proposed methodology and demonstrate its effectiveness.

In accelerated degradation testing (ADT), test data from higher than normal stress conditions are used to find stochastic models of degradation, e.g., Wiener process, Gamma process, and inverse Gaussian process models. In general, the selection of the degradation model is made with reference to one specific product and no consideration is given to model uncertainty. In this paper, we address this issue and apply the Bayesian model averaging (BMA) method to constant stress ADT. For illustration, stress relaxation ADT data are analyzed. We also make a simulation study to compare the s-credibility intervals for single model and BMA. The results show that degradation model uncertainty has significant effects on the p-quantile lifetime at the use conditions, especially for extreme quantiles. The BMA can well capture this uncertainty and compute compromise s-credibility intervals with the highest coverage probability at each quantile.

Prognostics is an engineering discipline utilizing in-situ monitoring and analysis to assess system degradation trends, and determine remaining useful life. This paper discusses the benefits of prognostics in terms of system life-cycle processes, such as design and development, production, operations, logistics support, and maintenance. Challenges for prognostics technologies from the viewpoint of both system designers and users will be addressed. These challenges include implementing optimum sensor systems and settings, selecting applicable prognostics methods, addressing prognostic uncertainties, and estimating the cost-benefit implications of prognostics implementation. The research opportunities are summarized as well.