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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Interval availability, defined as the fraction of time that a system is operational during a period of time [ 0,T ], is an important indicator of system performance, especially for industries with a Service Level Agreement, e.g., telecommunication industry, computer industry, etc. Most existing methods to compute interval availability are based on numerical simulations. In this paper, we present a new analytical solution for interval availability of Markov repairable systems. Three interval availability indexes, i.e., interval availability, interval availability in a general interval, and interval availability in multiple intervals, are considered. The interval availability indexes are derived based on aggregated stochastic processes and the results are obtained in closed form using Laplace transforms. A numerical example is presented and the results are compared with those of Monte Carlo simulation. The developed methods are applied to calculate the interval availability of a fault-tolerant database system from the literature. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]