Proceedings of the Institution of Mechanical Engineers,Part O: Journal of Risk and Reliability

A nonlinear integer programming model is developed in this article to solve redundancy allocation problems with multiple components having different failure rates in the series–parallel configuration using an active strategy. The main objective of this research is to select the number and the type of each component in subsystems so as the reliability of the system under certain constraints is maximized. To this aim, a weighted K-means clustering method is proposed, in which the analytical network process is employed to assign weights to the components of each cluster. As the proposed model belongs to the class of nondeterministic polynomial-time hardness problems, precise solution methods cannot solve it in large scale. Therefore, an invasive weed optimization algorithm, due to its proven high efficiency, is utilized to solve the problem. As there is no benchmark available in the literature, a harmony search algorithm and a genetic algorithm are employed as well to validate the results obtained. In order to find better solutions, response surface methodology is used to tune the parameters of the solution algorithms. Some numerical illustrations are solved in the end to not only show the application of the proposed methodology but also to validate the solution obtained and to compare the performance of the three solution algorithms. Experimental results are generally in favor of the invasive weed optimization.

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

This article develops a particle swarm optimization algorithm based on a feed-forward neural network architecture to fit software reliability growth models. We employ adaptive inertia weight within the proposed particle swarm optimization in consideration of learning algorithm. The dynamic adaptive nature of proposed prior best particle swarm optimization prevents the algorithm from becoming trapped in local optima. These neuro-prior best particle swarm optimization algorithms were applied to a popular flexible logistic growth curve as the FLG C p P S A N N model based on the weights derived by the artificial neural network learning algorithm. We propose the prior best particle swarm optimization algorithm to train the network for application to three different software failure data sets. The new search strategy improves the rate of convergence because it retains information on the prior particle, thereby enabling better predictions. The results are verified through testing approaching of constant, modified, and linear inertia weight. We assess the fitness of each particle according to the normalized root mean squared error which updates the best particle and velocity to accelerate convergence to an optimal solution. Experimental results demonstrate that the proposed FLG C p P S A N N model based prior best Particle Swarm Optimization based on Neural Network (pPSONN) improves predictive quality over the FLG C ANN , FLG C PSANN , and existing model.

The reliability of a weighted- k -out-of- n system that consists of three-state components is studied. The system is assumed to comprise n three-state components, namely, perfect functioning, partial working, and complete failure and functions if the total weight of all the working components is at least k . Reliability expressions are presented when the times spent by components in perfect functioning and partial working states are dependent with a given joint distribution. Sufficient conditions are also provided to compare the expected total weights of two systems.

Based on the reliability analysis, this work presents a model of the preventive maintenance for the hydraulic system of platform firefighting vehicle, considering the working age regression factor and the equivalent service life. In this model, both the equipment availability and average maintenance cost are treated as the objective functions and constrained by the equipment reliability as well as the total working time. The non-dominated sorting genetic algorithm II (NSGA-II) algorithm is adopted to solve the previous optimization problem, wherein the constrained inequality functions in the stages of initialization, mutation, and crossover are introduced to assess the solution to meet the constraints or not, through the improvements in three aspects, namely, the improvement of the algorithm’s initialization to ensure the initial variables meet the equality constraint, the utilization of the mean division of the difference values to adjust the variables after the selection, and crossover and mutation of the gene. Numerical analysis is carried out to verify the feasibility of the improved algorithm, wherefrom the Pareto-optimal solutions for the preventive maintenance of the platform firefighting vehicle are obtained to provide the optimum strategy for the service engineers with different weighted factors.

Multi-objective system reliability optimization has attracted the attention of several researchers, due to its importance in industry. In practice, the optimization regards multiple objectives, for example, maximize the reliability, minimize the cost, weight, and volume. In this article, an adaptive particle swarm optimization is presented for multi-objective system reliability optimization. The approach uses a Lévy flight for some particles of the swarm, for avoiding local optima and insuring diversity in the exploration of the search space. The multi-objective problem is converted to a single-objective problem by resorting to the weighted-sum method and a penalty function is implemented to handle the constraints. Nine numerical case studies are presented as benchmark problems for comparison; the results show that the proposed approach has superior performance than a standard particle swarm optimization.

For efficiently estimating the dynamic failure probability of the structure with random variables, stochastic processes and temporal and spatial multi-parameter, an estimation strategy is presented based on the random field transformation. The random field transformation focusing on the dynamic reliability with only one time parameter is further investigated, and it is extended to temporal and spatial multi-parameter issue, which simulates the output as multi-dimensional Gaussian random field. Also, the active learning Kriging method is used to construct the surrogate models for the mean function and auto-covariance function of performance function. After that, the temporal and spatial dynamic failure probability can be obtained by the simulation method. Although it doesn’t need to call the real performance function during the process of simulation method, it is time computationally expensive. To address this issue, the optimization algorithm procedure is established to estimate the dynamic failure probability. Several examples including an aero engine turbine disk and a cylindrical pressure vessel are introduced to illustrate the significance and effectiveness of the proposed methods for analyzing the temporal and spatial multi-parameter dynamic failure probability.

In reality, the forecast of uncertainties often becomes more accurate with the approaching of the forecasted period. This article proposes a rolling horizon approach to dynamically determine the production plan and the maintenance plan for a degradation system under uncertain environment. In each rolling horizon, demand forecasts are updated with new information from customers, and the degradation level of system is confirmed by inspection. By taking advantage of the updated uncertainties, at each decision point, the maintenance plan is determined by an advance-postpone balancing approach and the production plan is optimized by a heuristic algorithm in a two-stage stochastic model. Numerical results validate that the rolling horizon approach has great superiority over traditional stochastic programming approach in terms of real total cost and service level.

The reliability of k-barrier coverage for wireless sensor networks is evaluated in this article. We construct a two-dimensional k-within-consecutive-r × s-out-of-m × n:F system to describe the k-barrier coverage problem and propose the definition of the k-barrier coverage reliability. If the sensing radius r of each sensor is equal to half of the horizontal distance d between two adjacent sensors, then the formula for calculating the k-barrier coverage reliability can be derived directly. If r is a positive integer multiple of d, then a recursive algorithm is applied to calculate the coverage reliability. The effects of the probability that sensors are active, the number of rows of deployed sensors and the number of sensors in each row on the coverage reliability are also analyzed using some illustrative examples. The results show that, if r = d/2, the reliability of a barrier decreases with an increase in the length of the barrier; if r = t × d (t is a positive integer), the reliability of a barrier hardly decreases with an increase in the length of the barrier.

In the life cycle of a long-life structure, multiple maintenances are often required to ensure safety or normal performance. This article developed a multi-mission selective maintenance optimization model for a system with several multistate components over a finite time horizon. The model aims to minimize the total cost by determining the optimal intervention time and the corresponding maintenance option of each component. The system reliability requirement is taken as the constraint. The degradation process of each component is characterized by a homogeneous continuous time Markov chain in this model. Considering the uncertainties that exist during the deterioration–maintenance process, the condition state of each component at any time is described by a state probability vector. In addition, the components in the system are considered to be structurally dependent during the maintenance process, and a directed graph is used to represent the precedence relations among these components. A differential evolution algorithm is utilized to solve this complicated optimization model. A numerical example and an engineering application are presented to illustrate the availability of the proposed model.

The reliability of high-speed railway network is an important issue for the sustainable development of railway traffic. A high reliable railway network not only has a longer service life but also has a greater ability to resist destruction of the network. In this article, based on the theory of complex network, we construct a topological networked model to study and analyze the reliability of high-speed railway network with respect to the destruction caused by natural disasters, geological disasters, equipment failure, or man-made disasters. In real world, heavy rain and snow storms are frequent on a large scale. These destructed regions are represented by network communities. Here, we put forward an evaluation index to quantify the network reliability. Taking China high-speed railway network as an example, the results show that some key communities has great influence on the network reliability. When these key communities are destructed by some natural factors, the reliability of railway network would reduce greatly or even breakdown. In addition, we find that the network reliability with the number of deleted communities approximately shows an exponential law.

Due to the high failure rates and the high cost of operation and maintenance of wind turbines, not only manufacturers but also service providers try many ways to improve the reliability of some critical components and subsystems. In reality, redundancy design is commonly used to improve the reliability of critical components and subsystems. The load dependencies and failure dependencies among redundancy components and subsystems are crucial to the reliability assessment of wind turbines. However, the redundancy components are treated as a parallel system, and the load correlations among them are ignored in much literature, which may lead to the wrong system’s reliability and much higher costs. For this reason, this article explores the influences of load-sharing on system reliability. The whole system’s reliability is quantitatively evaluated using fault tree analysis and the Markov-chain method. Following this, the optimisation of the redundancy allocation problem considering the load-sharing is conducted to maximise the system reliability and reduce the total cost of the system subjecting to the available system cost and space. The results produced by this methodology can show a realistic reliability assessment of the entire wind turbine from a quantitative point of view. The realistic reliability assessment can help to design a cost-effective and more reliable system and significantly reduce the cost of wind turbines.

To build more credible degradation models, it is necessary to consider measurement errors in degradation analysis. This article proposes an inverse Gaussian-based state space model with measurement errors that can capture the unit-to-unit variability of the degradation rate by incorporating a random effect. Then, the lifetime distribution and alarm probabilities are derived. Under the non-Gaussian assumptions, conventional parameter estimation algorithms cannot be applied directly. Therefore, an improved expectation–maximization algorithm that is combined with particle methods is developed to estimate parameters. Finally, this article concludes with a simulation study and two case applications to demonstrate the applicability and advantages of the proposed model.

This article presents an algorithm for optimal redundancy and repair team allocation with respect to minimum system cost and a system availability constraint. Four scenarios are considered for the failures occurring in the subsystems of the system: independence, linear dependence, weak dependence, and strong dependence. An adaptive cuckoo optimization algorithm is developed for solving the nonlinear integer optimization problem of allocation. A series–parallel system with six subsystems is considered as a case study for demonstration purposes. The results obtained highlight the good performance of the developed algorithm.

The ride quality and running safety of high-speed trains are directly influenced by uncertainties of some key parameters, such as the damping and stiffness coefficients of suspension systems, wheel–rail coefficient of friction and wheel–rail profiles. Dynamic reliability problems of vehicle–track coupled systems under the influence of the above random parameters are studied in this article. An efficient numerical method is presented by combining a prediction-based iterative solution technique with subset simulation method. The solution efficiency of deterministic responses is improved by means of efficient prediction of wheel–rail forces, and the number of deterministic solutions required is reduced by expressing a small failure probability as a product of large conditional probabilities. The accuracy and the efficiency of the present method are verified by comparing with the direct Monte Carlo simulation. The failure probability distribution curves of the lateral ride index on straight track and the derailment coefficient during curve negotiation are obtained and the reliability sensitivity analyses are also carried out. The main conclusions are given as follows: the reliability of the system is higher when the randomness of the parameters with greater sensitivity is not considered; the increase of the damping of anti-yaw damper or the wheel–rail coefficient of friction will improve the ride quality on straight track, but will lower the running safety when negotiating a curved track.