Reliability modeling and analysis of load-sharing systems with continuously degrading components

This paper presents a reliability modeling and analysis framework for load-sharing systems with identical components subject to continuous degradation. It is assumed that the components in the system suffer from degradation through an additive impact under increased workload caused by consecutive failures. A log-linear link function is used to describe the relationship between the degradation rate and load stress levels. By assuming that the component degradation is well modeled by a step-wise drifted Wiener process, we construct maximum likelihood estimates (MLEs) for unknown parameters and related reliability characteristics by combining analytical and numerical methods. Approximate initial guesses are proposed to lessen the computational burden in numerical estimation. The estimated distribution of MLE is given in the form of multivariate normal distribution with the aid of Fisher information. Alternative confidence intervals are provided by bootstrapping methods. A simulation study with various sample sizes and inspection intervals is presented to analyze the estimation accuracy. Finally, the proposed approach is illustrated by track degradation data from an application example

A performance-based warranty for products subject to competing hard and soft failures

This article studies a performance-based warranty for products subject to competing hard and soft failures. The two failure modes are competing in the sense that either one, on a "whichever-comes-first" basis, can cause the product to fail. A performance-based warranty not only covers the repair or replacement of any defect, but also guarantees the minimum performance level throughout the warranty period. In this article, we propose three compensation policies—that is, free replacement, penalty, and full refund, when a product's performance fails to meet the guaranteed level. The expected warranty servicing costs for the three policies are derived, based on the competing risks concept. A warranty design problem is further formulated to simultaneously determine the optimal product price, warranty length, and performance guarantee level so as to maximize the manufacturer's total profit. Numerical studies are conducted to demonstrate and compare the three performance-based compensation policies. It is shown that the full refund policy always leads to the lowest total profit, whereas neither of the other two policies can dominate each other in all scenarios. In particular, the free replacement policy results in a higher total profit than the penalty policy when the replacement cost is low, the penalty cost coefficient is high, and/or the product reliability is high

A mixture of variational canonical correlation analysis for nonlinear and quality-relevant process monitoring

Proper monitoring of quality-related variables in industrial processes is nowadays one of the main worldwide challenges with significant safety and efficiency implications.Variational Bayesian mixture of canonical correlation analysis (VBMCCA)-based process monitoring method was proposed in this paper to predict and diagnose these hard-to-measure quality-related variables simultaneously. Use of Student's t-distribution, rather than Gaussian distribution, in the VBMCCA model makes the proposed process monitoring scheme insensitive to disturbances, measurement noises, and model discrepancies. A sequential perturbation (SP) method together with derived parameter distribution of VBMCCA is employed to approach the uncertainty levels, which is able to provide a confidence interval around the predicted values and give additional control line, rather than just a certain absolute control limit, for process monitoring. The proposed process monitoring framework has been validated in a wastewater treatment plant (WWTP) simulated by benchmark simulation model with abrupt changes imposing on a sensor and a real WWTP with filamentous sludge bulking. The results show that the proposed methodology is capable of detecting sensor faults and process faults with satisfactory accuracy

Accelerated degradation tests planning with competing failure modes

Accelerated degradation tests (ADT) have been widely used to assess the reliability of products with long lifetime. For many products, environmental stress not only accelerates their degradation rate but also elevates the probability of traumatic shocks. When random traumatic shocks occur during an ADT, it is possible that the degradation measurements cannot be taken afterward, which brings challenges to reliability assessment. In this paper, we propose an ADT optimization approach for products suffering from both degradation failures and random shock failures. The degradation path is modeled by a Wiener process. Under various stress levels, the arrival process of random shocks is assumed to follow a nonhomogeneous Poisson process. Parameters of acceleration models for both failure modes need to be estimated from the ADT. Three common optimality criteria based on the Fisher information are considered and compared to optimize the ADT plan under a given number of test units and a predetermined test duration. Optimal two- and three-level optimal ADT plans are obtained by numerical methods. We use the general equivalence theorems to verify the global optimality of ADT plans. A numerical example is presented to illustrate the proposed methods. The result shows that the optimal ADT plans in the presence of random shocks differ significantly from the traditional ADT plans. Sensitivity analysis is carried out to study the robustness of optimal ADT plans with respect to the changes in planning input

Maintenance optimisation for systems with multi-dimensional degradation and imperfect inspections

In this paper, we develop a maintenance model for systems subjected to multiple correlated degradation processes, where a multivariate stochastic process is used to model the degradation processes, and the covariance matrix is employed to describe the interactions among the processes. The system is considered failed when any of its degradation features hits the pre-specified threshold. Due to the dormancy of degradation-based failures, inspection is implemented to detect the hidden failures. The failed systems are replaced upon inspection. We assume an imperfect inspection, in such a way that a failure can only be detected with a specific probability. Based on the degradation processes, system reliability is evaluated to serve as the foundation, followed by a maintenance model to reduce the economic losses. We provide theoretical boundaries of the cost-optimal inspection intervals, which are then integrated into the optimisation algorithm to relieve the computational burden. Finally, a fatigue crack propagation process is employed as an example to illustrate the effectiveness and robustness of the developed maintenance policy. Numerical results imply that the inspection inaccuracy contributes significantly to the operating cost and it is suggested that more effort should be paid to improve the inspection accuracy

3-Hydr­oxy-4-nitro­phenyl acetate

In the mol­ecule of the title compound, C8H7NO5, the acetate group is oriented with respect to the aromatic ring at a dihedral angle of 85.30 (3)°. An intra­molecular O—H⋯O hydrogen bond results in the formation of a non-planar six-membered ring, adopting an envelope conformation. In the crystal structure, inter­molecular C—H⋯O hydrogen bonds link the mol­ecules

Warranty service contracts design for deteriorating products with maintenance duration commitments

With the increasing diversification of customers’ demand and purchasing behaviors, more and more manufacturers have focused their attention on the warranty service contracts design. The maintenance duration of the sold product, which plays an important role in the normal production and operation process of the user, is frequently taken into consideration in warranty contracts. In this study, we design different warranty contracts with various combinations of maintenance duration and availability requirements. The manufacturer commits to compensate for each overdue repair or failing to satisfy the availability target. The customers’ choice behavior is described by the multinomial logit (MNL) model, and customers often form their own minimum acceptable levels (also referred to as reference points) of maintenance duration and availability when making purchasing decisions, which have an impact on the contract choice. The expected warranty servicing profit is maximized to determine the optimal price, maintenance duration and availability. Finally, the proposed warranty contracts are demonstrated by numerical examples. We find that the maintenance duration affects not only the warranty cost but also the customer choice, which further affects the optimal contract pricing and profits

Online reinforcement learning for condition-based group maintenance using factored Markov decision processes

We investigate a condition-based group maintenance problem for multi-component systems, where the degradation process of a specific component is affected only by its neighbouring ones, leading to a special type of stochastic dependence among components. We formulate the maintenance problem into a factored Markov decision process taking advantage of this dependence property, and develop a factored value iteration algorithm to efficiently approximate the optimal policy. Through both theoretical analyses and numerical experiments, we show that the algorithm can significantly reduce computational burden and improve efficiency in solving the optimization problem. Moreover, since model parameters are unknown a priori in most practical scenarios, we further develop an online reinforcement learning algorithm to simultaneously learn the model parameters and determine an optimal maintenance action upon each inspection. A novel feature of this online learning algorithm is that it is capable of learning both transition probabilities and system structure indicating the stochastic dependence among components. We discuss the error bound and sample complexity of the developed learning algorithm theoretically, and test its performance through numerical experiments. The results reveal that our algorithm can effectively learn the model parameters and approximate the optimal maintenance policy

Variability of Gene Expression After Polyhaploidization in Wheat (Triticum aestivum L.)

Interspecific hybridization has a much greater effect than chromosome doubling on gene expression; however, the associations between homeologous gene expression changes and polyhaploidization had rarely been addressed. In this study, cDNA–single strand conformation polymorphism analysis was applied to measure the expression of 30 homeologous transcripts in naturally occurring haploid (ABD, 2n = 21) and its polyploid maternal parent Yumai 21A (AABBDD, 2n = 42) in wheat. Only one gene (TC251989) showed preferentially silenced homoeoalleles in haploids. Further analyses of 24 single-copy genes known to be silenced in the root and/or leaf also found no evidence of homeologous silencing in 1-month-old haploids and two ESTs (BF484100 and BF473379) exhibit different expression patterns between 4-month-old haploids and hexaploids. Global analysis of the gene expression patterns using the Affymetrix GeneChip showed that of the 55,052 genes probed, only about 0.11% in the shoots and 0.25% in the roots were activated by polyhaploidization. The results demonstrate that activation and silencing of homoeoalleles were not widespread in haploid seedlings

1-Benzyl-3-methyl­imidazolium chloride 0.25-hydrate

The asymmetric unit of the title compound, C11H13N2 +·Cl−, contains two independent ion pairs and and half a solvent water mol­ecule (m site symmetry for the O atom). The imidazole ring is oriented at dihedral angles of 66.61 (3) and 89.17 (3)° with respect to the aromatic ring in the two cations. In the crystal, O—H⋯(O,Cl) hydrogen bonds and π–π stacking inter­actions between the imidazole ring of one mol­ecule and the aromatic ring of another [perpendicular distance = 3.4 (4) Å] link the mol­ecules