ABSTRACT. Accurate prediction of the cumulative number of software faults as well as quantitative software reliability has been still a challenging issue in software reliability for a long time. Especially, weighted combinational models based on multiple software reliability growth models (SRGMs) have received a considerable attention to improve the prediction accuracy, but have not been satisfactorily formulated during the last five decades. In this paper, we develop novel approaches to predict the future behavior of the cumulative number of software faults detected in the system testing, by means of multimodel inference consisting of both the model averaging and clustering techniques, where the underlying SRGMs are described by the common non-homogeneous Poisson processes. The model averaging techniques employed here possess an information-theoretic and frequentist perspective, and are characterized by well-known information criteria to determine the each model weight. Several clustering techniques are also applied to cluster the underlying SRGM candidates for prediction. In comprehensive numerical experiments with both time-domain and time-interval software fault count data, we compare our SRGM averaging techniques with the common approach based on the single use of SRGM. It is shown with actual software fault count data that SRGM averaging enabled us to improve the prediction accuracy significantly.

ABSTRACT. Systems are often subject to the interaction of internal degradation and external random shocks, making them prone to premature failures. This study aims to explore the impacts of random shocks and resilience (self-healing capabilities) on the maintenance policy for a deteriorating system to minimize the expected total cost rate. This study considers the scenario where resilience diminishes with both the system operational time and the number of random shocks and investigates the impact of preventive maintenance actions on various levels of resilience. Mathematical models for the expected total cost rate under proportional resilience systems are constructed, and the optimal preventive maintenance policy for each system is determined when the lifetime distribution of the system is Weibull. Finally, some conclusions are drawn through numerical analysis for decision-makers in assessing system replacement and preventive maintenance policies.

ABSTRACT. In this work we derive exact and easy to compute expressions for simple repair policies of coherent systems subject to simultaneous failures of its components. Indeed, we consider a reliability system where each component can be in a working or failed state, and each configuration of these implies that the system is also in either a working or failed state. We assume that the system is coherent, i.e., roughly speaking, a system where more working components imply a higher "chance" of the system being working. Moreover, we consider that the components can fail simultaneously, say by shocks that take down several components at once. We model these shocks using the Lévy-frailty Marshall-Olkin distribution for the vector of lifetimes of the components. In this setting, we study simple repair policies, where we replace all failed components when there are r or more broken components or when the system fails. That is, we assume that failed components can be replaced, incurring a component replacement cost, and also that the system can be repaired after failure, at a higher system repair cost. In this way, there is a trade-off between saving the replacement cost of components by letting them fail, but at the risk of having a higher chance of the system failing and thus having to pay a higher system repair cost. Our main result is an exact and easily computable expression for the long-term average cost of these repair policies. We validate our results with Monte Carlo simulations.

ABSTRACT. In this investigation, a preventive replacement policy for a system with shock damage interaction is considered, in which the concept of replacement last is adopted. The system is subject to shocks. As shock occurs, the system experience either type I (minor) or type II (major) failure. The former brings some random additional damage to the system and is rectified via minimal repair, while the latter causes the system failure. The probabilities of these two failure types depend on the number of shocks suffered since the last replacement. We assume that shocks occur at a nonhomogeneous pure birth process. The system with cumulative damage y also undergoes a minor failure with probability q(y) at type I failure instant. Such failure is removed via minimal repair. A system fails when the total damage exceeds a failure level K or a type II failure occurs. To control the deterioration process, the preventive replacement is implemented before failure at age T or at the nth type I failure, or when the total damage exceeds a pre-defined level Z but less than a failure level K, whichever comes last. This work aims to analytically and numerically determine the optimal preventive replacement schedule which minimize the average cost rate.

ABSTRACT. This paper considers two important opportunity-based block type models under the assumption that the arrival of opportunities obeys a stochastic point process. For more details, the block type models under the replacement first and replacement last disciplines are formulated in the environment where the opportunity process obyes a Markovian arrival process (MAP). Replacement first is the preventive replacement is performed at the prescheduled time T or the opportunity point YN , whichever comes first. Conversely, Replacement last is the preventive replacement is performed at the prescheduled time T or the opportunity point YN , whichever comes last. The MAP is one of the general point processes and involves a Poisson process and some renewal process classes. In this paper, the expected costs in the steady state under replacement first and replacement last disciplines are formulated.

ABSTRACT. In our previous work, we developed a highly reliable FE model for calculating low circumferential fatigue under multiaxial loading. Subsequently, we generated high-confidence datasets using the FEA models. By leveraging the strengths of both deep learning methods and LightGBM, we proposed a fusion surrogate model called DL-LGBM-DRS. The DL-LGBM-DRS can efficiently and accurately predict low-cycle fatigue life under various multiaxial loading conditions.

ABSTRACT. Engineering components such as engine blades, turbofans, external parts, etc., are often subject-ed to complex loads in the serving environment. Fatigue failure of components under multiaxial loading will occur, causing a severe influence on operational safety. Centered on low-cycle fatigue under multiaxial loading conditions, we have developed a novel fatigue life prediction framework, which utilizes the physics-guided machine learning approach as a surrogate model for fatigue life prediction. We conducted preliminary experiments to obtain the material's mechanical properties and established reliable Finite Element Analysis (FEA) models based on these properties. Eventually, we can successfully predict low-cycle fatigue life in various loading environments.

ABSTRACT. Accurate prediction for the remaining useful life (RUL) of Lithium-ion batteries is important to the prognosis and health management of the batteries. This study focus on the rest effect of capacity regeneration, i.e., the battery capacity will increase after a period of rest time. Our research explores the relationship of the battery conditions, such as continuous charge-discharge cycle number and rest time with the capacity degradation. We propose the piecewise random coefficient models to capture the trend of capacity degradation under the given continuous charge-discharge cycle number and rest day. Our models improve the prediction accuracy of the RUL more effectively than those don’t consider the regeneration effect. We provide the point estimation, interval estimation, and the distribution of the RUL.

ABSTRACT. Accurate and timely detection of anomalies in lithium-ion batteries is crucial for ensuring their reliability and safety. Complex degradation patterns and limited availability of labeled data pose significant challenges in identifying abnormal battery behaviors at earlier cycles of reliability test in real applications. This paper proposes an unsupervised adaptive mixture distribution-based Bayesian convolutional autoencoder (AMDBCAE) method for anomaly detection in lithium-ion batteries at earlier stages of cycling test. We propose a mixture of the Laplace and Student's t distributions as the prior in the BCAE model. Using a modified form of the Bayes by backprop algorithm, the parameter of mixture proportion is adaptively updated to capture diverse and complex degradation patterns in battery degradation data more efficiently. Extracted (latent) features are then processed through unsupervised clustering algorithms to identify abnormal behaviors of lithium-ion batteries. The analysis of a real-world lithium-ion battery dataset demonstrates the efficiency and accuracy of the proposed unsupervised framework with limited number of testing data. The proposed method addresses the limitations of manual feature extraction and the need for extensive experimental knowledge by leveraging the adaptive BCAE model to automatically extract latent features as a virtual health indicator in a sparse data environment.

ABSTRACT. The warm standby system has been widely used in engineering. Hence, exploring both theoretical and practical aspects of this system holds significant practical implications. This talk introduces a special warm standby system featured with two spare parts. Based on the attributions of the system, various reliability metrics are computed through Markov models. Notably, the warm standby system is redefined through the aggregated Markov model. Furthermore, two optimal spare parts problems are addressed. Finally, numerical illustrations are employed to elucidate the results obtained in the talk.

ABSTRACT. Reliability analysis of balanced system has become a key factor for the safe operation of some important equipment and the perfect completion of some important missions. As some real systems consisting of several subsystems with different levels of performance and under degradation processes when in operations are relatively common, they have received widely concerned in the recent years, but are rarely in the new reliability research field of balanced systems, the researches on the balanced systems by considering multi-state are rare, and even few researches are in combination with degradation processes. In this paper, a new balanced system for the multi-state system under degradation processes by considering new failure criteria is put forth. The system consists of two subsystems and fails when either subsystem enters into absorbing states, a new model is proposed and applied to two special cases by assuming that the thresholds of the sojourn time in upcoming unbalanced subsets are constant and random variables respectively, and this paper is the first to extend balanced systems into competing risks. The related expressions of the reliability indexes are derived by employing the theory of aggregated stochastic processes. Finally, numerical examples are presented and some future research topics are also discussed.

ABSTRACT. In this paper, several linear two-dimensional consecutive k-type systems are studied, which include the linear connected-(k, r)-out-of-(m, n):F system and the linear l-connected-(k, r)-out-of-(m, n):F system without/with overlapping. Reliabilities of these systems are studied via the finite Markov chain imbedding approach (FMCIA) in a novel way. Some numerical examples are provided to illustrate the theoretical results established here and also to demonstrate the efficiency of the developed method. Finally,some possible applications and generalizations of the developed results are pointed out.

ABSTRACT. The information criteria are often used for model selection to determine the best fit model to the observed data, but do not guarantee the best prediction model for the future (unknown) data. The present article concerns the dependency relationship between software bug prediction and information criteria, and investigates the applicability of software reliability models selected by the information criteria through empirical experiments with actual software bug count data.

ABSTRACT. Software reliability evaluation is important. Among various methods, interval estimation is easy to feed back to flexible decision making by providing upper and lower bound. Thus, we consider the interval estimation of software reliability in this paper. The limitation of existing studies is that creating resamples for constructing the confidence interval is time-consuming. We address this problem by introducing parametric simulation methods, and we verify the effectiveness of the proposed method by analyzing real data.

ABSTRACT. When software fails due to small or large problems, such as coding or operational errors, it can cause major problems in the field, so research has been continuously conducted to reduce software failures and increase software reliability. In the past, many software reliability models were developed by assuming NHPP, but there was a problem that they only fit well in special cases where assumptions were made. In this study, we propose a new software reliability model using deep learning that does not include assumptions and relies on data. The deep learning techniques used are DNN, RNN, LSTM, and GRU, and we demonstrate the superiority of the models using the NTDS failure dataset. The results show that the software reliability model using LSTM has the best results.

ABSTRACT. For artificial systems, the rising cost and inaccessible scenes for maintenance have increased the need of self-healing, which intends to give systems the ability to heal the damage and faults without external intervention like living organisms. Although self-healing techniques have been widely studied and applied in many engineering systems, reliability research for such systems is limited, especially for the multi-component systems. To bridge this gap, a multi-component system with self-healing components is investigated in this paper. The self-healing behavior of the component implies the process that components remove some types of faults automatically during the system operation. States of the system are classified into three types: working, break and failed. Systems in both the break states and the failed states would stop working, but the main difference is that systems in a break state may have opportunities to return a working state if some components are self-healed. Once a system enters a failed state, the system can never be back to a working state until some maintenance actions are made. Then based on the assumptions, evolutions of the system states could also be modelled by a continuous-time homogeneous Markov process. Some reliability measures are derived, including the system reliability and the distribution of some duration times. Moreover, systems under both the break and failed states would experience some periods of downtime. In practice, if the downtime is shorter than a predefined threshold, the downtime will have little influence on the performance of the systems, thus can be neglected. For the self-healing multi-component system, a new reliability model is developed in this paper. Instantaneous and limiting average availabilities are derived to characterize the reliability of the system. Some reliability-related time distributions, i.e., distribution for the real working time in an effective working period, distribution for the neglected downtime in an effective working period, are also derived to provide a more comprehensive description of the reliability of the system.

ABSTRACT. Cascading failure is a phenomenon that minor disturbances trigger a chain reaction failure of the system, causing the disaster to quickly spread in the system and causing part or all of the system to collapse. In this paper, a reliability model for coupled cascade failure systems is developed based on Markov process. The model describes the dynamic propagation process of the cascade between coupled systems. In such systems, the subsystems are affected not only by component failures leading to load redistribution, but also by the states of other subsystems coupled to them. Three load effect modes are proposed that consider the number of working components, the influence range, and the distance. The reliability and safety of the systems with different types of cascading failures is analyzed, and formulas computing reliability indexes are derived.

ABSTRACT. In this paper, we investigate the maintenance problem of a production system where maintenance delay and dynamic environmental accessibility are considered. The system can be a single-component system or a series system with multiple components. It operates in a dynamic environment modelled by a discrete time Markov chain. The impact of the environment is twofold. Both the system productivity and the maintenance activity depend on the environment state. A preventive maintenance framework for a general production system. The component(s) are ageing with time, described either by their degradation levels or the time elapsed since their last renewal epochs. For a specific maintenance scheduling, some reliability and production measure are proposed to assess the system characteristics. The maintenance cost in the long-run horizon is also derived. We solve these problems in the framework of a semi-regenerative process. To further illustrate the properties of the policy, we show how the model is adaptive to single-component systems in detail. An example concerning a two-component production system is also presented. The model can provide theoretical references for decision-makers when maintenance delay and dynamic maintenance accessibility needs to be taken into account.

ABSTRACT. In many knowledge fields, we frequently encounter variables belonging to the interval (0, 1) such as percentages, proportions, fractions, index, among others. Regressions are often considered for modelling the functional relationship of these response variables with suitable covariates. However, few articles can be tracked about quantile regressions, mixture regressions, and change-point regressions for data lying on the unit interval. Compared with mean regressions, quantile regressions are known to be more robust and provide complete views of data. Mixture regressions are helpful for exploring and classifying data. Change-point regressions provide the important information about the time and the pattern of changes in the functional relationships. Both mixture regressions and change-point regressions are important techniques for data analyzers. In this study, we developed switching quantile regression models by using the unit-Weibull distribution to analyze continuous data on the unit interval. There are few articles relate to this study and we can foresee the widely applications of this study. Coping with the logit link, the mixture regression parameters are solved through maximum likelihood estimations by using the expectation-maximization (EM) algorithm. Simulation results show the proposed method is feasible for modeling the quantile data based on switching regressions. For the practicability of this method, we applied our algorithms on a real data set also.

ABSTRACT. Mixture regression models are employed for determining the relationship between variables from several unknown latent groups. They have been widely applied in real applications including econometrics, biology, epidemiology, engineering, and marketing, among others. Moreover, finite mixture modelling has been a longstanding topic in the research of model-based clustering. Mixture regressions are known as switching regressions. Modelling data with outliers or having heavy tails, multimodal, and skew distributions is often encountered in practice. It is in demand of a simple and efficient method in analyzing switching regressions with skew distributed errors. We propose a method by using a finite mixture of normal distributions to capture the skewness of data and embed it in the switching regression models. Our study focuses on two parts. We start from modeling data by assuming regression errors follow a finite mixture of normal distributions. Next, we extend it to the mixture regression models that each component model has errors following a finite mixture of normal distributions. For each part of the study, we develop an expectation and maximization (EM)-type algorithm, which is good at handling data with unobserved variables, to estimate regression coefficients and other model parameters simultaneously. In order to show the efficacy of the proposed methods, some simulations of the proposed algorithm have been done. Simulation results show the proposed method is feasible for modelling skew data based on mixture regressions. We applied our algorithms to real data, and compared the performance of our method with the existing methods in the literature. The proposed method is feasible and can be applied to skew data sets.

ABSTRACT. To ensure accurate reliability analysis for products, we usually use multivariate data regarding the products. Since the reliability varies from product to product, it can be modeled by probability distributions. However, existing probability distributions lack the flexibility to account for dependence among multivariate data. In particular, most multivariate distributions, such as the multivariate normal distribution, are unable to express asymmetric dependence among variables. Such incomplete probabilistic modeling may yield dubious results of the reliability analysis if the dependence is asymmetric. The objective of this study is to propose a new class of multivariate distributions that can express asymmetric dependence as well as symmetric one by combining copulas. Copulas are multivariate distributions whose all marginal distributions are uniform distributions in the interval [0,1], and they are powerful tools for modeling high-dimensional and non-linear dependence of variables. In this study, we provide a practical application of the proposed distribution for a geotechnical problem as an example in the reliability analysis. The result demonstrates that the proposed distribution fits the data better than existing models by appropriately considering the asymmetric dependence observed in the data.

ABSTRACT. Good warranty data is scarce, and even data that has been collected reliably is subject to censoring. This can limit the amount of data available for conducting warranty cost analysis, or can require the use of specialised statistical methods for censored data. An alternative method is to identify products that have been fully-observed for the warranty coverage period, and then generate synthetic data based on this subset. This provides a larger set of data, which can be used for further analysis. This paper presents an approach for synthetic data generation. The approach will be demonstrated and evaluated using an example with automotive warranty data. Opportunities for future work will be discussed.