Surface Defect Recognition (SDR) is crucial in the manufacturing industry. Recent advancements in deep learning and computer vision have significantly improved the precision and efficiency of SDR. However, the scarcity of defect samples presents a challenge for training deep learning models, making few-shot learning necessary for the SDR task. For this, this paper explores innovative contributions of Large Generative Models (LGM) to few-shot SDR by integrating Large Language Models (LLM) and Multimodal Generative Models (MGM). We present an LGM-based Training-Free Data Augmentation (LTDA) method to efficiently expand few-shot datasets without additional training. LTDA employs a conditional generation framework that leverages text instructions provided by LLM as conditions to guide the generation process of MGM. Additionally, multiple prompting templates have been designed for LLM to provide more precise instructions, thereby better guiding the conditional generation process. Finally, we employ two strategies for utilizing generated data to accomplish enhanced few-shot SDR by LTDA. The effectiveness of these approaches is demonstrated through two cases of defect recognition on steel surfaces, where the results demonstrate that the proposed method achieves an average accuracy improvement of 29% and 13% over the baseline method. The code will be released at https://github.com/jackiddd/LTDA.

Previous research on event log data analysis has primarily focused on identifying critical and frequent events, as well as qualitatively assessing correlations between event occurrences. However, the probabilistic behavior of frequently occurring events over time remains poorly understood. Through an in-depth exploratory analysis, we reveal that the (log) inter arrival times of events follow some mixture distributions with two modes, suggesting the presence of transitions between latent states. To better understand the data-generating mechanism underlying these frequent events, we employ Markov Modulated Renewal Processes (MMRPs), a type of hidden Markov model, to capture the patterns exhibited in the inter-arrival times between successive events. Due to limitations in record precision, some inter-arrival times are recorded as zero. To address this issue, we propose a simple data imputation algorithm to generate non zero inter-arrival times, facilitating inference on the inter-arrival time distributions and the underlying MMRPs. The effectiveness of the algorithm is validated using synthetic data. Finally, we evaluate the proposed model on real manufacturing system data, uncovering key insights into system states.

Non-destructive testing (NDT), particularly X-ray inspection, is vital for industrial quality assurance, yet existing deep-learning-based approaches often lack interactivity, interpretability, and the capacity for critical self-assessment, limiting their reliability and operator trust. To address these shortcomings, this paper proposes <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">InsightX Agent</small>, a novel LMM-based agentic framework designed to deliver reliable, interpretable, and interactive X-ray NDT analysis. Unlike typical sequential pipelines, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">InsightX Agent</small> positions a Large Multimodal Model (LMM) as a central orchestrator, coordinating between the Sparse Deformable Multi-Scale Detector (SDMSD) and the Evidence-Grounded Reflection (EGR) tool. The SDMSD generates dense defect region proposals from multi-scale feature maps and sparsifies them through Non-Maximum Suppression (NMS), optimizing detection of small, dense targets in X-ray images while maintaining computational efficiency. The EGR tool guides the LMM agent through a chain-of-thought-inspired review process, incorporating context assessment, individual defect analysis, false positive elimination, confidence recalibration and quality assurance to validate and refine the SDMSD's initial proposals. By strategically employing and intelligently using tools, <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">InsightX Agent</small> moves beyond passive data processing to active reasoning, enhancing diagnostic reliability and providing interpretations that integrate diverse information sources. Experimental evaluations on the GDXray+ dataset demonstrate that <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">InsightX Agent</small> not only achieves a high object detection F1-score of 96.54% but also offers significantly improved interpretability and trustworthiness in its analyses, highlighting the transformative potential of LMM-based agentic frameworks for industrial inspection tasks.

Intelligent Fault Diagnosis (IFD) has achieved notable advancements through deep learning technologies, yet it continues to confront significant challenges in complex industrial environments. Current methodologies exhibit limited frequency perception capabilities, which impedes the comprehensive capture of critical frequency components within fault signals, thereby affecting diagnostic accuracy. Furthermore, existing IFD approaches lack interpretability, making it challenging to correlate selected features with physical fault phenomena effectively, thereby diminishing the practical applicability of diagnostic outcomes. To address these issues, this paper presents an adaptive feature learning framework that integrates kurtosis-based explainable attention and frequency domain encoding(K-FDE) to enhance both the interpretability and accuracy of fault feature selection. The proposed framework incorporates a kurtosis-based interpretable fault feature selection module and an Fast Fourier Transform (FFT) based frequency domain encoding module, which together dynamically capture fault-relevant features while improving the interpretability of feature selection. Additionally, this framework introduces a Discrete Wavelet Transform (DWT)-driven frequency decomposition module and a Convolutional Neural Network (CNN)-driven feature learning module, facilitating detailed frequency decomposition from coarse to fine and multi-resolution frequency feature learning. Empirical evaluations on high-speed aerospace bearings and motor bearings datasets validate that the proposed method demonstrates exceptional noise robustness and superior frequency perception capabilities.

This study proposes a nonparametric sparse feature extraction approach based on a periodic Gaussian process (PGP) for highly nonlinear sparse periodic signals, which may not be effectively modeled by conventional linear models based on user-specified dictionaries. The PGP model is reformulated as a mixed-effects model. Hence a regularization term is allowed to be imposed on the random effect of the PGP model, called regularized PGP (RPGP) in this study, for sparse feature extraction. Unlike conventional sparse models, the proposed RPGP can simultaneously model fixed and random effects (global trend and local sparsity) of the signals. A computationally scalable algorithm based on the alternating direction method of multipliers (ADMM) is tailored for RPGP to iteratively optimize the fixed and random effects. The efficient computation of RPGP is achieved by a customized circulant-based acceleration technique that utilizes fast Fourier transform on circulant matrices. The performance of RPGP is evaluated through a simulation study on synthetic signals and a case study on real vibration signals.Note to Practitioners—This work is motivated by the problem of sparse feature extraction from highly nonlinear periodic signals with a complex global trend. The key issues involved in this problem include: 1) how to model the highly nonlinear periodic signals; 2) how to separate the periodic signals and the global trend from noisy signals; 3) how to extract the sparse periodic feature. Existing approaches for sparse feature extraction assume that the signals have a constant trend and can be effectively modeled by certain dictionaries. This work proposes a novel approach that leverages a regularized PGP to simultaneously extract the sparse periodic feature and the global trend. Moreover, the nonparametric nature of the PGP model enables automatic feature extraction, eliminating the need to manually select a dictionary for sparse periodic feature extraction. The proposed approach involves four main steps: 1) collecting periodic signals from embedded sensors; 2) modeling the signals with PGP models following the fixed effects framework; 3) training the model parameters using the proposed optimization procedure; 4) extracting the global trend and sparse periodic feature based on the model parameters. This paper demonstrated the application of rolling bearing vibration signals, while the effectiveness of the proposed model is not limited to this topic. Other periodic signals with similar characteristics can also be analyzed by applying the proposed model. In the future, this approach will be extended to handle sparse feature extraction from pseudo-periodic signals in a more complex noise environment.

Industrial data often consist of continuous variables (CVs) and binary variables (BVs), both of which provide crucial information about process operating conditions. Due to the coupling between industrial systems or equipment, these hybrid variables are usually high-dimensional and highly correlated. However, existing methods generally model hybrid variables directly in the observation space and assume independence between the variables to overcome the curse of dimensionality. Thus, they are ineffective at capturing dependencies among hybrid variables, and the effectiveness of process monitoring will be compromised. To overcome the limitations, this study proposes to seek a unified subspace for hybrid variables using the probabilistic latent variable (LV) model. By introducing a low-dimensional continuous LV, the proposed method can avoid the curse of dimensionality while capturing the dependencies between hybrid variables. Nevertheless, the inference of LV is analytically intractable and thus time-consuming due to the heterogeneity of CVs and BVs. To accelerate offline learning and online inference procedures, this study originally derives an analytical Gaussian distribution to approximate the true posterior distribution of the LV, based on which an efficient expectation-maximization algorithm is developed for parameter estimation. The Gaussian approximation is simultaneously optimized with the latest parameters to achieve a high approximation accuracy. The LV is then estimated by the posterior mean of the Gaussian approximation. By mapping the heterogeneous variables into a unified subspace, the proposed method defines three monitoring statistics, which are physically interpretable and thoroughly evaluate the probability of hybrid variables being normal. The effectiveness of the proposed method in detecting anomalies in CVs and BVs is shown through a numerically simulated case and a real industrial case.

Domain adaptation (DA) techniques are becoming increasingly proficient in cross-domain fault diagnosis tasks. However, DA-based methods are not always applicable due to the target domain data is not always accessible. Although there have been some interesting domain generalization methods for fault diagnosis under unseen conditions, most of them can only be used to mine the fault features on source domain distributions, and the improvement of model generalization performance is limited. To solve this problem, the multiplicative noise Gaussian perturbation strategy and the additive noise linear fusion strategy are proposed to capture fault information beyond source domain distributions. The former is used to randomly perturb feature statistics of multisource domains to simulate the uncertainty of domain shift, while the latter is used to perform the additive noise linear operation on feature statistics of multiple source domains to ensure the authenticity of the generated feature styles. Further, the feature statistics generated by both strategies are mixed with random convex weights to obtain new feature styles, achieving the best compromise between reliability and diversity. The network can learn more fault information from features with diversified styles. Extensive experimental results on both public and real datasets verify the effectiveness of our approach.

Although quality-related process monitoring has achieved the great progress, scarce works consider the detection of quality-related incipient faults. Partial least square (PLS) and its variants only focus on faults with larger magnitudes. In this article, a deep quality monitoring network (DQMNet) for quality-related incipient fault detection is developed. DQMNet includes the feature input layer, feature extraction layers, and the output layer. In the feature input layer, collected variables are divided according to quality variables, and then, features are extracted, respectively, through base detectors. For the feature extraction layers, singular values (SVs) of sliding-window patches and principal component analysis (PCA) are adopted to mine the hidden information layer by layer. For the output layer, statistics are constructed from quality-related/unrelated feature matrix through Bayesian inference. The superiority of DQMNet is demonstrated by a numerical simulation and the benchmark data of Tennessee Eastman process (TEP).

In the realm of pairwise lifetime model discrimination, it is a customary practice to frame it as a hypothesis test. In literature, generalized pivotal quantity (GPQ) emerges as an effective tool with complete observations, primarily owing to its advantages in addressing challenges posed by intricate parameter functions and limited sample size. In practical lifetime tests, the occurrence of censoring observations is not uncommon. Under this circumstance, the GPQ-based discrimination is infrequently employed primarily due to the inherent challenge of directly constructing the requisite GPQ. To tackle it, the present study first introduces an algorithm directly integrating data filling with GPQ. Then to mitigate the impact of data filling to GPQ, the generated samples from fiducial distribution also emulate the censoring and filling processes. This novel algorithm is thus designated as the “Mimic filling Algorithm.” For application purposes, this algorithm is applied to Type I censoring data, with the simulation study centered around widely encountered discrimination scenarios for Lognormal, Gamma, and Weibull distributions. In terms of two types errors, simulation results unequivocally demonstrate its superior performance compared to the direct integration of data filling with bootstrap, asymptotic normal approximation, and GPQ. Finally, this study applies the mimic-filling algorithm to discriminate two lithium-ion battery lifetime models with close-fitting results.

Capacity degradation of lithium-ion batteries largely determines the cost, performance and environmental impact of various products such as renewable energy production systems, portable electronics, and electric vehicles. Degradation assessment is thus of great importance for prognostic and health management of batteries, which ensures a stable production and operation. There are typically two leading sources contributing to the degradation of a lithium-ion battery, namely, cycling aging during charge/discharge cycles and calendar aging during idle states. However, most existing studies on degradation assessment either only consider a single source or ignore the coupling of these two sources, which makes the evaluation inefficient. A common observation in practice is that a battery tends to degrade faster when it experiences charge/discharge cycles continuously for a longer time. To capture this feature, this paper introduces the concept of the cumulative uninterrupted cycling duration (CUCD), which is defined as the consecutive operation duration since a battery ends the idle state. The CUCD can also help to model the coupling between the calendar and cycling aging. This paper then proposes to model the drift rate of cycling aging as a function of the CUCD and the functional form is determined with the monotonic spline. We estimate the model parameters by maximizing the likelihood function. Hypothesis testings toward the significance of the coupling between two aging sources and the monotonicity of the drift rate function under cycling aging are also provided. The effectiveness and the superiority of the model are validated using numerical and real case studies.Note to Practitioners—This study aims to characterize the degradation of lithium-ion battery simultaneously considering calendar and cycling agings and the coupling effect. Unlike previous research that only supplied experimental results to qualitatively illustrate the existence of the coupling effect between these two aging sources, this study provides procedures to quantitatively test the significance of such an effect. In addition, previous research ignored the coupling effect in the degradation modeling as it is difficult to capture, this study propose the concept of CUCD to characterize it. The CUCD is also introduced as a stress factor for cycling aging, which is based on the fact that a battery will degrade faster when it experiences charge/discharge cycle continuously for a longer time. Hypothesis testing is also provided to illustrate this monotonicity. To deal with another challenge that the expert knowledge of the functional form between cycling aging and CUCD is unavailable except for the monotonicity, a nonparametric method with the shape-restricted spline is adapted. The estimation procedures for the model parameters are also presented.

Maintenance logs of industrial equipment record descriptive and unstructured operation and maintenance (O&M) information, which is the basis of reliability, availability, and maintainability investigations. However, the construction of failure knowledge graphs as a basis for understanding the failure and maintenance properties of systems is challenging due to the requirement of annotation efforts and domain knowledge. This article proposes a novel semi-supervised method for failure knowledge graph construction. Initially, a semantic module is proposed to extract hidden contextual information from maintenance records and identify corresponding failure modes. The semantic module is trained by unlabeled maintenance records with the assistance of the hard pseudo-label acquisition and the proposed self-training algorithm. Subsequently, a taxonomy induction module is presented to extract failure items and their relationships to construct failure knowledge graphs that provide decision support. The feasibility and superiority of the proposed method are validated by maintenance logs from real wind farms. Overall, the proposed method provides an effective tool for semantic information digitalization of well-cumulated industrial O&M data.

Degradation analysis is essential in system health management and remaining useful life prediction. Since the observed degradation data are inevitably contaminated by measurement error, degradation state estimation is hence important for a more accurate evaluation of the health status. There are two challenges for estimating the degradation state. The first is the uncertainty associated with the estimated parameters for the model, and the other is the measurement outlier. Current models usually assume Gaussian measurement errors and they are sensitive to the measurement outlier. To deal with these two challenges, we develop a framework for degradation state estimation under the context of the distributionally robust optimization, which is robust to the parameter uncertainty. We further incorporate the Huber loss into this framework to make it robust to the measurement outlier. A procedure for estimation of the model parameters as well as setting the parameters of the ambiguity set is provided. The effectiveness of the model is validated using numerical and real case studies.

Applying machine vision to facilitate railway anomaly detections faces a grand challenge in that anomalous samples for model training are insufficient due to their infrequent occurrence and wide diversity. An anomaly-free representation learning approach (ARLA) is developed in this article to realize a machine vision-powered railway foreign object detection (RFOD) that does not rely on anomalous samples. The ARLA consists of two components, a memory-suppress diffusion network module and a contrastive dissimilarity network. The former network module well considers the diversity of normal patterns and reconstructs high-fidelity normal images. The latter network module enables image-level and pixelwise foreign object detections based on well-defined dissimilarity scores and distance maps. The ARLA realizes an efficient RFOD, which leverages only normal images in training and does not compromise the detection performance at the inference stage. Improvements offered by ARLA in terms of pixelwise detection performance and model complexity against two groups of benchmarks have been consistently observed based on computational studies using the railway dataset.

Degradation has become the dominant failure mode for highly reliable engineering systems. Cracking, a fatigue phenomenon composed of sequential phases of crack initiation and propagation, is a major concern for critical aircraft structures. Traditional fracture mechanics analysis cannot fully meet the requirements for assessing reliability indicators from a reliability analysis perspective. Alternatively, the empirical Lifetime Delayed Degradation Process (LDDP) provides an explanatory framework for sequential hard&soft failure mode. This study further generalizes the LDDP framework by introducing the Bayesian method as a Bayes-LDDP model, which incorporates a weakly informative prior derived from historical data of similar systems for both non-destructive and destructive inspections. Additionally, we compare our proposed method to the LDDP approach using specific inspection datasets. Two practical applications are conducted to demonstrate the effectiveness of the Bayes-LDDP model for reliability monitoring and remaining useful life (RUL) prediction in critical aircraft structures using field data. The crack inspection datasets of a transport aircraft and an aircraft core automated maintenance system (CAMS) are utilized for non-destructive and destructive inspections, respectively. The Markov Chain Monte Carlo (MCMC) sampling algorithm is adopted for the Bayes-LDDP, improving the computational efficiency of model parameters estimation compared to the stochastic expectation maximum (SEM) algorithm. Furthermore, the Bayes-LDDP model enables precise inference including the mean time to failure (MTTF) of cracks for destructive inspections and the RUL for non-destructive inspections under the selected optimal model. This extended novel framework provides a clear depiction of the lifetime delayed degradation process from a Bayesian perspective.

Reliability evaluation of complex systems like bridge systems or network model is of great interest but challenging as such reliability models cannot be recursively decomposed into combinations of series and parallel systems. The task becomes even more challenging if imprecise parameters are involved. To address such challenges, this article proposes a survival signature-based reliability framework for an imprecise multistate system (IMSS). For probability estimation, the survival signature of IMSS is first defined according to the combination of states of composing elements, and corresponding multistate survival functions are obtained. A simulation method is then developed to calculate thep-box when imprecision is involved. To further address the uncertainty, an approximate Bayesian computation method with a novel Jensen–Shannon divergence-based kernel is developed to perform a stochastic model updating. This method allows a better reliability evaluation result with less uncertainty by calibrating imprecise parameters in the presence of mixed uncertainty. A typical bridge system, which cannot be decomposed as simpler ones, is first cited as a numerical case, followed by a real application example for validation and benefit illustration.

Industrial process data are usually high-dimensional with dynamic characteristics, and a mix of continuous and binary quantities. However, current dynamic latent variable (DLV) methods primarily focus on analyzing continuous variables (CVs), overlooking the prevalence and significance of binary variables (BVs). BVs often serve as control references, indicating operating conditions or specific states and influencing the behavior of CVs. Integrating BVs into DLV models is crucial for elucidating the correspondence between CVs and BVs and uncovering the real operating patterns of the system. The main challenge lies in effectively accommodating the statistical heterogeneity exhibited by CVs and BVs, while comprehensively investigating their contemporaneous and temporal dependencies. To address this challenge, this study proposes a novel DLV model called hybrid probabilistic slow feature analysis (HPSFA). The HPSFA algorithm is specifically designed to extract slow features (SFs) from CVs while incorporating supervision from BVs. To efficiently infer posterior distributions of SFs, a variational recursive filter (VRF) is developed using the local approximation method, providing closed-form posterior estimations. Leveraging the VRF, an efficient expectation-maximization algorithm is proposed for parameter estimation. For process monitoring, three statistics are designed based on prediction or reconstruction errors, which are separated from dynamic variations and exhibit reduced variability. This reduction in variability enables the definition of narrower control regions while maintaining the desired confidence level. The HPSFA method is thoroughly evaluated through both simulated and real industrial case studies to demonstrate its validity and superior performance over existing approaches. The experimental results show that HPSFA timely detects both static and dynamic anomalies of the hybrid variables, and achieves the highest-fault detection rate (85.89%) while maintaining a considerably low-false alarm rate (2.67%) in the practical industrial case.

Condition monitoring plays a significant role in guaranteeing the reliability and safety of rotating machinery, which aims to detect an incipient fault and assess the degradation tendency. The construction of a health index (HI) is a crucial step to realize above tasks. At present, kurtosis, crest factor, and so on have been recognized as popular HIs to depict the operating condition. However, shortcomings of these classical HIs still exist: 1) classical HIs are prone to be affected by strong white Gaussian noise; 2) classical HIs are not sensitive to incipient faults. To deal with these two shortcomings, a reinforced noise resistant correlation method is proposed in this paper. Firstly, a new signal is constructed using the steps of segmenting and averaging to suppress the interference of noise. Then, a novel correlation function is used to get the hidden period. The proposed HI is constructed based on the discrete version of this correlation function to increase the sensitivity of incipient faults. Subsequently, theoretical values of the proposed HI under healthy states are investigated. The effectiveness of the method is demonstrated using simulated degradation processes and two accelerated degradation datasets of rolling element bearings. Through comparisons with other classical HIs, the proposed HI can simultaneously suppress the interference of strong noise and detect incipient faults. The comparison results identify the effectiveness of the proposed method in monitoring the condition of rotating machinery. Note to Practitioners—This work aims to provide a novel health index construction method for rotating machinery condition monitoring. The key issues involved in this problem include 1) how to capture the complex relationship between the measured vibration signals and the underlying health condition of rotating machinery; 2) how to suppress the interference of environmental noise. The novelty of this work is that it develops a method for condition monitoring considering the measured signals with strong white Gaussian noise. It properly captures the complex relationship between measured signals and the underlying health condition. There are four main steps to implement this approach: 1) collecting the vibration signals from rotating machinery; 2) constructing new periodic signal to suppress the interference of strong background noise; 3) constructing novel correlation functions to establish the relationship between the vibration signals and the underlying health condition of the rotating machine; 4) modeling the HI. A simulation and two real cases of the bearing degradation process are used to show that the proposed HI can simultaneously suppress the interference of strong noise and detect the incipient faults compared with some classical HI construction methods. In the future, the problem of how to address the measured signals contaminated by non-Gaussian noise and the machinery containing compound faults should be solved to extend this method in a complex system.

A real system may go through several states ranging from full performance to complete failure, carrying out infinite partial performances during service time. This article portrays such a nonbinary state of systems via the fuzzy membership function. Then, the relation between the system reliability under the binary state and that under the fuzzy state is deduced, on which a multitype component allocation problem (MCAP) is investigated to search for the optimal permutation of different types of components to maximize the fuzzy system reliability. After that, we inherit the exploration ability of genetic algorithm (GA) and the exploitation ability of Birnbaum importance (BI) to propose a fuzzy-BI-based two-stage approach combined with GA in order to deal with the MCAP under fuzzy state assumption efficiently and accurately. The k-out-of-n systems in both low and high dimensions are presented to illustrate the effectiveness of the proposed algorithm and demonstrate the similarity and difference between the MCAP under binary state and that under fuzzy state. The experimental results showcase that the proposed approach outperforms the existing state-of-the-art approaches for MCAP.

With the rapid progress of the industrial Internet of Things (IIoT), reducing data uncertainty has become a critical issue in predicting the development trends of systems and formulating future maintenance strategies. This article proposes an end-to-end, deep hybrid network-based, short-term, multivariate time-series prediction framework for industrial processes. First, the maximal information coefficient is adopted to extract the nonlinear variate correlation features. Second, a convolutional neural network with a residual elimination module is designed to eliminate data uncertainty. Third, a bidirectional gated recurrent unit network is connected in a time-distributed form to achieve step-ahead prediction. Last, an optimized Bayesian optimization method is adopted to optimize the model's learning rate. A comparison with other state-of-the-art, deep learning-based, time-series prediction methods in the case study illustrates the superiority of the proposed framework in noisy IIoT environments.

Nowadays, profile data mining techniques facilitate effective process monitoring, quality control, fault diagnosis, etc., with considerable benefits to manufacturing industry. However, regarding the complex system in modern manufacturing industry, there are two significant challenges for application development based on profile data mining. First, the staggering data volume leads to high memory and computational requirements. Second, the noisy signals in collected data may deteriorate useful information and model performance. This article proposes a novel algorithm for profile data mining called profile abstract, which simultaneously enables profile data compression and segmentation. The proposed algorithm mainly considers the scenario of fault diagnosis and can be utilized as a pre-processing step to address the above challenges. Profile abstract seeks to find a subset of raw data or a group of models as representatives that preserve the essential characteristics of raw data. Finding the data representatives helps reduce data redundancy while maintaining the model performance. Model representatives assist in describing the complex pattern of the profile, which can be used for pattern-based data segmentation. After data segmentation, information gain is adopted to determine the critical primitives for model improvement. In this article, validation of the proposed method's superiority is performed with two datasets from a real production line and one simulation dataset.

Suspension systems are significant for safe and comfort operation of high-speed trains. Health assessment is a useful tool to schedule maintenance plans of suspension systems, and furthermore ensure safety operation of high-speed railway transportation. In real operating condition, two problems, i.e. data imbalance and shortage of labelled data, result in difficult for health assessment of the suspension system using deep learning. In this work, a multi-sensor information fusion method, called as multi-sensor graph transfer network (MSGTN), is proposed in basis of deep transfer learning and graph neural network. In the proposed method, a domain-share multi-sensor graph neural network (MSGNN) is firstly proposed to extract features from vibration signals collected from three different positions in train vehicles. A graph-based fusion layer in MSGNN is proposed to fuse multi-sensor information by combining frequency response curves of the suspension system. The MSGTN mainly includes two parts in source and target domains respectively. In the source domain, a simple physical dynamic model of high-speed rail suspension system is built to generate labelled simulation datasets to pre-train MSGNN. In the target domain, the initial hyper-parameters of MSGNN are that of the pre-train model in the source domain. The labelled data in the target domain is fed to fine-tune MSGNN and then the final model for health assessment can be obtained by minimizing the loss function. The effectiveness of the proposed method was verified using real-work operation data.

A main challenge in reliability analysis of repairable systems is to model the heterogeneity in their failure behavior, which can be reflected by the corresponding recurrent failure-time data. To capture the system heterogeneity for data analysis, a system-specific random effect is typically introduced in most existing statistical models. In practice, the random effect of repairable systems tends to be time varying; for example, each repair action could change system's physical properties. Prior studies, however, generally do not take account of this time-varying nature and few of them circumvent the risk of model misspecification on the parametric distribution of frailty. In this article, we propose a semiparametric model that uses multivariate Gaussian convolution processes (MGCPs) to meet the above challenges. First, we use the trend RP to model the baseline intensity function of each repairable system. Based on the baseline intensity function, we then introduce MGCPs to simultaneously factor in heterogeneity and infer commonalities across multiple systems. A Bayesian framework is used for parameter estimation and time-to-failure prediction. Simulation studies show the advantages of our model in terms of robustness and estimation accuracy. A group of oil and gas well systems are used to illustrate the application of the proposed model.

Most classical accelerated degradation test (ADT) planning models implicitly overlook the errors when measuring the degradation levels of the test units. However, the sensor measurement errors are inevitable and the magnitude of the errors may have a trend to increase over time due to sensor degradation. As a consequence improperly overlooking the sensor degradation in ADT planning could result in a test plan with unsatisfactory performance. This article addresses this issue by proposing a sequential ADT planning model that factors in sensor degradation. The system degradation level is periodically measured, based on which we dynamically adjust the stress level during ADT. We adopt a Bayesian framework that periodically updates the posterior distribution of model parameters considering the sensor degradation. An approximate Bayesian computation algorithm is developed to circumvent the difficulty of directly evaluating the complicated likelihood function in our problem. Numerical studies on a gas turbine reveal that our sequential model outperforms several traditional ADT designs that overlook the sensor degradation.

Reliability-based design optimization (RBDO) is one of the most crucial techniques in complex and reliability-critical engineering systems. This has been a research hotspot over the past few decades. RBDO allows us to take into consideration the uncertainties from various sources, during the early design stage. It provides a design that satisfies various constraints as well as the reliability of the designed system performing the expected functions. Such capabilities can serve as countermeasures against the foreseeable uncertainties in the manufacturing or application process. Following a short preliminary overview of RBDO as well as the canonical strategies, this article sets out to review how surrogate models have been explored to streamline RBDO. This is done through a systematic study, outlining their respective advantages as well as disadvantages, and discussing the problems that need to be solved.

This article investigates the event-triggered output feedback control problem for unmanned aerial vehicle (UAV) systems over cognitive radio (CR) networks. A periodic event-triggered scheme is proposed in the presence of CR networks. By modeling the CR network as anon–offswitch, a new switched time-delay system model is developed for the event-triggered UAV. Based on the new model, the exponential stability and$H_{\infty }$performance criteria are derived by using the constructed Lyapunov function. Then, a co-design method is proposed to obtain mode-dependent controller gains and trigger parameters simultaneously. Finally, the proposed scheme is verified by a UAV system.

This paper proposes a condition-based maintenance (CBM) policy for a deteriorating system whose state is monitored by a degraded sensor. In the literature of CBM, it is commonly assumed that inspection of system state is perfect or subject to measurement error. The health condition of the sensor, which is dedicated to inspect the system state, is completely ignored during system operation. However, due to the varying operation environment and aging effect, the sensor itself will suffer a degradation process and its performance deteriorates with time. In the presence of sensor degradation, the Kalman filter is employed in this paper to progressively estimate the system and the sensor state. Since the estimation of system state is subject to uncertainty, maintenance solely based on the estimated state will lead to a suboptimal solution. Instead, predictive reliability is used as a criterion for maintenance decision-making, which is able to incorporate the effect of estimation uncertainty. Preventive replacement is implemented when the estimated system reliability at inspection hits a specific threshold, which is obtained by minimizing the long-run maintenance cost rate. An example of wastewater treatment plant is used to illustrate the effectiveness of the proposed maintenance policy. It can be concluded through our research that: 1) disregarding the sensor degradation while it exists will significantly increase the maintenance cost and 2) the negative impact of sensor degradation can be diminished via proper inspection and filtering methods.Note to Practitioners—This paper was motivated by the observation of sensor degradation in wastewater treatment plants but the developed approach also applies to other systems such as manufacturing systems, chemical plants, and pharmaceutical factories, where sensors are dedicated to a long-time operation in a harsh environment. This paper investigates the impact of sensor degradation on CBM and suggests that the effect of sensor degradation should be carefully addressed while making maintenance decisions. Otherwise, it will lead to a suboptimal maintenance decision and increase the operating cost. An optimal maintenance decision, which contains the optimal inspection interval and reliability threshold, is achieved via minimizing the long-run cost rate. In the presence of measurement noise and intrinsic uncertainty from degradation, a stochastic filtering approach is employed to estimate the system and sensor state. Based on the estimated states and the calculated reliability, a dynamic maintenance decision is obtained at each inspection. This paper can be further extended considering non-Gaussian noise and alternative degradation processes.

This article investigates the event-triggered observer-based output feedback load frequency control (LFC) problem for power systems. To reduce the amount of the transmitted signals, a dynamic event-triggered scheme is proposed by adding an exponential term. Moreover, an adaptive event-triggered scheme is proposed to provide a balance between the control performance and the number of the transmitted signals. Under the proposed schemes, a new model is formulated for the observer-based output feedback LFC system via a time-delay system method. By employing the Lyapunov functional method, sufficient conditions are derived for global asymptotical stability and$\mathcal L_{\infty }$performance. Then, a controller design method is developed. Finally, two examples are given to illustrate the effectiveness of the proposed schemes.

Traditional maintenance planning problems usually presume that preventive maintenance (PM) policies will be executed exactly as planned. In reality, however, maintainers often deviate from the intended PM policy, resulting in unpunctual PM executions that may reduce maintenance effectiveness. This article studies two imperfect PM policies with unpunctual executions for infinite and finite planning horizons, respectively. Under the former policy, imperfect PM actions are periodically performed and the system is preventively replaced at the last PM instant. The objective is to determine the optimal number of PM actions and associated PM interval so as to minimize the long-run average cost rate. However, the latter policy specifies that a system is subject to periodic PM activities within a finite planning horizon and there is no PM activity at the end of the horizon. The aim is then to identify the optimal number of PM activities to minimize the expected total maintenance cost. In this article, we discuss the modeling and optimization of the two unpunctual PM policies and then explore the impact of unpunctual executions on the optimal PM decisions and corresponding maintenance expenses in an analytical or numerical way. The resulting insights are helpful for practitioners to adjust their PM plans when unpunctual executions are anticipated.

One goal of software testing strategies is to detect faults faster. Dynamic Random Testing (DRT) strategy uses the testing results to guide the selection of test cases, which have shown to be effective in the fault detection process. However, the effectiveness of DRT still can be improved. In this paper, a distance-based DRT (D-DRT) strategy is proposed. The vectorized test cases are partitioned with k-means clustering method to obtain better classification, and the distance information are used to guide the test case selection, then the test cases that are close to failure-causing test cases are more likely to be selected, thus the testing process can be optimized. In the case study, the performance of D-DRT and other testing strategies are compared. The experiment results show that the proposed D-DRT strategy has better fault detection effectiveness than the others without significant increase in computational cost.

A particularly good software testing strategy is to achieve the underlying testing goal while solving the problems of tradeoffs between testing effectiveness and efficiency. To improve the fault detection effectiveness of software testing, the principle of feedback control theory was adopted, which motivated the proposal of dynamic random testing (DRT). The main idea behind DRT is using the testing results to guide the test case selection to increase the selection probabilities of the subdomains with higher fault detection rates. Previous works show that DRT strategy can achieve better effectiveness than random testing strategy and random partition testing strategy, and has significantly lower computational costs than adaptive testing strategy. However, the essential factors that affect the performance of DRT, i.e., adjusting parameters, initial profile, and test case classification have not been thoroughly investigated. Besides, some experimental assumptions are inconsistent with real scenarios. Therefore, this paper gives a series of investigations on DRT with a set of practical subject programs. More specifically, the effectiveness and efficiency of DRT are presented, and the extended experiments on DRT with relevant factors are conducted. The results indicate that the effectiveness of DRT is robust to different initial profiles and affected noticeably by the adjusting parameter settings and test case classification methods.

Transient fault (TF) and intermittent fault (IF) of complex electronic systems are difficult to diagnose. As the performance of electronic products degrades over time, the results of fault diagnosis could be different at different times for the given identical fault symptoms. A dynamic Bayesian network (DBN)-based fault diagnosis methodology in the presence of TF and IF for electronic systems is proposed. DBNs are used to model the dynamic degradation process of electronic products, and Markov chains are used to model the transition relationships of four states, i.e., no fault, TF, IF, and permanent fault. Our fault diagnosis methodology can identify the faulty components and distinguish the fault types. Four fault diagnosis cases of the Genius modular redundancy control system are investigated to demonstrate the application of this methodology.

Digital networked control systems are of growing importance in safety-critical systems and perform indispensable function in most complex systems today. Networked degradations such as transmission delay and packet dropout cause such systems to fail to satisfy performance requirements, and eventually affect the overall reliability. It is necessary to get a model to verify and evaluate the system reliability in early design phase, prior to its implementation. However, existing probabilistic models only provide partial descriptions of such coupled networks and control system. In this paper, a new stochastic model represented by linear discrete-time approach is proposed, considering data packet transmissions in both channels: controller-to-actuator and sensor-to-controller. Different from pervious works, the historical behaviors of networked degradations are modeled by multistate Markov chains with uncertainties, releasing the assumption that faults of all periods are independent of each other. The concept of domain requirements for such systems is considered here, contributing to the integration of control and reliability engineering. Methodologies for quantitatively assessing the reliability of the single- and sequential-control goal are derived from the Monte Carlo method. An example of an industrial heat exchanger digital networked control system is provided to illustrate the effectiveness of the model and method.

Fault diagnosis is useful in helping technicians detect, isolate, and identify faults, and troubleshoot. Bayesian network (BN) is a probabilistic graphical model that effectively deals with various uncertainty problems. This model is increasingly utilized in fault diagnosis. This paper presents bibliographical review on use of BNs in fault diagnosis in the last decades with focus on engineering systems. This work also presents general procedure of fault diagnosis modeling with BNs; processes include BN structure modeling, BN parameter modeling, BN inference, fault identification, validation, and verification. The paper provides series of classification schemes for BNs for fault diagnosis, BNs combined with other techniques, and domain of fault diagnosis with BN. This study finally explores current gaps and challenges and several directions for future research.

This paper develops a maintenance policy for a multicomponent system subject to hidden failures. Components of the system are assumed to suffer from hidden failures, which can only be detected at inspection. The objective of the maintenance policy is to determine the inspection intervals for each component such that the long-run cost rate is minimized. Due to the dependence among components, an exact optimal solution is difficult to obtain. Concerned with the intractability of the problem, a heuristic method named “base interval approach” is adopted to reduce the computational complexity. Performance of the base interval approach is analyzed, and the result shows that the proposed policy can approximate the optimal policy within a small factor. Two numerical examples are presented to illustrate the effectiveness of the policy.

Control systems are among the most important subsystems for their ability to undertake indispensable functions in safety-critical systems. Since many key components of such systems follow different performance degradation paths, therefore it is important to have an approach capable of correctly estimating the performance of control systems containing a variety of degraded components. One solution is to endow an existing estimation approach to equip with a capability to cope with uncertainties and inadequate system specifications. This paper presents a hybrid model capable of improving existing approaches by applying the Laplace transform to the time-varying model of the control system while taking into account the varying behaviors of components over different time slices. Reliability is estimated through an event-based Monte Carlo simulation that does not require knowledge of the exact reliability function. System reliability is improved by using the particle swarm optimization method. The method searches for the optimal parameters of the control strategy by compensating for the loss in effectiveness caused by degraded components. The proposed approach is validated through a case study conducted on a simulated cooling system. Numerical results have shown that the proposed approach is capable of improving the reliability of control systems subject to total run time constraints.

Software reliability is one of the most significant attributes in various safety-critical systems. One popular approach to estimate the software reliability is based on Bayesian statistics. However, there are few attempts on Bayesian approaches considering fault correction process. In this paper, we present parameter estimation method based on Bayesian statistics for combined fault detection and correction processes. A practical example is devoted to investigating the fitting performance of the proposed Bayesian approach.

Software quality prediction is an important yet difficult problem in software project development and management. Historical datasets can be used to build models for software quality prediction. However, the missing data significantly affects the prediction ability of models in knowledge discovery. Instead of ignoring missing observations, we investigate and improve incomplete-case k-nearest neighbor based imputation. K-nearest neighbor imputation is widely applied but has rarely been improved to have the most appropriate parameter settings for each imputation. This work conducts imputation on four well-known software quality datasets to discover the impact of the new imputation method we proposed. We compare it with mean imputation and other commonly used versions of k-nearest neighbor imputation. The empirical results show that the proposed dynamic incomplete-case nearest neighbor imputation performs better when the missingness is completely at random or non-ignorable, regardless of the percentage of missing values.

Software reliability growth modeling plays an important role in software reliability evaluation. To incorporate more information and provide more accurate analysis, modeling software fault detection and correction processes has attracted widespread research attention recently. However, the assumption of the stochastic fault correction time delay brings more difficulties in modeling and estimating the parameters. In practice, other than the grouped fault data, software test records often include some more detailed information, such as the rough time when one fault is detected or corrected. Such semi-grouped dataset contains more information about fault removal processes than commonly used grouped dataset. Using the semi-grouped datasets can improve the accuracy of time delayed models. In this paper, a fault removal modelling framework for software reliability with semi-grouped data is studied and extended into multi-released software. Also, the corresponding parameter estimation is carried out with Maximum Likelihood estimation method. One test dataset with three releases from a practical software project is applied with the proposed framework, which shows satisfactory performance with the results.

The IG process models have been shown to be an important family in degradation analysis. In this paper, we are interested in optimal constant-stress accelerated degradation tests (ADTs) planning when the underlying degradation follows the inverse Gaussian (IG) process. We first consider ADT planning for the IG process without random effects. Asymptotic variance of the estimate of a lower quantile is derived, and the objective of the planning is to minimize this variance by properly choosing the testing stresses, and the number of samples allocated to each stress. Next, ADT planning for a random-effects IG process model is considered. We then applied the IG process to fit the stress relaxation data of a component, and use the developed methods to help with the optimal ADT design.

Reliability analysis of complex systems is a critical issue in reliability engineering. Motivated by practical needs, this paper investigates a Bayesian approach for system reliability assessment and prediction with multilevel heterogeneous data sets. Two major imperatives have been handled in the proposed approach, which provides a comprehensive Bayesian framework for the integration of multilevel heterogeneous data sets. In particular, the pass-fail data, lifetime data, and degradation data at different system levels are combined coherently for system reliability analysis. This approach goes beyond the alternatives that deal with solely multilevel pass-fail or lifetime data, and presents a more practical tool for real engineering applications. In addition, the indices for reliability assessment and prediction are constructed coherently within the proposed Bayesian framework. It gives rise to a natural manner of incorporating this approach into a decision-making procedure for system operation and management. The effectiveness of the proposed approach is illustrated with reliability analysis of a navigation satellite.

This paper proposes a sequential failure limit maintenance policy for a repairable system. The objective system is assumed to have$k+1$states, including one working state and$k$failure states, and the multiple failure states are classified potentially by features such as failure severity or failure cause. The system deteriorates over time and will be replaced upon the$N$th failure. Corrective maintenance is performed immediately upon each of the first$(N-1)$failures. To avoid the costly failure, preventive maintenance actions will be performed as soon as the system's reliability drops to a critical threshold$R$. Both preventive maintenance and corrective maintenance are assumed to be imperfect. Increasing and decreasing geometric processes are introduced to characterize the efficiency of preventive maintenance and corrective maintenance. The objective is to derive an optimal maintenance policy$(R^{\ast},N^{\ast})$such that the long-run expected cost per unit time is minimized. The analytical expression of the cost rate function is derived, and the corresponding optimal maintenance policy can be determined numerically. A numerical example is given to illustrate the theoretical results and the maintaining procedure. The decision model shows its adaptability to different possible characteristics of the maintained system.

The operation process or environment usually has a significant influence on system lifetime. In this paper, a lifetime optimization approach based on linear programming (LP) is proposed to maximize the transportation system lifetime, in which a semi-Markov (SM) model is used to model the operation process. In the proposed method, we first formulate the optimization problem as an LP model that is used to find the optimal transient probability of each state. Then, an analytical method is performed to obtain the corresponding optimal sojourn-time distribution parameters of the SM process. Finally, the proposed approach is applied to a port oil transportation system to show that it can efficiently ensure that the transportation system has a long lifetime.

In this paper, a new quantitative risk analysis model of integrating fuzzy fault tree (FFT) with Bayesian Network (BN) is proposed. The first step involves describing a fuzzy fault tree analysis technique based on the Takagi and Sugeno model. The second step proposes the translation rules for converting FFT into BN. Based on this, the integration algorithm is demonstrated by an offshore fire case study. The example clearly shows that FFT can be directly converted into BN and the classical parameters of FFT can be obtained by the basic inference techniques of BN. By using the advantages of both techniques, the model of integrating FFT with BN is more flexible and useful than traditional fault tree model. This new model not only can be used for describing the causal effect of accident escalation but also for computing the occurrence probability of accident based on historical data and fuzzy logic.

Abstract With the enhancement of hardware and software engineering, the effectiveness and correctness of software is less and less doubted and customers are more aware about whether software services are available or not when needed. Software maintenance is one of the main reasons that make software unavailable and it is often very expensive to perform maintenance tasks. Common approaches of studying software maintenance are to consider it as a static by‐product of software operation and only the maintenance cost is covered. In this paper, software maintenance policies are studied with the consideration of unavailable service time. A non‐homogeneous continuous Markov chain is adopted for modeling the software operation and maintenance process, and the cost of software unavailability that is brought in by software maintenance is investigated and analyzed for searching the optimal maintenance policy, which aims at minimizing the average maintenance time cost. The optimality of our proposed policy is shown and checked by numerical examples with discussions of its possible application perspectives. Copyright © 2010 John Wiley & Sons, Ltd.

There has been quite some research on the development of tools and techniques for grid systems, yet some important issues, e.g., grid service reliability and task scheduling in the grid, have not been sufficiently studied. For some grid services which have large subtasks requiring time-consuming computation, the reliability of grid service could be rather low. To resolve this problem, this paper introduces Local Node Fault Recovery (LNFR) mechanism into grid systems, and presents an in-depth study on grid service reliability modeling and analysis with this kind of fault recovery. To make LNFR mechanism practical, some constraints, i.e. the life times of subtasks, and the numbers of recoveries performed in grid nodes, are introduced; and grid service reliability models under these practical constraints are developed. Based on the proposed grid service reliability model, a multi-objective task scheduling optimization model is presented, and an ant colony optimization (ACO) algorithm is developed to solve it effectively. A numerical example is given to illustrate the influence of fault recovery on grid service reliability, and show a high efficiency of ACO in solving the grid task scheduling problem.

In this paper, a nonparametric method is proposed for the estimation of decreasing mean residual life with type II censored data. This method is based on the comparison between two estimators of the reliability function: the Kaplan-Meier estimator, and an estimator derived from the empirical MRL function. Simulation results indicate that the new approach is able to give good performance, and can outperform some existing parametric methods when censoring is heavy.

Mean residual life is an important statistic in reliability analysis. Based on a general functional form of the derivative of the mean residual life, we propose a new lifetime distribution with an upside-down bathtub-shaped mean residual life function. The model has its mean residual life function in a simple, closed form so that further analysis based on the mean residual life can be easily carried out. We study the analysis and applications on both the mean residual life function, and the failure rate function of this model. Maximum likelihood method is used for parameter estimation. Numerical examples and comparisons indicate that the new model performs well in modeling lifetime data with bathtub-shaped failure rate functions, and upside-down bathtub-shaped mean residual life function.

Software maintenance effort estimation is essential for the success of software maintenance process. In the past decades, many methods have been proposed for maintenance effort estimation. However, most existing estimation methods only produce point predictions. Due to the inherent uncertainties and complexities in the maintenance process, the accurate point estimates are often obtained with great difficulties. Therefore some prior studies have been focusing on probabilistic predictions. Analogy Based Estimation (ABE) is one popular point estimation technique. This method is widely accepted due to its conceptual simplicity and empirical competitiveness. However, there is still a lack of probabilistic framework for ABE model. In this study, we first propose a probabilistic framework of ABE (PABE). The predictive PABE is obtained by integrating over its parameter k number of nearest neighbors via Bayesian inference. In addition, PABE is validated on four maintenance datasets with comparisons against other established effort estimation techniques. The promising results show that PABE could largely improve the point estimations of ABE and achieve quality probabilistic predictions.

Grid computing is a recently developed technique for complex systems with large-scale resource sharing, wide-area communication, and multi-institutional collaboration. Although the development tools and techniques for the grid have been extensively investigated, the availability of the grid resource management system (RMS) has not been comprehensively studied. In order to contribute to this lacking but important field, this paper first models the grid RMS availability by considering both the failures of resource management (RM) servers and the length limitation of request queues. A hierarchical Markov reward model is implemented to evaluate the grid RMS availability. Based on the availability model, an optimization problem for designing the grid RMS is studied in order to minimize the cost by determining the best number of RM servers. Then, the sensitivity analysis is conducted, and a dynamic switching scheduling method is further presented based on the sensitivity analysis.

Software reliability modeling & estimation plays a critical role in software development, particularly during the software testing stage. Although there are many research papers on this subject, few of them address the realistic time delays between fault detection and fault correction processes. This paper investigates an approach to incorporate the time dependencies between the fault detection, and fault correction processes, focusing on the parameter estimations of the combined model. Maximum likelihood estimates of combined models are derived from an explicit likelihood formula under various time delay assumptions. Various characteristics of the combined model, like the predictive capability, are also analyzed, and compared with the traditional least squares estimation method. Furthermore, we study a direct, useful application of the proposed model & estimation method to the classical optimal release time problem faced by software decision makers. The results illustrate the effect of time delay on the optimal release policy, and the overall software development cost.

Any population of components produced might be composed of two sub-populations: weak components are less reliable, and deteriorate faster whereas strong components are more reliable, and deteriorate slower. When selecting an approach to classifying the two sub-populations, one could build a criterion aiming to minimize the expected mis-classification cost due to mis-classifying weak (strong) components as strong (weak). However, in practice, the unit mis-classification cost, such as the cost of mis-classifying a strong component as weak, cannot be estimated precisely. Minimizing the expected mis-classification cost becomes more difficult. This problem is considered in this paper by using ROC (Receiver Operating Characteristic) analysis, which is widely used in the medical decision making community to evaluate the performance of diagnostic tests, and in machine learning to select among categorical models. The paper also uses ROC analysis to determine the optimal time for burn-in to remove the weak population. The presented approaches can be used for the scenarios when the following information cannot be estimated precisely: 1) life distributions of the sub-populations, 2) mis-classification cost, and 3) proportions of sub-populations in the entire population.

In software reliability modeling, the parameters of the model are typically estimated from the test data of the corresponding component. However, the widely used point estimators are subject to random variations in the data, resulting in uncertainties in these estimated parameters. Ignoring the parameter uncertainty can result in grossly underestimating the uncertainty in the total system reliability. This paper attempts to study and quantify the uncertainties in the software reliability modeling of a single component with correlated parameters and in a large system with numerous components. Another characteristic challenge in software testing and reliability is the lack of available failure data from a single test, which often makes modeling difficult. This lack of data poses a bigger challenge in the uncertainty analysis of the software reliability modeling. To overcome this challenge, this paper proposes utilizing experts' opinions and historical data from previous projects to complement the small number of observations to quantify the uncertainties. This is done by combining the maximum-entropy principle (MEP) into the Bayesian approach. This paper further considers the uncertainty analysis at the system level, which contains multiple components, each with its respective model/parameter/ uncertainty, by using a Monte Carlo approach. Some examples with different modeling approaches (NHPP, Markov, Graph theory) are illustrated to show the generality and effectiveness of the proposed approach. Furthermore, we illustrate how the proposed approach for considering the uncertainties in various components improves a large-scale system reliability model.

Grid computing focuses on large-scale resource sharing. Using a general reliability model for grid computing to relax some impractical assumptions, a heuristic algorithm is presented to evaluate grid program/service reliability. The heuristic algorithm is based on two heuristic criteria that determine the significance of an entity and prune those insignificant ones. Through algorithm analysis, the heuristic algorithm is shown to have a linear complexity. This is much better than the previous algorithms, which are of exponential complexity. Another advantage of the heuristic algorithm is that the running time is controllable by adjusting the parameter of significant level (SL) and significant rate. A regression method is proposed to adjust the SL and predict the running time. Two examples are given

Generally, software reliability models can provide accurate reliability measurement in the later phase of testing. However, predictions in the early phase of software testing are useful as cost-effective and timely feedback. Early prediction is also feasible in practice with information from previous releases or similar projects. Such information has been utilized well for early reliability prediction with NHPP models by assuming the same failure rate between two similar projects. Alternatively, in this paper, we propose to "reuse" failure data from past projects/releases with ANN models to improve early reliability for current project/release. To illustrate the proposed approach, two numerical examples are developed. Better prediction performance is observed in early phase of testing compared with original ANN model without failure data reuse. Furthermore, the optimal switching point from proposed approach to original ANN model in the whole testing phase is studied, with specific analysis on the two examples

It is well-known that accurate reliability estimates can be obtained by using software reliability models only in the later phase of software testing. However, prediction in the early phase is important for cost-effective and timely management. Also this requirement can be achieved with information from previous releases or similar projects. This basic idea has been implemented with nonhomogeneous Poisson process (NHPP) models by assuming the same testing/debugging environment for similar projects or successive releases. In this paper we study an approach to using past fault-related data with artificial neural network (ANN) models to improve reliability predictions in the early testing phase. Numerical examples are shown with both actual and simulated datasets. Better performance of early prediction is observed compared with original ANN model with no such historical fault-related data incorporated. Also, the problem of optimal switching point from the proposed approach to original ANN model is studied, with three numerical examples

Most of the models for software reliability analysis are based on reliability growth models which deal with the fault detection process only. In this paper, some useful approaches to the modeling of both software fault detection and fault correction processes are discussed. Since the estimation of model parameters in software testing is essential to give accurate prediction and help make the right decision about software release, the problem of estimating the parameters is addressed. Taking into account the dependency between the fault correction process and the fault detection process, a new explicit formula for the likelihood function is derived and the maximum likelihood estimates are obtained under various time delay assumptions. An actual set of data from a software development project is used as an illustrative example. A Monte Carlo simulation is carried out to compare the predictive capability between the LSE method and the MLE method

Grid is a type of large-scale distributed system. This paper develops a fast algorithm to efficiently evaluate the grid program/service reliability. It is shown to have a linearly increasing complexity. Compared to the previous exponential algorithms, it broadens the applicability of the generic model into large/complex grid service problems. Moreover, the running time of the fast algorithm is controllable. A regression method is proposed to predict and manage running time.

Software inspection has been broadly accepted as a cost effective approach for defect removal during the whole software development lifecycle. To keep inspection under control, it is essential to measure its effectiveness. As human-oriented activity, inspection effectiveness is due to many uncertain factors that make such study a challenging task. Bayesian networks modeling is a powerful approach for the reasoning under uncertainty and it can describe inspection procedure well. With this framework, some extensions have been explored in this paper. The number of remaining defects in the software is proposed to be incorporated into the framework, with expectation to provide more information on the dynamic changing status of the software. In addition, a different approach is adopted to elicit the prior belief of related probability distributions for the network. Sensitivity analysis is developed with the model to locate the important factors to inspection effectiveness.

Most software reliability models assume independence of successive software runs. It is a strict assumption, and usually not valid in reality. Goseva-Popstojanova & Trivedi (2000) presented an interesting study on failure correlation among successive software runs. In this paper, by extending their results, a software reliability model is developed based on a Markov renewal process for the modeling of the dependence among successive software runs, where more than one type of failure is allowed in general formulation. Meanwhile, the cases of restarting with repair, and without repair, are considered. Although such a model is more complex than the traditional approach based on reliability growth, it incorporates more information about the failures, and system structure. A numerical example is also shown to illustrate the procedure, and provide some comparison.

The effect of a repair of a complex system can usually be approximated by the following two types: minimal repair for which the system is restored to its functioning state with minimum effort, or perfect repair for which the system is replaced or repaired to a good-as-new state. When both types of repair are possible, an important problem is to determine the repair policy; that is, the type of repair which should be carried out after a failure. In this paper, an optimal allocation problem is studied for a monotonic failure rate repairable system under some resource constraints. In the first model, the numbers of minimal & perfect repairs are fixed, and the optimal repair policy maximizing the expected system lifetime is studied. In the second model, the total amount of repair resource is fixed, and the costs of each minimal & perfect repair are assumed to be known. The optimal allocation algorithm is derived in this case. Two numerical examples are shown to illustrate the procedures.

The PLP (power-law process) or the Duane model is a simple model that can be used for both reliability growth and reliability deterioration. GOF (goodness-of-fit) tests for the PLP have attracted much attention. However, the practical use of the PLP model is its graphical analysis or the Duane plot, which is a log-log plot of the cumulative number of failures versus time. This has been commonly used for model validation and parameter estimation. When a plot is made, and the coefficient of determination, R/sup 2/, of the regression line is computed, the model can be tested based on this value. This paper introduces a statistical test, based on this simple procedure. The distribution of R/sup 2/ under the PLP hypothesis is shown not to depend on the true model parameters. Hence, it is possible to build a statistical GOF test for the PLP. The critical values of the test depend only on the sample size. Simulations show that this test is reasonably powerful compared with the usual PLP GOF tests. It is sometimes more powerful, especially for deteriorating systems. Implementing this test needs only the computation of a coefficient of determination. It is much easier than, for example, computing an Anderson-Darling statistic. Further study is needed to compare more precisely this new test with the existing ones. But the R/sup 2/ test provides a very simple and useful objective approach for decision making with regard to model validation.

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

It is widely recognized that the debugging processes are usually imperfect. Software faults are not completely removed because of the difficulty in locating them or because new faults might be introduced. Hence, it is of great importance to investigate the effect of the imperfect debugging on software development cost, which, in turn, might affect the optimal software release time or operational budget. In this paper, a commonly used cost model is extended to the case of imperfect debugging. Based on this, the effect of imperfect debugging is studied. As the probability of perfect debugging, termed testing level here, is expensive to be increased, but manageable to a certain extent with additional resources, a model incorporating this situation is presented. Moreover, the problem of determining the optimal testing level is considered. This is useful when the decisions regarding the test team composition, testing strategy, etc., are to be made for more effective testing.

Grid computing system is different from conventional distributed computing systems by its focus on large-scale resource sharing, where processors and communication have significant influence on grid computing reliability. Most previous research on conventional small-scale distributed systems ignored the communication time and processing time when studying the distributed program reliability, which is not practical in the analysis of grid computing systems. This paper describes the property of the grid computing systems and presents algorithms to analyze the grid program and system reliability.

For many safety critical systems, redundancy is the only acceptable method to achieve high operational reliability as individual modules can hardly be certified to have reached that level. When limited resources are available in the testing of a redundant software system, it is important to allocate the testing-time efficiently so that the maximum reliability of the complete system is achieved. In this paper, this problem is investigated in detail. A general formulation is presented and a specific case is used to illustrate the procedure. The case where individual module reliability requirements are given is also considered.

The traditional approach of reliability prediction using software reliability growth models requires a large number of failures which might not be available at the beginning of the testing. The commonly used maximum likelihood estimates may not even exist or converge to a reasonable value. In this paper, an approach of making use of information from similar projects in order to obtain an early estimation of one model parameter for a current project is studied. As most of the two-parameter reliability growth models contains one parameter related to the number of faults in the software and a reliability growth rate parameter related to the testing efficiency, information from a similar project can used to estimate the reliability growth rate parameter and the limited failure data from initial testing is used to estimate the other parameter. Our case study shows that this approach is very easy to use as the estimation does not require a numerical algorithm and it always exists. It is also very stable and when the maximum likelihood estimates exist and are reasonable, our approach gives values very close to that, and the approximate confidence interval is overlapping for most cases.

Handbook of Software Reliability a software product is also discussed, but in a Engineering.

Most software reliability models are applicable to a single piece of software. For more complex systems, Markov models have been studied assuming that complete reliability information at the module level is available. We study an additive model which assumes that each subsystem or module undergoes independent testing and the reliability of the complete system has to be assessed. Subsystem reliabilities are estimated and the system reliability is assessed using the additive model. The approach is simple, but generic in a sense that existing models can be combined. An example is also presented based on the log-power-model, a model with simple graphical interpretation and it shows that the modular information should be used for system reliability assessment whenever such information is available.

In the development of software systems, it is important to determine when the software testing can be stopped and when the system can be released. An optimum release time is usually determined by minimizing the expected total cost under a reliability requirement. Usually the optimum release time depends on the unknown parameters in the underlying reliability growth models and these parameters have to be estimated based on collected testing data. Because of the random nature of the software failure process, there are some problems with the stability of the estimates of model parameters. This makes the conventional procedures for the determination of optimum software release time not robust. Although an extensive literature exists on the problem of software release time determination, few papers address the robustness issue. In this paper, the robustness of optimum release time procedures is studied. The variation of the optimum release time, due to the variation of the estimated parameters, is considered. It is recommended that the optimum release time with its standard error should be taken into consideration. Specifically, the interval estimation of the optimum release time is given for the Goel-Okumoto model and we demonstrate that the robustness can be achieved using interval estimation. Some numerical examples using both real testing data and simulated ones are presented to illustrate the idea.

Abstract Many articles on software reliability models have been published in the last two decades. Because of the importance of this area and increasing interest in it, this annotated bibliography of 100 selected publications has been prepared. First, books, edited works and review papers of general interest are summarized and this is followed by separate introductions to various types of models.

A software reliability model based on a nonhomogeneous Poisson process (NHPP) was proposed by N.F. Schneidewind (Sigplan Notices, vol.10, p.337, 1975). Since then, many other NHPP models have been suggested and studied by various authors. The authors show that several NHPP models can be derived based on the general assumptions made by Schneidewind. Also, they note that in the original paper, there are several interesting approaches worth further consideration. To mention a few, Schneidewind modelled both the software correction process and the software detection process. Methods of weighted least squares were adopted together with the software reliability forecasting based on previous measurements. In this paper, the Schneidewind model is revisited and some further research result are presented.>

A simple software reliability model, the log-power nonhomogeneous Poisson process (NHPP) model, is studied. The log-power NHPP model has several interesting properties, such as simple graphical interpretations and simple forms of the maximum likelihood estimates for the parameters. The authors assess this model by considering its simplicity, data fitting and predicting ability. They have applied the log-power model to many sets of existing software reliability data. The results show that this model is able to fit different data sets and has a relatively high predicting ability. This, together with its simplicity and the graphical interpretation which provides a useful reliability engineering tool, shows that the log-power model is an applicable software reliability model in practice.>

One of the important applications of software reliability models is the determination of software release time. The author presents some software release policies and discusses the problem of determination of optimum test time. Both reliability requirements and cost models are considered in obtaining specific release policies. It is noted that acceptable failure intensity should be used as a reliability goal and optimum release policy should be based on sequential approach. Some other interesting software release policies are also reviewed.>