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In industry, many highly reliable products possess multiple performance characteristics (PCs) and they typically degrade simultaneously. When such PCs are governed by a common failure mechanism or influenced by a shared operating environmental condition, interdependence between these PCs arises. To model such dependence, this article proposes a novel multivariate reparameterized inverse Gaussian (rIG) process model. It utilizes an additive structure; that is, the degradation of each marginal PC is considered as the result of the sum of two independent rIG processes, with one capturing the shared common effects across all PCs and the other describing the intrinsic randomness specific to that PC. The model has some nice statistical properties, and the system lifetime distribution can be conveniently approximated. An expectation-maximization algorithm is proposed for estimating the model parameters, and a parametric bootstrap method is designed to derive the confidence intervals. Comprehensive numerical simulations are conducted to validate the performance of the inference method. Two case studies are thoroughly investigated to demonstrate the applicability of the proposed methodology. for this article are available online. [ABSTRACT FROM AUTHOR]

Qu, Dassios, and Zhao (2021) suggested an exact simulation method for tempered stable Ornstein–Uhlenbeck processes, but their algorithms contain some errors. This short note aims to correct their algorithms and conduct some numerical experiments. [ABSTRACT FROM AUTHOR]

The step-stress accelerated degradation test (ADT) provides a feasible method for assessing the storage life of high-reliability, long-life products. However, this method results in a slower rate of performance degradation at the beginning of the test, significantly reducing the test efficiency. Therefore, this article proposes an assessment method for the step-down stress ADT that considers random effects and detection errors (SDRD). Firstly, a new Inverse Gaussian (IG) model is proposed. The model introduces the Gamma distribution to characterize the randomness of the product degradation path and uses the normal distribution to describe the detection errors of performance parameters. In addition, to solve the problem that the likelihood function of the IG model is complex and has no explicit expression, the Monte Carlo (MC) method is used to estimate unknown parameters of the model. This approach enhances computational accuracy and efficiency. Finally, to verify the effectiveness of the SDRD method, it is applied to the step-down stress ADT data from a specific missile tank to assess its storage life. Comparing the life assessment results of different methods, the conclusion shows that the SDRD method is more effective for assessing the storage life of high-reliability, long-life products. [ABSTRACT FROM AUTHOR]

The accelerated Degradation testing (ADT) experiments are important technical methods in reliability studies. Different type of accelerating degradation models has developed with the time and can be used in different types of situations. However, it has become necessary for the manager to test how many numbers of unit should be tested at a particular stress level so that the cost of testing is less. Accelerated Degradation testing (ADT) is preferred to be used in mechanized industries to obtain the required information about the reliability of product components and materials in a short period of time. Accelerated test conditions involve higher than usual pressure, temperature, voltage, vibration or any other combination of them. Data collected at such accelerated conditions are extrapolated through a physically suitable statistical model to estimate the lifetime distribution at design condition stress the life data collected from the high stresses the need to be extrapolated to estimate the life distribution under the normal-use condition. A special class of the ADT is the step-stress testing which regularly increases the stress levels at some pre-fixed time points until the test unit fails. Such experiments allow the experimenter to run the test units at higher-than-usual stress conditions in order to secure failures more quickly. The Inverse Gaussian process is flexible in incorporating random effects and explanatory variables. The different types of models based on IG process are random drift model, random volatility model and random drift-volatility model. In this paper we have considered random drift model for the study on stochastic degradation models for simple step-stress model using inverse Gaussian process observed in degradation problems. [ABSTRACT FROM AUTHOR]

A system of n$$ n $$ components is here considered, with component deterioration modeled by non decreasing time‐scaled Lévy processes. When a component fails, a sudden change in the time‐scaling functions of the surviving components is induced, which makes the components stochastically dependent. We compute the reliability function of coherent systems under this new dependence model. We next study the distribution of the ordered failure times, and establish some positive dependence properties. We also provide stochastic comparison results in the usual multivariate stochastic order between failure times of two dependence models with different parameters. Finally, some numerical experiments illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Albeit not equivalent, in many applications the gamma and the inverse Gaussian processes are treated as if they were. This circumstance makes the misspecification problem of these models interesting and important, especially when data are affected by measurement errors, since noisy/perturbed data do not allow to verify whether the selected model is actually able to adequately fit the real (hidden) degradation process. Motivated by the above considerations, in this paper we conduct a large Monte Carlo study to evaluate whether and how the presence of measurement errors affects this misspecification issue. The study is performed considering as reference models a perturbed gamma process recently proposed in the literature and a new perturbed inverse Gaussian process that share the same non‐Gaussian distributed error term. As an alternative option, we also analyze the more classical case where the error term is Gaussian distributed. We consider both the situation where the true model is the perturbed gamma and the one where it is the perturbed inverse Gaussian. Model parameters are estimated from perturbed data using the maximum likelihood method. Estimates are retrieved by using a new sequential Monte Carlo EM algorithm, which use allows to hugely mitigate the severe numerical issues posed by the direct maximization of the likelihood. The risk of incurring in a misspecification is evaluated as percentage of times the Akaike information criterion leads to select the wrong model. The severity of a misspecification is evaluated in terms of its impact on maximum likelihood estimate of the mean remaining useful life. [ABSTRACT FROM AUTHOR]

Accelerated degradation tests (ADTs) are widely used to assess lifetime information under normal use conditions for highly reliable products. For the accelerated tests, two basic assumptions are that changing stress levels does not affect the underlying distribution family and that there is stochastic ordering for the life distributions at different stress levels. The acceleration invariance (AI) principle for ADTs is proposed to study these fundamental assumptions. Using the AI principle, a theoretical connection between the model parameters and the accelerating variables is developed for Hougaard processes. This concept can be extended to heterogeneous gamma and inverse Gaussian processes. Simulation studies are presented to support the applicability and flexibility of the Hougaard process using the AI principle for ADTs. A real data analysis using the derived relationship is used to validate the AI principle for accelerated degradation analysis. All technical details, simulation results for nonlinear cases and model mis‐specification analysis are available online as Supporting Information. [ABSTRACT FROM AUTHOR]

In response to the issue of neglecting the inherent differences in samples in the traditional degradation analysis of long-life aerospace products, a degradation modeling method combining a frailty model is proposed to quantify the unobservable heterogeneity in random degradation processes. Firstly, the frailty term is described using a generalized inverse Gaussian distribution to more comprehensively capture random effects. Secondly, an inverse Gaussian degradation model is established, combined with the frailty model to consider the unobservable heterogeneity in practical use. Through maximum likelihood estimation, parameter estimation is carried out, and Bayesian theory is used to infer an independent frailty term in order to quantify differences between individual products. Finally, reliability analysis is conducted on a core chamber cooling control valve of a certain aerospace engine. The results indicate that neglecting the unobservable heterogeneity will lead to overly ideal reliability estimates, and quantifying random effects reasonably can make the model’s estimation closer to the actual situation.

Accelerated life test provides a viable method for assessing the life of complex electromechanical products. However, it is difficult to directly assess their storage life using the failure count for complex electromechanical products with few or no failures during storage life tests. Therefore, based on the step-stress accelerated degradation test, this article proposes a new storage life assessment method (RDSA), which is particularly suitable for the storage life assessment of complex electromechanical products based on performance degradation. Firstly, this article proposes a performance degradation model that comprehensively considers the heterogeneity between units and detection errors. This model is based on the Inverse Gaussian (IG) model and introduces unit-specific random effects to capture the heterogeneity and monotonicity of product degradation paths. Additionally, it uses a normal distribution to address the challenges posed by detection errors in data analysis, thereby enhancing the accuracy of life assessment for the product. Secondly, a Quasi-Monte Carlo method (QMC) based on distribution transformation is proposed to estimate the model parameters and reliability. This method overcomes the limitations of traditional Monte Carlo methods (MC), and can significantly reduce errors, decrease computation, and accelerate convergence. Finally, the proposed method is applied to performance degradation data of the electromechanical fuzes to verify its robustness and applicability. By comparing the proposed method with other more advanced methods, the results indicate that this method is more suitable for the storage life assessment of complex electromechanical products.

The unit heterogeneity of products and the nonlinear parameter-stress relationship often exist in practice. Therefore, considering the unit heterogeneity, the nonlinear accelerated model and inverse Gaussian process are developed to depict the accelerated degradation data. On the other hand, this more realistic model leads a challenge to derive the model parameter interval estimation. Thereby, a novel two-step interval estimation method is proposed for the proposed accelerated degradation model. First, generalized confidence intervals of the parameters characterizing random effect are derived from the Cornish–Fisher expansion, and their cumulative distribution functions are obtained. Then, using the generalized pivotal quantity procedure, generalized confidence intervals of the accelerated model parameters are derived. In addition, generalized confidence intervals of predictive reliability indexes are derived to guide the practical application. Finally, simulation studies and two real examples on Spiral springs and integrated circuit devices are presented to demonstrate the implementation of the proposed method. • An Inverse Gaussian degradation model with unit heterogeneity is developed. • The nonlinear accelerated model is used to fit the stress-parameter relationship. • Generalized confidence intervals of the accelerated model parameters are derived. • A two-step interval estimation method for the proposed model is given. • Simulations and real case studies show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Degradation tests are used when there is a quality characteristic related to the life of a product. In this paper, we investigate the model mis-specification effect on the estimation precision of product's mean time to failure (MTTF) and consider a degradation test design problem. The Wiener and inverse Gaussian (IG) processes are two possible models considered. We derive expressions for the mean and variance of the estimated product's MTTF when the true model is an IG process, but is wrongly fitted by a Wiener process. We further discuss the experimental design problem and derive the explicit functional form of the estimation variances. Using the derived functions, optimal degradation test plans assuming a Wiener process model is correctly or wrongly specified are both proposed. The derived plans are applied to a laser data example. We evaluate the test efficiency of the plans derived from a Wiener process assumption when the model is mis-specified. For many optimization criteria, we observe that the obtained plans are robust even when the fitted model is mis-specified. For some criteria that may result in very different test plans under different models, we use a weighted ratio criterion to find practically useful degradation plans under model uncertainty. [ABSTRACT FROM AUTHOR]

The step-stress accelerated degradation test (ADT) provides a feasible method for assessing the storage life of high-reliability, long-life products. However, this method results in a slower rate of performance degradation at the beginning of the test, significantly reducing the test efficiency. Therefore, this article proposes an assessment method for the step-down stress ADT that considers random effects and detection errors (SDRD). Firstly, a new Inverse Gaussian (IG) model is proposed. The model introduces the Gamma distribution to characterize the randomness of the product degradation path and uses the normal distribution to describe the detection errors of performance parameters. In addition, to solve the problem that the likelihood function of the IG model is complex and has no explicit expression, the Monte Carlo (MC) method is used to estimate unknown parameters of the model. This approach enhances computational accuracy and efficiency. Finally, to verify the effectiveness of the SDRD method, it is applied to the step-down stress ADT data from a specific missile tank to assess its storage life. Comparing the life assessment results of different methods, the conclusion shows that the SDRD method is more effective for assessing the storage life of high-reliability, long-life products.

Simultaneous degradation of multiple dependent performance characteristics (PCs) is a common phenomenon for industrial products. The associated degradation modeling is of practical importance yet challenging. The dependence of the PCs can usually be attributed to two sources, one being the overall system health status and the other the common operating environments. Based on the observation, this study proposes a parsimonious multivariate Wiener process model whose number of parameters increases linearly with the dimension. We introduce a common stochastic time scale shared by all the PCs to model the dependence from the dynamic operating environment. Conditional on the time scale, the degradation of each PC is modeled as the sum of two independent Wiener processes, where one represents the common effects shared by all the PCs, and the other represents degradation caused by randomness unique to this PC. An EM algorithm is developed for model parameter estimation, and extensive simulations are implemented to validate the proposed model and the algorithms. For efficient reliability evaluation under a multivariate degradation model, including the proposed one, a bridge sampling-based algorithm is further developed. The applicability and the advantages of the proposed methods are demonstrated using a multivariate degradation dataset of a coating material. for this article are available online. [ABSTRACT FROM AUTHOR]

The scoring processes of home and away team in basketball games are modeled by two dependent inverse Gaussian processes with a team-specific parameter that measures the team strength. A common latent variable that measures the game pace is designed to characterize the dependence. A moment estimation method combined with maximum likelihood estimation is proposed to fit the parameters and a Bayesian method is applied to update the estimation and make in-game predictions. It is shown that the proposed model can obtain the same performance as the benchmark model, Gamma process model, in outcome prediction, point spread betting and model gambling. [ABSTRACT FROM AUTHOR]

The stochastic modelling of degradation processes requires different characteristics to be considered, such that it is possible to capture all the possible information about a phenomenon under study. An important characteristic is what is known as the drift in some stochastic processes; specifically, the drift allows to obtain information about the growth degradation rate of the characteristic of interest. In some phenomenon’s the growth rate cannot be considered as a constant parameter, which means that the rate may vary from trajectory to trajectory. Given this, it is important to study alternative strategies that allow to model this variation in the drift. In this paper, several hazard rate functions are integrated in the inverse Gaussian process to describe its drift in the aims of individually characterize degradation trajectories. The proposed modelling scheme is illustrated in two case studies, from which the best fitting model is selected via information criteria, a discussion of the flexibility of the proposed models is provided according to the obtained results. [ABSTRACT FROM AUTHOR]

Reliability estimation for key components of a mechanical system is of great importance in prognosis and health management in aviation industry. Both degradation data and failure time data contain abundant reliability information from different sources. Considering multiple variable-dependent degradation performance indicators for mechanical components is also an effective approach to improve the accuracy of reliability estimation. This study develops a bivariate-dependent reliability estimation model based on inverse Gaussian process and copulas fusing degradation data and failure time data within one computation framework. The inverse Gaussian process model is used to describe the degradation process of each performance indicator. Copula functions are used to capture the dependent relationship between the two performance indicators. In order to improve the reliability estimation accuracy, both degradation data and failure time data are used simultaneously to estimate the unknown parameters in the degradation model based on the likelihood function transformed using the zeros-ones trick. A simulation study and a real application in the reliability estimation of mechanical seal used in airborne hydraulic pump are conducted to validate the effectiveness and accuracy of the proposed model compared with existing reliability models. [ABSTRACT FROM AUTHOR]

In view of the disadvantage that traditional evaluation method of accelerated degradation testing (ADT) complex statistical analysis, in this paper, the randomness and monotonicity of the degradation path for products with high reliability and long lifetime are taken into consideration based on Inverse Gaussian (IG) process. The evaluation method of step-down-stress ADT as well as its reliability function are established based on IG process. At same time, both the simple IG process and IG process with random effects are considered, respectively. The maximum likelihood estimation method and Markov Chain Monte Carlo (MCMC) estimation method are presented to estimate the unknown parameters in the proposed degradation models, respectively. Finally, the proposed evaluation methods are demonstrated by the step-down-stress ADT data of a certain type of missile tank. The results show that the proposed evaluation method is reasonable and valid in this paper. In addition, compared with simple IG process model, IG process with random effects model has many superb properties when dealing with random effects of products in ADT.

In this work, we have analyzed data sets from various fields using a coupled Ornstein–Uhlenbeck (OU) system of equations driven by Lévy processes. The Ornstein–Uhlenbeck model is well known for its ability to capture stochastic behaviors when used as a predictive model. There's empirical evidence showing that there exist dependencies or correlations between events; thus, we may be able to model them together. Here we show such correlation between data from finance, geophysics and health as well as show the predictive performance when they are modeled with a coupled Ornstein–Uhlenbeck system of equations. The results show that the solution to the stochastic system provides a good fit to the data sets analyzed. In addition by comparing the results obtained when the BDLP is a Γ (a , b) process or an IG(a,b) process, we are able to deduce the best choice out of the two to model our data sets. [ABSTRACT FROM AUTHOR]

The high reliability and extended life of seawater hydraulic components is dependent on the tribological properties of key friction pairs, more and more attention has been given to the performance degradation and lifetime of the friction pairs. In this paper, the wear process of Tungsten carbide (WC) with 6%wt of Ni (WC–6Ni)/SiC friction pair is studied through the tribological test under seawater lubrication. Considering the random effects and the complex wear mechanism of WC-6Ni/SiC, an efficient Inverse Gaussian (IG) process supported lifetime prediction model is established by coupling the multiple stresses under seawater lubrication, and the parameters in the proposed IG process model are derived. Two actual cases are used to validate the proposed method. The prediction model and experimental results show the high accuracy in time-varying lifetime prediction of WC-6Ni/SiC, which is of great significance to the evaluation of friction pair and the maintenance for seawater hydraulic components. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A warranty product often has an interval structure, resulting in different warranty periods for each component due to their distinct degradation paths. From the manufacturer's perspective, it is reasonable to establish appropriate warranty periods for each part to achieve cost savings. This paper introduces a dependent series configuration consisting of a main component and an auxiliary component. The failure of the main component leads to system failure, while the failure of the auxiliary component only causes a random damage to the main component. These two components follow different Wiener degradation paths, and then their first passage times (FPTs) follow disparate inverse Gaussian distributions. Assuming a pre-deterministic warranty period, W , for the main component, and η W , 0 < η < 1 , for the auxiliary component, the warranty period can be divided into two stages: [ 0 , η W ] and [ η W , W ]. In this context, the paper proposes warranty claim policies for replacement, objective-oriented imperfect repair (OOIR), and refund. The corresponding warranty costs sustained by manufacturer and consumer within these two stages are considered. Finally, a numerical example is presented to illustrate the warranty costs sustained by manufacturer and consumer under different scenarios, as well as the total warranty costs. • The degradation paths, warranty periods and warranty costs of the series system is analyzed. • The warranty costs sustained by manufacturer and consumer under different scenarios is analyzed. • The interdependence between various components is considered. [ABSTRACT FROM AUTHOR]

Condition-based maintenance has been widely used in the maintenance strategy of equipment or systems. Aiming at the maintenance decision-making of the equipment with dynamic degradation characteristics, a dynamic condition-based maintenance model is proposed based on Inverse Gaussian process in this paper. Firstly, an Inverse Gaussian process with stochastic parameter is proposed to describe the change of the equipment degradation characteristics during operation, and the important stochastic properties related to condition-based maintenance is deduced. Secondly, the dynamic maintenance threshold function is proposed, and its different values at different degradation stages can reduce the early failure risk of the equipment while ensuring a lower expected cost ratio. On this basis, a dynamic maintenance decision-making model with multi-objectives is established. A numerical example is illustrated to verify the correctness and practicability of the proposed method, and the sensitivity analysis results of the related parameters prove the necessity of considering the dynamic degradation characteristics of equipment. The comparison result proves that the method proposed in this paper can obtain better safety and economy of maintenance than the method with fixed thresholds.

Remaining useful life (RUL) prediction plays a crucial role in prognostics and health management (PHM). Recently, the adaptive model-based RUL prediction, which is proven effective and flexible, has gained considerable attention. Most research on adaptive degradation models focuses on the Wiener process. However, since the degradation process of some products is accumulated and irreversible, the inverse Gaussian (IG) process that can describe monotonic degradation paths is a natural choice for degradation modelling. This article proposes a nonlinear adaptive IG process along with the corresponding state space model considering measurement errors. Then, an improved particle filtering algorithm is presented to update the degradation parameter and estimate the underlying degradation state under the nonGaussian assumptions in the state space model. The RUL prediction depending on historical degradation data is derived based on the results of particle methods, which can avoid high-dimensional integration. In addition, the expectation-maximization (EM) algorithm combined with an improved particle smoother is developed to estimate and adaptively update the unknown model parameters once newly monitored degradation data become available. Finally, this article concludes with a simulation study and a case application to demonstrate the applicability and superiority of the proposed method.

In manufacturing, cutting tools gradually wear out during the cutting process and decrease in cutting precision. A cutting tool has to be replaced if its degradation exceeds a certain threshold, which is determined by the required cutting precision. To effectively schedule production and maintenance actions, it is vital to model the wear process of cutting tools and predict their remaining useful life (RUL). However, it is difficult to determine the RUL of cutting tools with cutting precision as a failure criterion, as cutting precision is not directly measurable. This paper proposed a RUL prediction method for a cutting tool, developed based on a degradation model, with the roughness of the cutting surface as a failure criterion. The surface roughness was linked to the wearing process of a cutting tool through a random threshold, and accounts for the impact of the dynamic working environment and variable materials of working pieces. The wear process is modeled using a random-effects inverse Gaussian (IG) process. The degradation rate is assumed to be unit-specific, considering the dynamic wear mechanism and a heterogeneous population. To adaptively update the model parameters for online RUL prediction, an expectation–maximization (EM) algorithm has been developed. The proposed method is illustrated using an example study. The experiments were performed on specimens of 7109 aluminum alloy by milling in the normalized state. The results reveal that the proposed method effectively evaluates the RUL of cutting tools according to the specified surface roughness, therefore improving cutting quality and efficiency. [ABSTRACT FROM AUTHOR]

Reliability estimation for key components of a mechanical system is of great importance in prognosis and health management in aviation industry. Both degradation data and failure time data contain abundant reliability information from different sources. Considering multiple variable-dependent degradation performance indicators for mechanical components is also an effective approach to improve the accuracy of reliability estimation. This study develops a bivariate-dependent reliability estimation model based on inverse Gaussian process and copulas fusing degradation data and failure time data within one computation framework. The inverse Gaussian process model is used to describe the degradation process of each performance indicator. Copula functions are used to capture the dependent relationship between the two performance indicators. In order to improve the reliability estimation accuracy, both degradation data and failure time data are used simultaneously to estimate the unknown parameters in the degradation model based on the likelihood function transformed using the zeros-ones trick. A simulation study and a real application in the reliability estimation of mechanical seal used in airborne hydraulic pump are conducted to validate the effectiveness and accuracy of the proposed model compared with existing reliability models.

The accelerated degradation test (ADT) is an effective method for evaluating the lifetime of high-reliability products. In this paper, a doubly accelerated degradation model based on the inverse Gaussian process is proposed to characterize the ADT data, and then an objective Bayesian approach is presented to analyze the model. Some important noninformative priors including the Jeffreys prior and reference priors under different group orderings are derived. The propriety of the posterior distributions under each prior is validated. A simulation study is carried out to show the superiority of objective Bayesian approach compared with the parametric Bootstrap method. Finally, the approach is applied to analyze a carbon film data. [ABSTRACT FROM AUTHOR]

Until now, in the literature, a variety of acceptance reliability sampling plans have been developed based on different life test plans. In most of the reliability sampling plans, the decision procedures to accept or reject the corresponding lot are developed based on the lifetimes of the items observed on tests, or the number of failures observed during a pre-specified testing time. However, frequently, the items are subject to degradation phenomena and, in these cases, the observed degradation level of the item can be used as a decision statistic. In this paper, we develop a variables acceptance sampling plan based on the information on the degradation process of the items, assuming that the degradation process follows the inverse Gaussian process. It is shown that the developed sampling plan improves the reliability performance of the items conditional on the acceptance in the test and that the lifetimes of items after the reliability sampling test are stochastically larger than those before the test. A study comparing the proposed degradation-based sampling plan with the conventional sampling plan which is based on a life test is also performed. [ABSTRACT FROM AUTHOR]

Traditional reliability analysis techniques focus on the occurrence of failures over time. Nevertheless, in certain cases where the occurrence of failures is tiny or almost null, the estimation of the quantities that describe the failure process is compromised. In this context, we introduce a reliability model for systems adopting the degradation process using frailty. The evolved degradation model has as experimental data, not the failure, but a quality feature attached to it. Degradation analysis can provide information about the lifetime distribution components without actually observing failures. In this paper, we propose an inverse Gaussian process model with frailty as a possible tool to investigate the effect of unobserved covariates. Moreover, a comparative study with the classical inverse Gaussian process based on simulated data was performed, revealing that the asymptotic properties of the maximum likelihood estimators are compromised when the presence of frailty is ignored. The application was based on two real data sets in the literature, showing that the inverse Gaussian process frailty models are propitious to use; however, gamma and inverse Gaussian distributions for frailty present similar results. [ABSTRACT FROM AUTHOR]

We present a general framework for the estimation of corporate default based on a firm's capital structure, when its assets are assumed to follow a pure jump Lévy processes; this setup provides a natural extension to usual default metrics defined in diffusion (log-normal) models, and allows to capture extreme market events such as sudden drops in asset prices, which are closely linked to default occurrence. Within this framework, we introduce several pure jump processes featuring negative jumps only and derive practical closed formulas for equity prices, which enable us to use a moment-based algorithm to calibrate the parameters from real market data and to estimate the associated default metrics. A notable feature of these models is the redistribution of credit risk towards shorter maturity: this constitutes an interesting improvement to diffusion models, which are known to underestimate short-term default probabilities. We also provide extensions to a model featuring both positive and negative jumps and discuss qualitative and quantitative features of the results. For readers convenience, practical tools for model implementation and GitHub links are also included. [ABSTRACT FROM AUTHOR]

Degradation trajectories over time provide information that is important for the life estimation of products and systems. However, most of the time the degradation measurements are disturbed by different conditions that cause uncertainty. This is an important problem in the area of reliability assessment based on degradation data, because the multiple observed measurements characterize the degradation path, which ends defining a failure time. Thus, in the presence of measurement error the observed failure time may be different from the true failure time. As the measurement error is inherent to the degradation testing, it results important to establish models that allow to obtain the true degradation from the observed degradation and some measurement error. In this article, a modeling approach to assess reliability under measurement error is proposed. It is considered that the true degradation is obtained by deconvoluting the observed degradation and the measurement error. We considered the inverse Gaussian and Wiener processes to describe the observed degradation of a particular case study. Then, the obtaining of the true degradation is performed by developing the proposed deconvolution method which considers that the measurement error follows a Gaussian distribution. An illustrative example is presented to implement the proposed modeling, and some important insights are provided about the reliability assessment.

Stochastic processes are widely used to analyze degradation data, and the Gaussian process is a particularly common one. In this article, we propose a robust statistical model using a Student-t process to assess the lifetime information of highly reliable products. This model is statistically plausible and demonstrates a substantially improved fit when applied to real data. A computationally accurate approach is proposed to calculate the first-passage-time density function of the Student-t degradation-based process; related properties are investigated as well. In addition, this article provides parameter estimation using the EM-type algorithm and a simple model-checking procedure to evaluate the appropriateness of the model assumptions. Several case studies are performed to demonstrate the flexibility and applicability of the proposed model with random effects and explanatory variables. Technical details, datasets, and R codes are available as . [ABSTRACT FROM AUTHOR]

• An inverse Gaussian degradation model with both unit-specific and subpopulation-specific heterogeneities is proposed. • An Expectation-Maximization algorithm is proposed for point estimation. • Two real degradation datasets study are conducted to validate the significance of the proposed model and algorithm. This study proposes a random effects model based on inverse Gaussian process, where the mixture normal distribution is used to account for both unit-specific and subpopulation-specific heterogeneities. The proposed model can capture heterogeneities due to subpopulations in the same population or the units from different batches. A new Expectation-Maximization (EM) algorithm is developed for point estimation and the bias-corrected bootstrap is used for interval estimation. We show that the EM algorithm updates the parameters based on the gradient of the loglikelihood function via a projection matrix. In addition, the convergence rate depends on the condition number that can be obtained by the projection matrix and the Hessian matrix of the loglikelihood function. A simulation study is conducted to assess the proposed model and the inference methods, and two real degradation datasets are analyzed for illustration. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

• A new model is introduced for age- and state-dependent degradation modelling. • Closed-form expressions of reliability function and RUL distribution are derived. • Explanatory variables and random effects are included for heterogeneity modelling. • Bayesian parameter estimation and model selection are developed and illustrated. In this paper, a transformed inverse Gaussian (TIG) process is introduced as a new family of monotonic degradation models. Different from most state-of-the-art degradation models, which can only characterize age-dependent performance degradation, the TIG process model is mainly introduced for degradation modelling of industrial products with age- and state-dependent performance degradation. With this new model, promising properties include (1) the modelling capability for characterizing products observed at discrete time points with age- and state-dependent degradation, (2) the mathematical tractability for calculating the reliability function and remaining useful life distribution with high efficiency, and (3) the modelling flexibility of incorporating explanatory variables and random effects for investigating a product population with unit-to-unit heterogeneity. To facilitate the degradation modelling and analysis, methods for parameter estimation and model selection are developed under a coherent Bayesian framework. Simulation studies and real cases are presented to demonstrate the proposed degradation model and the Bayesian methods. [ABSTRACT FROM AUTHOR]

As the existing research of condition-based Maintenance (CBM) decision-making neglects the influence of regular detection and maintenance (RDM) on the recovery of equipment performance, it is impossible to accurately describe the state degradation characteristics and life distribution law in this case, which is not helpful to formulate reasonable and effective maintenance strategies. Aimed at this problem, a maintenance strategy combining RDM and CBM is proposed in this paper, and the performance degradation modeling and maintenance optimization model under this strategy are studied deeply. Considering the discontinuous and catastrophic performance degradation characteristics of equipment under this condition, a performance degradation model is established by using the Inverse Gaussian process from the failure mechanism. On this basis, a combined maintenance decision model constrained by risk function is constructed. The optimal maintenance cycle and preventive maintenance threshold are obtained by optimizing the equipment maintenance cost under long-term operation conditions. The relationship between the cost rate and the maintenance strategy value is obtained through the example analysis of the equipment components, and it is proved that the joint maintenance strategy can not only prolong the service life and maintenance interval of equipment, but also reduce the maintenance risk and cost. [ABSTRACT FROM AUTHOR]

• A new class of reference priors for IG process degradation model is proposed. • The modified reference priors are proved to have proper posterior distributions and probability matching properties. • Gibbs sampling algorithms for modified reference priors are proposed. • Simulation and real data studies show that the proposed method behaves better than the MLE and subjective Bayesian method. In this paper, objective Bayesian method is applied to analyze degradation model based on the inverse Gaussian process. Noninformative priors (Jefferys prior and two reference priors) for model parameters are obtained and their properties are discussed. Moreover, we propose a class of modified reference priors to remedy weaknesses of the usual reference priors and show that the modified reference priors not only have proper posterior distributions but also have probability matching properties for model parameters. Gibbs sampling algorithms for Bayesian inference based on the Jefferys prior and the modified reference priors are studied. Simulations are conducted to compare the objective Bayesian estimates with the maximum likelihood estimates and subjective Bayesian estimates and shows better performance of the objective method than the other two estimates especially for the case of small sample size. Finally, two real data examples are analyzed for illustration. [ABSTRACT FROM AUTHOR]

Most modern products that are highly reliable are complex in their inner and outer structures. This situation indicates quality characterization by the interaction of multiple performance characteristics, which motivates the utilization of robust reliability models to obtain robust estimates. It is paramount to obtaining substantial information about a product's life cycle; therefore, when multiple performance characteristics are dependent, it is important to find models that address the joint distribution of performance degradation of such. In this paper, a reliability model for products with 2 fatigue‐crack growth characteristics related to 2 degradation processes is developed. The proposed model considers the dependence among degradation processes by using copula functions considering the marginal degradation processes as inverse Gaussian processes. The statistical inference is performed by using a Bayesian approach to estimate the parameters of the joint bivariate model. A time‐scale transformation is considered to assure monotone paths of the degradation trajectories. The comparison results of the reliability analysis, under both dependent and independent assumptions, are reported with the implementation of the proposed modeling in a case study, which consists of the crack propagation data of 2 terminals of an electronic device. [ABSTRACT FROM AUTHOR]

In manufacturing, cutting tools gradually wear out during the cutting process and decrease in cutting precision. A cutting tool has to be replaced if its degradation exceeds a certain threshold, which is determined by the required cutting precision. To effectively schedule production and maintenance actions, it is vital to model the wear process of cutting tools and predict their remaining useful life (RUL). However, it is difficult to determine the RUL of cutting tools with cutting precision as a failure criterion, as cutting precision is not directly measurable. This paper proposed a RUL prediction method for a cutting tool, developed based on a degradation model, with the roughness of the cutting surface as a failure criterion. The surface roughness was linked to the wearing process of a cutting tool through a random threshold, and accounts for the impact of the dynamic working environment and variable materials of working pieces. The wear process is modeled using a random-effects inverse Gaussian (IG) process. The degradation rate is assumed to be unit-specific, considering the dynamic wear mechanism and a heterogeneous population. To adaptively update the model parameters for online RUL prediction, an expectation–maximization (EM) algorithm has been developed. The proposed method is illustrated using an example study. The experiments were performed on specimens of 7109 aluminum alloy by milling in the normalized state. The results reveal that the proposed method effectively evaluates the RUL of cutting tools according to the specified surface roughness, therefore improving cutting quality and efficiency.

Accelerated degradation testing (ADT) is commonly used to obtain degradation data of products by exerting loads over usage conditions. Such data can be used for estimating component lifetime and reliability under usage conditions. The design of ADT entails to establish a model of the degradation process and define the test plan to satisfy given criteria under the constraint of limited test resources. Bayesian optimal design is a method of decision theory under uncertainty, which uses historical data and expert information to find the optimal test plan. Different expected utility functions can be selected as objectives. This paper presents a method for Bayesian optimal design of ADT, based on the inverse Gaussian process and considering three objectives for the optimization: relative entropy, quadratic loss function, and Bayesian D-optimality. The Markov chain Monte Carlo and the surface fitting methods are used to obtain the optimal plan. By sensitivity analysis and a proposed efficiency factor, the Bayesian D-optimality is identified as the most robust and appropriate objective for Bayesian optimization of ADT.