Programme MMR2017 Grenoble

Models for degradation and maintenance of items based on first passage times of stochastic processes have proven useful in diverse applications such as production machines or pipelines. While the gamma process seems to be the preferred process in applications, we will here consider the inverse Gaussian process. As a concrete example, we consider items that are inspected and maintained at sequentially determined random times, with degradation modeled by increasing stochastic processes. Two threshold levels will be considered for the deterioration process, a lower one corresponding to a degraded state, for which a preventive maintenance action may be performed, and a higher one corresponding to the failure state at which the item is replaced. A simulation based algorithm is developed to calculate long-run expected costs. An interesting part of the algorithm involves bridge sampling from the degradation process.

The aim of this paper is to introduce and study a new model of imperfect maintenance in reliability. A model of geometric reduction of intensity is assumed on the inter-arrival times of failures on a system subject to recurrent failures. Based on observation of several series of failures and imperfect maintenances on a single system, we introduce estimators of the parameters (euclidean and functional) of this semiparametric model and we prove their asymptotical normality. Then a simulation study is carried out to learn the behavior of these estimators on samples of small or moderate size. We end this work with an application on a real dataset.

Virtual age models are very useful to analyse recurrent events data. Among the strengths of these models is their ability to account for the effects of an intervention or treatment just after an event occurrence. So far it has been assumed in the nonparametric or semiparametric setting that the virtual age function is known. One way to overcome this is to consider semiparametric virtual age models with parametrically specified virtual age functions. Yet, fitting semiparametric virtual age models with parametrically specified virtual age functions is a difficult task. In this talk we show that consistent estimators can be constructed by smoothing the profile log-likelihood function appropriately. We show that our general result can be applied to most of the relevant virtual age models of the literature. Our approach also shows that empirical process techniques may be a worthwhile alternative to martingale methods for studying asymptotic properties of these inference methods. A short simulation study is provided to illustrate our consistency results together with an application to real data.

The study of stochastic comparisons of systems with different structures is a relevant topic in reliability theory. Here we study distribution-free comparisons, that is, orderings which do not depends on the component distributions. We consider different assumptions for the component lifetimes and we use different comparisons techniques accordingly. Thus, if they are independent and identically distributed (IID) or exchangeable, the orderings are obtained by using signatures. If the are just ID (homogeneous components), then we use ordering results for distorted distributions. In the general case or in the case of independent components (heterogeneous components), we use a similar technique for generalized distorted distributions. In these cases, the ordering results may depend on the copula used to model the dependence between the component lifetimes. Some illustrative examples are included in each case.

Based on the observed lifetimes of two systems with shared components, we construct exact nonparametric confidence intervals for quantiles of component and system lifetimes using the minimum and maximum lifetimes, as well as by using all component lifetimes. The coverage probabilities and expected widths of these confidence intervals are then compared for several signature matrices and sample sizes.

In system reliability engineering, systems are made up of different components and these systems can be complex. For various purposes, engineers and researchers are often interested in the lifetime distribution of the system as well as the lifetime distribution of the components which make up the system. In many cases, the lifetimes of an n-component coherent system can be observed, but not the lifetimes of the components. In the recent years, parametric and nonparametric inference for the lifetime distribution of components based on system lifetime lifetimes has been developed. We further investigate the estimation of the parameters in component lifetime distributions based on censored system-level data. Specifically, we consider the maximum likelihood estimation and propose alternative computational methods and approximations to the maximum likelihood estimators. Based on the special features of the system lifetime data, we treat the system lifetime data as incomplete data and apply the Expectation-Maximization (EM) algorithm to obtain the maximum likelihood estimators (MLEs) and apply the stochastic EM (SEM) algorithm to approximate the MLEs. Different implementations of the EM and SEM algorithms are proposed and their performances are evaluated. We have shown that the proposed methods are feasible and easy to implement for various families of component lifetime distributions.

The survivability of microgrids after cyber-attacks has received attention due to the pervasive use of open communication networks. Cyber-attacks can incapacitate the communication between physical components and control centers, and lead to unstable system frequency. Current works do not represent the uncertainty of the attacker behavior and the performance of the remaining physical components in delivering the required functionality. In this work, we use the outcome of a contest between the attacker and defender to quantify the cyber components unavailability, and a two-stage game to model the microgrid survivability. We employ the data-driven distribution of the peak-demand time to represent the uncertain attack behavior. The microgrid fails if its frequency cannot satisfy the requirements, even though the remaining capacity can meet the demand. Case studies investigate optimal defensive strategies in terms of the trade-off between protection allocation to cyber components and redundancy allocation to physical units, which enhance the microgrid ability in providing required load frequency control performance. The defender distributes more resource on the protection to reduce the cyber component’s unavailability if the uncertainty about the most probable attack time is small and the contest intensity is large.

This paper models a situation when a user partitions and distributes sensitive data among several virtual machines to make unauthorized access to the entire data difficult in a cloud environment subject to the co-resident attacks. The attacker creates virtual machines in the same environment aiming to get access to users’ data. The cloud resource management system distributes all virtual machines among servers at random. The unauthorized access to data associated with user's virtual machine is possible only if this machine co-resides in the same server with the attacker's virtual machines. The arrival of attacker’s requests for creating virtual machines is modelled by Poisson stochastic process. Probabilistic model is suggested to obtain dynamic data security index.

Networked critical infrastructures, such as electricity, telecommunication and transportation, are critical for both economic development and social wellbeing of modern societies. In order to ensure their continued effective performance, cost-effective maintenance is necessary. Existing studies on selective maintenance are generally restricted to systems with relatively simple structures, such as series and parallel. Moreover, they need the system to be entirely shut down so as to conduct the maintenance actions. However, current critical infrastructures usually consist of complex topologies and needs to be functioning continuously without any interruption. To deal with this problem, this research proposes a new selective maintenance approach that can help determine optimal selective maintenance strategies for critical infrastructures with general structure. Our approach can also ensure the infrastructure’s performance able to satisfy customers’ demand continuously even during the process of maintenance.

A maintenance model for a system equipped on ship taking a voyage with a random duration is proposed. When a failure occurs, one action is chosen from three, return to the base, instantaneous repair on-site and to leave it alone and repair it after the end of the voyage. Our goal is to determine the optimal action depending on the occurrence time of failures, where the optimal policy minimizes the expected cost until the completion of one voyage, ensuring a certain mean availability.

We consider a multi-state system whose deterioration is modeled as a semi-Markov Process with an absorbing state. The system can suffer major and minor failures. When the system reaches the absorbing state, major failure occurs and the system is replaced. Meanwhile, minor failure can occur at each state. Upon the occurrence of minor failure, the system is minimally repaired. For the system, we propose a state-age-dependent replacement policy which minimizes the expected long-run cost rate. We investigate structural properties of the optimal replacement policy and show that a control-limit policy holds under several assumptions.

We present a model for the delayed reporting of faults: multiple non-fatal faults are accumulated and then simultaneously reported and repaired. The reporting process is modelled as a stochastic process dependent on the underlying stochastic process generating the faults. The joint distribution of the reporting times and numbers of reported faults is derived. We will also present a few extensions of the above model, which deal with multiple fault types, planned preventative maintenance and customer rush.

A recent formulation that connects the structural reliability problem and Bayesian updating has been established. This opens up the possibility of efficient model updating using Subset Simulation. The formulation, called ``Bayesian Updating with Structural reliability methods'' requires the prudent choice of a multiplier, which has remained an open question. Motivated by this problem, this paper discusses a revised formulation that allows Subset Simulation to be used for Bayesian updating without having to choose a multiplier in advance.

In a structural reliability problem, the random input parameters are described by a probabilistic model generally obtained from expert feedbacks or data from experimental tests. However, in numerous cases, this model is incomplete. Indeed, some information may be unavailable or too costly to obtain, especially for the dependence structure between the input variables. The most common industrial practice consists in assuming the independence of the inputs for the pairs of variables for which the dependence structure is unknown. This solution can lead to an overly optimistic evaluation of the risk. Therefore, in order to guarantee the conservatism of the method, we suggest to explore a set of dependency scenarios in order to determine the most penalizing structure. This approach leads to a more pessimistic estimate of margins, but is also more robust with respect to regulatory criteria.

When premature breaks of mechanical components are detected on an in-service system, the actions to be implemented to redesign the component are often expensive and difficult to define precisely. With help of a coupling between numerical simulation methods (Finite Element Analysis with ANSYS) and well-known probabilistic methods for sensitivity and reliability analysis (available in PhimecaSoft), PHIMECA define the most efficient way to redesign a railway component under measured vibratory fatigue loading. First, the transient analysis that calculates the stress level evolution is developed and validated. Then, the probabilistic distribution of each component parameter (dimensions, material characteristics (E, Re, Rm), soil thickness), is defined by railway standard and expert judgment. A global sensitivity analysis using a surrogate model (Polynomial Chaos) based on a global design of experiment is performed. It allows to rank the influences of each variable on the spread of damage. The reliability is too estimated by using simulation methods on the surrogate model for different damage limit-states associated to different lifetimes. The damage mean and standard-deviation can be evaluated and it is then possible to improve the performance in the best way (regarding cost and lifetime improvement) by modifying the most sensible parameters mean value or standard-deviation.

For a coherent reliability system composed of several components configured according to some structure function, its time-to-failure or system life distribution is usually of interest. This distribution may be estimated by simply using observations of the system lifetimes. However, if component lifetime data is available, a better estimator of the system failure time may be obtained. In this work, we demonstrate that shrinkage ideas may further be exploited to gain more efficiency in the estimation of the system reliability function even under nonparametric assumptions about the component time-to-failure distributions.

Event history analysis can be particularly complex due to competing risks and interval-censored and clustered event times. Multi-state model allows individuals to move from several states and to take into account competing risks. Regression models like proportional transition intensities models are used to assess the impact of individual factors on each transition. For inference, right and interval censoring as well as left-truncation have to be dealt with. We incorporate random effects for dealing with group-specific factors. To illustrate this, two examples are presented. The aim of the first one is to study risk factors of dementia from cohort data and to estimate life expectancies. Subjects are ``grouped'' because their are living in 75 municipalities of South western France. The aim of the second example is to compare the life expectancy of a filling in a primary tooth between two types of treatments. Several fillings can be placed in the same mouth, possibly by the same dentist implying a hierarchical cluster structure.

Although recurrent event data analysis is a rapidly evolving area of research, rigorous studies on modeling and estimation of the effects of time-varying covariates on the risk of recurrent events have been lacking. Existing methods for analyzing recurrent event data usually require that the covariate processes are observed throughout the entire follow-up period. However, covariates are often observed periodically rather than continuously. We propose a novel semiparametric estimator for the regression parameters in the popular proportional rate model. The proposed estimator is based on an estimated score function where we kernel smooth the mean covariate process. We show that the proposed semiparametric estimator is asymptotically unbiased, normally distributed and derive the asymptotic variance. Simulation studies are conducted to compare the performance of the proposed estimator and the simple methods carrying forward the last covariates.

We consider coherent systems with dependent heterogeneous components, in particular with stochastically ordered component lifetimes. We present lower and upper bounds on the reliability function and expected lifetime of such systems. The bounds on the system reliability function and expected system lifetime are expressed in the units of the mean of component reliability functions and the mean of component expected lifetimes, respectively.

Let $X$ and $Y$ be two random variables with marginal distributions $G$ and $H$, respectively and $X \le Y$ $ a.s.$. Let $\Psi$ be a function such that $\Psi(G)$ is again a distribution function. In this article, we propose two tests, one of Kolmogorov-Smirnov type and the other of Wilcoxon type, for the null hypothesis $\Psi(G) = H$ against the alternative $ H > \Psi(G)$. The tests are based on the empirical distribution functions of the observations on $X$ and $Y,$ which are dependent. We obtain their asymptotic null distributions. A relationship between the distribution functions of two dependent outcomes can be specified as a hypothesis to be tested in examples like the load sharing models, record values and auction bidding models. As an application, we consider in detail the problem of testing the effect of load sharing in two component parallel systems.

The lifetimes of interest need not be independent and identically distributed random variables. We consider a sequence of associated random variables with a common marginal distribution function $F(x)$. Exponential distribution is synonymous with 'no ageing' for lifetimes. As opposed to this units may age with time - which is the concept of positive ageing. Some common concepts of positive ageing are Increasing Failure Rate (IFR), Increasing Failure Rate Average (IFRA) and New Better than Used (NBU). We propose tests based on U-statistics to test for exponentiality against IFRA and NBU alternatives when the lifetimes of interest are associated.

In this paper a new noisy gamma degradation process is proposed where the noisy measurement is modelled as a non-gaussian random variable that depends stochastically on the hidden degradation level. The main features of proposed model are discussed. The expression of the likelihood function for a generic set of noisy degradation measurements is derived. The residual reliability of a degrading unit that fails when its degradation level exceeds a given threshold limit is formulated. A particle filter method is suggested that allows computing in a quick yet efficient manner the likelihood function and the residual reliability. An applicative example is also illustrated, where the parameters of the (hidden) gamma process and the residual reliability of the degrading units are estimated from a set of noisy degradation data by using the maximum likelihood method.

Let X(t) denote the wear of a machine and Y(t) the number of items it produces per unit time. A system of stochastic differential equations is considered for the vector process (X(t),Y(t)). The aim is to find the average time it takes the two-dimensional diffusion process to hit a certain boundary for the first time. The appropriate Kolmogorov backward equation is solved explicitly by making use of the method of similarity solutions.

A standard gamma process is widely used for cumulative deterioration modeling purpose and to make prediction over the system future behavior. However, this process may be restrictive within an applicative context since its variance-to-mean ratio is constant over time. Extended gamma process, which was introduced by Cinlar (1980), seems to be a good candidate to overcome the latter restriction. The aim of this paper is to investigate benefits of using an extended gamma process for modeling the system evolution instead of a standard gamma process, from a reliability point of view. With that goal, we propose a condition-based dynamic maintenance policy and evaluate its performance on a finite planning horizon. Numerical experiments are illustrated based on simulated data.

The availability and optimal maintenance policies of a competing-risk system undergoing periodic inspections are studied in this paper. Specifically, a repairable system with a working state and M failure modes is considered. Each failure mode has a random failure time. When the system fails from the ith(i=1,2,…,M) failure mode, corresponding corrective replacement (CR) is performed which takes a random time Yi. Some analytical results on the instantaneous availability and the steady-state availability for the system are derived. The model is then utilized to obtain the optimal maintenance inspection interval that maximizes the system steady-state availability or minimizes the average long-run cost rate.

This paper deals with optimal maintenance service contracts for warranty products among three parts: manufacturer, agents and customers. The service-repair process of the products is formulated as a queueing problem and the waiting times of failed products can be derived. The penalty cost in return for delaying the repair of the failed product is considered. Customers aim to find an optimal time interval between the preventive maintenance and replacement during the warranty period. The interaction among three parts is formulated as a game problem which is used to solve the optimal decision problem. We assume that the relationship between the agents and the manufacturer is non-cooperative. They both provide the same maintenance service for the warranted products. The Nash equilibrium warranty price structure is investigated from customer's perspective. Under this equilibrium price, we obtain the optimal number of customers to be served from the manufacturer's viewpoint.

In real world, most systems or products can be repaired or must be maintained routinely, so that the study on repairable systems in reliability field has been an interesting and hot topic. There has been much literature on this topic, for example, Limnios and Oprisan (2000), Zheng et al. (2006), Cui (2008), Bao and Cui (2010), Cui et al. (2013) and Yi et al. (2017) and others. In general, a repairable system consists of two parts: mission operating part and repair auxiliary part. As the complexity of systems become more and more high, and we need to understand the systems deeply and more detail, so that many maintenance indexes must be needed to satisfy these demands, the researches on this direction haven appeared more recently. The repairable systems have many performances which people are interested in, so that the related maintenance indexes have been invented more and more, the motivation on inventing new maintenance indexes results not only from theoretical study but also from applications. On the other hand, the detailed and deep descriptions on the repairable systems or products need the related indexes. In this talk, the recent developments on maintenance indexes are reviewed. The maintenance indexes can be classified into two categories: (1) deterministic ones which are expressed as deterministic function or values and, (2) random ones which are expressed as random variables or stochastic processes. In general, the deterministic maintenance indexes are popular or preferred, specially in applications, because of their simplicity and measurement. However, the random maintenance indexes may have some advantages in theoretical researches. The maintenance indexes may be for the whole repairable systems and may also for mission operating part and repair auxiliary part, respectively. The maintenance indexes contain mainly the following ones: (1) Availability; (2) Stability; (3) Failure frequency; (4) Up and down time; (5) Busy probability for repair auxiliary part; (6) Failure number; (7) Failure intensity; (8) Virtual age. The most researches have been focused on availability which can be classified based on the known results into: (1) point availability; (2)steady-state availability; (3) interval availability; (4) mixture of point and interval availability; (5) average availability and so on. In this talk, the summary shall be done based on recent works appeared in Journal of Applied probability, IEEE Transactions on Reliability, Reliability Engineering and System Safety, Annals of Operations Research, IIE Transactions, Methodology and Computing in Applied Probability, Quality Technology and Quantitative Management, and other journals and chapters in monographs. The talk will be presented by classifications, for example, for availability including definitions, formulas, relations under Markov process environment. (1). Instantaneous availability, steady-state availability; (2). Point availability, interval availability, mixture availability (single, multiple); (3). Deterministic availability, random availability; (4). Availabilities for mission operating part and repair auxiliary part. The other maintenance indexes shall be discussed in the talk as well. Finally, the trends and some future work in maintenance indexes are discussed. The main references are as follows. Barlow and Proschan (1965), Csenki (1994, 1995, 2007), Sericola (1990, 1994), Rubino and Sericola (1992), Finkelstein (1999), Hawkes et al. (2011, 2014), Liu et al. (2013), Du et al. (2014), Wu and Hillston (2015), Wang and Cui (2011), Yi and Cui (2017), Cui et al. (2007, 2012, 2014, 2016, 2017). This talk on survey of maintenance indexes intends to provide a clear picture on this aspect, which may be useful in the applications and further research work.

The paper continues the application of monmial ideals to system reliability which arose from the observation that the structure of the failure set for a system with multilevel components was similar to that of a monomial ideal. The natural inclusion-exclusion formulae for system reliability can then be mapped into the minimal free resolution of the ideal via the Hilbert series of the ideal. Here this is extended to the LCM filtration which covers the number of elementary cuts (generators) in failure situation. There are other filtrations and give way to summarise the robustness of systems.

The algebraic analysis of coherent systems uses the algebra of monomial ideals to compute reliability formulas and bounds for such systems. The authors have applied this framework to the analysis of several relevant systems such as networks, series-parallel systems, k-out-of-n and variants, etc. The present work introduces the algebraic operations of polarization and depolarization as a tool to study multistate systems via binary systems and vice versa. Polarization transforms a general monomial ideal into a squarefree monomial ideal that shares many relevant features with the original one.This idea can be applied to the algebraic analysis of coherent multistate systems. We provide several examples including multistate k-out-of-n systems.

A binary monotone system is an ordered pair (E, phi) where E is the component set, and phi, the structure function of the system, is a binary function defined for all subsets A of E which is non-decreasing with respect to set inclusion. If all components have the same probability p of functioning, the system reliability can be expressed in terms of the reliability polynomial h(p). Two binary systems are equivalent if their reliability polynomials are equal. An important class of binary monotone systems is the class of undirected network systems. This class belongs to the larger class of matroid systems. A matroid is and ordered pair (F, M) where M is a family of incomparable subsets of F, called circuits, satisfying a set of axioms. A matroid system is a binary monotone system, (E, phi), which can be associated with a matroid (E u x, M) in such a way that the minimal path sets of (E, phi) can be recovered by extracting all the circuits in M containing the element x, and then deleting x from these circuits. A subclass of such systems is the class of orientable matroid systems. If (E, phi) is a 2-terminal undirected network system, it is orientable since directions can be assigned to all the edges. By using the properties of orientable matroid systems we obtain a way of constructing equivalent systems.

In this paper we treat the problem of maintenance modeling and analysis for large scale complex systems. We discuss some specific factors the influence of which are particularly important for construction, investigation and applications of mathematical models for dependability and performance analysis, as well as for optimal synthesis of territorially distributed networks. The arguments are given for assertion that the consideration of above factors within the framework of classical mathematical theory of reliability (repairman problem) and classical queuing theory is almost impossible. The conclusion is made that it is necessary to develop novel queuing models within the framework of network maintenance problem. This problem is formulated in the paper. The diagram is adduced illustrating the network maintenance problem.

We provide the asymptotic expansion of the all- and $k$-terminal reliability of the complete graph $K_n$ for large $n$, improving on the results by Gilbert and by Frank and Gaul, which were restricted to the first order and $k = 2$. We have also numerically investigated recently defined performance indices such as the average reliability of a graph, and the average of the average of the reliability on all simple graphs having $n$ vertices, which can be expressed as a simple integral of the all-terminal reliability of $K_n$. We propose asymptotic expressions of these quantities in the $n \to \infty$ limit.

Machine learning have achieved great success in solving problems in a wide variety of fields. Interestingly, the machine learning methods can be employed to solve queuing problems. One such approach is proposed in this paper. At this moment, we point out the following advantages of this approach: it is possible to calculate flows with an arbitrary distribution, and probably make calculations faster in comparison with simulation modeling.

The Batch Markovian arrival process (BMAP) constitutes a general class of point processes suitable for the modeling of dependent and correlated batch events (as arrivals, failures or risk events). BMAPs have been widely considered in the literature from a theoretical viewpoint, especially from a queueing theory perspective. However, less works are devoted to study statistical inference which is of crucial importance in reliability contexts, often characterized by dependent and simultaneous failures. In this work, we consider estimation for a wide subclass of BMAPSs, namely, the Batch Markov-modulated Poisson processes (BMMPP) which generalize the well-known Markov-modulated Poisson process . A matching moments technique, supported by a theoretical result that characterizes the process in terms of its moments, is proposed to such aim. Numerical results with both simulated and real datasets will be presented to illustrate the performance of the novel approach.

The Batch Markovian arrival process (BMAP) constitutes a general class of point processes suitable for the modeling of dependent and correlated simultaneous events (as arrivals, failures or risk events). BMAPs have been widely considered in the literature from a theoretical viewpoint, being the identifiability one of the most studied aspects because of its implication for statistical inference. In this work, we prove the identifiability of a wide subclass of BMAPs, namely, the Batch Markov-modulated Poisson process (BMMPP) which generalizes the well-known Markov-modulated Poisson process (MMPP).

Recurrent failure data of repairable systems are getting information rich, containing detailed information about failure modes, failure causes, maintenance records, and so forth in addition to failure time themselves. In this paper, one type of recurrent failure data is analyzed, where the failures are categorized into two groups, i.e., the failures caused by operators’ misuse, and the failures occurred in normal operation. An interesting question is how to analyze the recurrent data with two different types of failure, where the misuse-induced failures may affect the event process of normal-operation failures in an uncertain way. This paper attempts to address this question by introducing a bivariate point process model and its corresponding Bayesian analysis method. The new model is developed for the joint modeling of misuse-induced failures, normal-operation failures and the influence of misuse-induced failures on normal-operation failures. The Bayesian method is developed for parameter estimation with uncertainty quantified. A case study with recurrence data from manufacturing systems is presented to demonstrate the proposed method.

The breakdown of the electrical insulation of high voltage components is typically described by a Weibull distribution with the scale parameter depending on the applied voltage or electric field by an inverse power law. In order to predict the lifetime of such components one needs to extrapolate the results performed on small samples and for a homogenous field to larger dimensions and inhomogenous electric field distributions. In this paper we discuss some aspects of this process: We compare the influcence of the parameter estimation method (either maximum likelihood or least square regression to the order statistics) applied to both uncensored and progressively censored data. The results are rescaled to the real geometry and a quantile of the lifetime is estimated. Due to the small amount of data available, the accuracy of this predicted lifetime needs to be evaluated as well. Single sided confidence bound for the lifetime are calculated using the Fisher information approach. We find that especially this leads to substantial underestimation of the expected lifetime.

Aerospace Integrated Circuit (IC) reliability increasingly demands a high level of performance. This article is based on a collaborative project between a production company in the aerospace industry (Atmel) and a statistical company (Ippon Innovation). The main objective is to develop an innovative advanced tool to detect multivariate outliers in small samples, based on measurements of thousands of parameters, which is called a high dimensional situation in statistics. After presenting the context and current computational methods used in this industry for the screening of abnormal dice, the article introduces two methods that are designed for dealing with the special case of high- dimensional datasets: the ROBPCA and the GAT algorithms. The two methods are compared in a case study. GAT has a definite advantage over other methods in detecting atypical instances. Finally, the integration of this algorithm with the production tool provides the ability to go back to the real measurements involved in the revealed anomalies. The use of a sound statistical method to adress small samples and high dimension data is needed to detect reliability issues in the space industry.

The reliability of road infrastructure play a major role in road safety. This is especially true if we are interested by autonomous cars traffic able to read road markings. This kind of vehicles needs an accurate maintenance strategy to guarantee a road with marking perceptible. To simplify the study of a road, a solution based on an Agglomerative Hierarchical Clustering (AHC) segments a road according to the retroreflection level in time. If the follow-up of the maintenance for markings doesn’t exist then a maintenance detector could estimate laying date. However, this strategy needs regular inspection data. Currently, French roads are irregularly inspected once a year and missing data appear. Three options are confronted: accept missing data, estimate missing data thanks to a linear interpolation or an original approach based also an AHC. The last possibility evaluates the most reliable estimations for missing data. This approach is a first step to analyze the useful life of markings with a Weibull analysis. The broken centerline of the French National Road 4 is considered to illustrate our approach.

Step-stress accelerated degradation test (SSADT) has become a common approach to assessing lifetime distribution for highly reliable products. The modeling of SSADT has been intensely investigated under the assumption that there is only on underlying degradation process. However, many products suffer from two or more degradation processes that directly lead to failures. The aim of this paper is to model SSADT data with two dependent degradations described by a bivariate inverse Gaussian process. The drift parameter of each process is assumed to be influenced by one stress factor. A failure is regarded to occur if either or both degradation processes reach the corresponding thresholds. The maximum likelihood estimation framework is established to model the data from SSADT. An illustrative example is presented to illustrate the proposed method.

The issue of accelerated degradation analysis, which has been widely studied recently, plays an important role in assessing reliability and making maintenance schedule for highly-reliable and long-life products. Therefore, in this paper, a well-adopted form of Wiener process with measurement errors is used for modeling the step-stress accelerated degradation test (SSADT). The probability distribution function (PDF) and the cumulative distribution function (CDF) of the failure time are derived in closed expressions based on the concept of the first hitting time (FHT). To model the accelerated degradation relationship, the drift parameter of Wiener process is assumed to depend on the accelerated variable. Moreover, an EM algorithm is adopted to estimate the unknown parameters.

In accelerated failure time (AFT) models, the covariate has effect on expanding or contracting the life time. When a covariate is not observed accurately but is repeat measured with random errors, an intuitive way is to use the average of replicates as the covariate. Such naive analysis yields bias and inconsistent estimate. We investigate how the naive estimating function is biased and motivate our correction method. The proposed method requires no distribution assumptions on covariate or random error. In other words, it is a functional method in the context of measurement error problems. We assess the performance of our method by a simulation study.

Existing studies on maintenance optimization for multiple machines generally ignore the required travel times to move from one machine to another. We consider the problem of a single repairman who is responsible for the maintenance activities of a set of geographically distributed machines with condition monitoring. The problem is formulated as a Markov decision process with to aim to obtain insights on when to relocate and when to carry out preventive and corrective maintenance activities.

This paper proposes an extended overtime policies for a cumulative damage model with damage level Z to replace the unit. Successive shocks occur at random time, and the unit suffers some damage due to the shocks. The unit fails when the total damage has exceeded a prespecified level K. The unit is replaced at failure or Nth shock over level Z (0 <= Z <= K), whichever occur first. For such a model, we obtain the expected cost rate, and discuss the optimal number of N and level Z which minimizes the expected cost rate. Further, numerical examples are given, and suitable discussions are made.

This paper studies a new maintenance policy for a system, which consists of multiple functionally interchangeable components. The maintenance policy combines component reallocation, minimal repair and replacement of components. The minimal repairs are operated for the emergency failures of components. Without consuming additional resource, the system increases its reliability and extends its useful time by reallocating its components over a certain period before touring out and replacing the entire wear-out system. In this paper, we establish a mathematical model to determine the time for component reallocation and the time for component replacement with the objective of minimizing annual expected maintenance cost. We present a numerical example to illustrate the applications and insights of the model.

Power grid is one typically type of critical infrastructures. Although it is heavily protected, its failure rate is still higher than expected. Resilience is a relevant concept to deal with such phenomenon. The resilient power grid should be able to ‘bounce back’ to its normal operation condition in a short time at a low cost. Different from the previous studies which are mainly focused on resilience assessment, this work aims to optimize the recovery process of the power gird after a cascading failure.

Wind turbine systems are able to provide the intended performance at different states. Reliability and maintainability are important not only to provide the electricity under the constraints of demand, but also to minimize unavailability costs and time. Thus, an effective maintenance policy should increase system performance so it can meet the electricity demand, and also reduce the consequences of deficiency (unavailability). In this study, we continue the work made on maintenance optimization under constraints of costs, and also introduce wind speed states and different load types and states in availability assessment. Maintenance policy is based on preventive repair and minimal repair policies. The objective function of this work is to find the system replacement policy that minimizes the costs of preventive and corrective maintenance under the constraints of system availability and maintenance expected duration limitation. Availability of system is also based on wind speed and load states. The presented model is based on the universal generating function (UGF) applied to evaluate multi-state system (MSS) performance.

A comparative study is presented between various extensions of a start-up demonstration procedure which is based on combinatorics. The expected number of required tests and the probability of accepting the tested unit are derived using a set of auxiliary functions. A constrained optimization problem is solved for minimizing the number of required tests subject to some confidence level requirements. The variables for this optimization include the total number of successes, failures, and the maximal lengths of runs of successes and failures.

In this paper we present techniques of computing moments of order statistics arising from independent but not necessarily identically distributed discrete random variables. We derive expressions for single moments of such order statistics. Next, we apply these expressions to establish moments of lifetimes of k-out-of-n systems consisting of heterogeneous components with discrete lifetimes. In particular we obtain formulas describing expectations and variances of lifetimes of such systems.

A practical way for estimating the reliability of a kms-within-m-out-of-n system is presented. Numerical calculations show full correlation to those given in other references. Then, the combined ks-out-of-n and kms-within-m-out-of-n: G system is examined. Its superiority over the individual procedures is demonstrated.

Generally, the failure of a system can be caused by both internal degradation and other external factors. Among the external factors, intentional attack which can choose attack strategy according to the system’s protection strategy is attracting a great deal of attention in recent years. When the system is exposed to intentional attacks, a defender which makes decisions about distribution of defense resources among different defensive measures is essential. Therefore, defending strategy against intentional external attacks becomes more and more important in system reliability and defense theory.This work studies the defense and attack for a consecutive system with n components, which fails if at least k consecutive components fails. At this stage, we first investigate the optimal attack strategies for given defense strategy. The optimal defense strategy will be explored in the future.

Multivariate survival analysis comprises of event times that are generally grouped together in clusters. Observations in each of these clusters relate to data belonging to the same individual or individuals with a common factor. Frailty models can be used when there is unaccounted association between survival times of a cluster. The frailty variable describes the heterogeneity in the data caused by unknown covariates or randomness in the data. In this article, we use the generalized gamma distribution to describe the frailty variable and discuss the Bayesian method of estimation for the parameters of the model. The baseline hazard function is assumed to follow the two parameter Weibull distribution. Data is simulated from the given model and the Metropolis-Hastings MCMC algorithm is used to obtain parameter estimates. It is shown that increasing the size of the dataset improves estimates. It is also shown that high heterogeneity within clusters does not affect the estimates of treatment effects significantly. The model is also applied to a real life dataset.

Reliability growth has always been an area of great interest. In the literature, most of the existing models regard failure intensity as constant in each test phase when considering test-find-test strategy. However, this assumption is questionable. This paper proposes a new model considering time-varying failure intensity in each phase. Moreover, the proposed model assumes that the scale parameters in each phases are a same constant, which utilizes more information of data from different phases. The example with real reliability growth data shows that the assumptions are reasonable, and the proposed model outperforms the existing models.

Nowadays, many products consist of both software and hardware subsystems (e.g. the 3C products (Computer, Communication and Consumer Electronics) and cars). As a result, the causes of warranty claims of those products can also be due to software or/and hardware failures. However, existing research on warranty management mostly focuses on the hardware or software systems separately, and interactions between them are ignored. This paper analyses warranty costs incurred due to the failures of the two subsystems. It considers two warranty policies for software systems, depending on the methods of software updating. Numerical examples are given to illustrate the proposed models.

In recent years, additive manufacturing (AM), also known as 3D printing, has developed rapidly. A promising application of this technology comes in the form of on-site and on-demand printing of spare parts. However, given the current limitations of AM technology, printed parts are subject to a lower reliability compared with their regular counterparts. Therefore, we investigate to what extent this on-site AM capacity is complementary to existing means of resupply. We consider a periodic-review, spare part inventory control system with three supply sources. Regular supply of spare parts is done via periodic resupply shipments. In between these shipments, backorders for spare parts can be met by means of expediting or by printing a part. We obtain insight into the operational cost reductions that can be attained by investing in on-site AM capacity and into how this capacity should be operated.

We are interested in estimating a failure probability, defined as a threshold-exceeding probability of a random variable which is costly to simulate and whose distribution is unknown. In view of the restricted number of available observations of this random variable, classical Monte Carlo simulation methods can not be used. That is why we adopt a Bayesian approach and assume that the failure probability is a realization of a random variable relied on the so-called Gaussian process regression model. In order to provide a reliable estimation of the failure probability, it is desirable to learn as much as possible about the posterior distribution of this random variable. Considering that this is not obvious, we propose an alternative random variable whose good properties, in term of simulation, improve the estimation of the failure probability. In particular, we show that there exists a convex order between these two variables and we exploit the resulting properties.

The Battery Management Systems (BMS) brought a new impetus in battery energy management which lead to an increase of battery life. But the BMS fails when the State of Charge (SoC), State of Health (SoH), State of Life (SoL) or Remaining Useful Life (RUL) prognostics systems doesn't provide the required accuracy. Despite the increase of complexity and accuracy of battery models, the low performance persist on floating temperature and load profiles. With the development of innovative products on wide-ranging applications, the battery materials, technologies, reliability and safety are being pressed to their limits. Therefore, a huge amount of work still to be done, not only on the development of new battery technologies but also on the BMS, battery models and metrics accuracy improvement. The paper gives an overview of the applicability, accuracy, weaknesses and advantages of the recent battery models. Will also be discussed how the Prognostics Health Management (PHM) it can support a technologic impetus on battery affairs with battery models and metrics accuracy improvements.

In this paper, we propose an approach for failure prognosis by online estimation of the residual life before the system performance requirement is no longer met. It consists in anticipating the onset of failures of a system for a specific mission. The proposed approach is based on the system behavior model. It was conducted in two phases: the first used the data available on this system to estimate unmeasured states and relevant parameters which are able to characterize system performance, given that the degradations may remain partially or totally hidden. To carry out this phase, we used an observer. In the second phase, to estimate online the duration before the system performance requirement is no longer met, the historical states and parameters obtained in the first phase were exploited. Thus, assuming unknown the models describing the parameter dynamics, we used time series prediction methods. To illustrate the proposed failure prognosis approach, a Li-ion battery was used.

This paper presents a prognosis approach based on an ensemble of two models for the remaining useful life (RUL) prediction of a fuel cell stack. Two different physics-based models are used, and the prognosis procedure is implemented using particle filters and fed by measurements taken at different levels in the system. The first particle filter receives in input a signal directly observable and related to the component degradation (e.g. the fuel cell output voltage) which can be frequently and easily measured and relies on a simplified model of the degradation trend. The second particle filter is fed by measurements from the physical characterization of the system, which are seldom acquired by periodic inspections, and uses a model of the health state evolution, from which the degradation state is estimated. The outcomes of the two particle filters are aggregated using a local approach to obtain the ensemble predictions.

We consider a Wiener process with linear drift for degradation modeling. Regularly, inspections are carried out, and the level of degradation is measured. At each inspection point a reduction of the degradation level is carried out. In the talk, we consider the influence of such maintenance actions to the further development of the degradation process and the resulting lifetime distribution. A connection between virtual age in Kijima-type models and degradation level in the underlying degradation process is developed. Further, estimators for the process parameters as well as for the degree of repair are developed.

There is no longer any need to demonstrate the relevance of the degradation versus the classical life test plans. One of the main advantages is an increasing amount of collected data and its ability of extrapolating the lifetime distributions when degradation models are available. Nevertheless, further developments for classical and accelerated tests in the context of degradation are still required especially when the degradation pattern is clearly non-homogeneous. The aim of this paper is to propose a degradation test plan for non-homogeneous gamma processes for products with cumulative degradation evolution. We first, propose a test plan, which is based on minimizing the asymptotic variance of the true reliability of the products. Next, we apply the proposed test on a specific parametric form of the shape function of a gamma process.

The degradation modelling has become a critical topic when investigating and predicting the reliability and lifetime of the modern engineering product and system. Various statistical models have been proposed to model the degradation of different products. A lot of existing researches assume that the degradation models are invariant with respect to time. However, the operation profile and environment of the products may change or subject to some external shocks. These could change the degradation pattern of the products. In particular, we consider the problem of testing a change in the trend of two linear degradation models under the periodical inspection plan. One is the linear regression model and the other is the Wiener process. Some simple statistics are recommended to test the existence of the shocks for these two models. The consequences of the misspecification of these two models are investigated via simulation study. A real case study on railway track degradation is presented to illustrate our procedure.

Phased-mission systems (PMSs) are widely used, especially in the aerospace industry. Travelling in the outer space, these systems are exposed to cosmic rays, such as the Galactic Cosmic Rays, which can cause a significant impact on the electronics of the equipment. In this paper, a model for PMS reliability assessment is proposed considering the random shocks coming from cosmic rays. To simplify the model for each phase and reduce the number of system states, the modularization method is applied. SMP (Semi-Markov Process) is adopted to deal with the complex dynamic behaviors in the modules. A Monte Carlo simulation procedure is proposed to assess the reliability of the PMS. As case study, the reliability of a phased AOCS (Altitude and Orbit Control System) is considered.

As epistemic uncertainty is inevitable in reliability analysis, this paper extends the composite Birnbaum importance measure of multi-state systems in the context of epistemic uncertainty. The epistemic uncertainties associated with components’ state discrimination are characterized by an evidential Markov model. The epis-temic uncertainty propagation from components to the entire system is manipulated by an evidential network. Additionally, the conditional belief and plausibility reliabilities can be computed by the evidential network when hard evidences or vacuous evidences are input. A new extended composite Birnbaum importance measure is then defined and converted into an optimization problem. A multi-state bridge system is exemplified to demonstrate the proposed importance measure.

In this paper, we develop a multistate model for resilience analysis of a distributed generation system. A quantitative index, the optimal recovery time, is defined to quantify the resilience of multistate systems and a simulation-based method is presented for its evaluation. The developed method is applied on a distributed generation system to demonstrate its applicability.