Simulation-based Reliability Evaluation of Maintenance the Efficiency of A Repairable System

  The aim of this paper is to study the asymptotic behavior of the Arithmetic Reduction of Intensity (ARI) and Arithmetic Reduction of Age (ARA) models as two imperfect maintenance models. These models have been proposed by Doyen & Gaudoin (2011), the failure process with bathtub failure intensity. The maintenance effect is characterized by the change induced by the failure intensity before and after a failure during the degradation period. To simplify the study, the asymptotic properties of the failure process are derived. Then, the asymptotic normality of several maintenance efficiency estimators can be proved in the case where the failure process without maintenance is known. Practically, the coverage rate of the asymptotic confidence intervals issued from those estimators is studied

Semiparametric estimate of the efficiency of imperfect maintenance actions for a gamma deteriorating system

International audienceA system is considered, which is deteriorating over time according to a non homogeneous gamma process with unknown parameters. The system is subject to periodic and instantaneous imperfect maintenance actions (repairs). Each imperfect repair removes a proportion ρ of the accumulated degradation since the previous repair. The parameter ρ hence appears as a measure for the maintenance efficiency. This model is called arithmetic reduction of degradation of order 1. The system is inspected right before each maintenance action, thus providing some multivariate measurement of the successively observed deterioration levels. Based on these data, a semiparametric estimator of ρ is proposed, considering the parameters of the underlying gamma process as nuisance parameters. This estimator is mainly based on the range of admissible ρ's, which depends on the data. Under technical assumptions, consistency results are obtained, with surprisingly high convergence rates (up to exponential). The case where several i.i.d. systems are observed is next envisioned. Consistency results are obtained for the efficiency estimator, as the number of systems tends to infinity, with a convergence rate that can be higher or lower than the classical square root rate. Finally, the performances of the estimators are illustrated on a few numerical examples

Modeling the Effects of Maintenance on the degradation of a Water-feeding Turbo-pump of a Nuclear Power Plant

International audienceThis work addresses the modelling of the effects of maintenance on the degradation of an electric power plant component. This is done within a modelling framework previously proposed by the authors, of which the distinguishing feature is the characterization of the component living conditions by influencing factors (IFs), i.e. conditioning aspects of the component life that influence its degradation. The original fuzzy logic-based modelling framework includes maintenance as an IF; this requires one to jointly model its effects on the component degradation together with those of the other influencing factors. This may not come natural to the experts who are requested to provide the if-then linguistic rules at the basis of the fuzzy model linking the IFs with the component degradation state. An alternative modelling approach is proposed in this work, which does not consider maintenance as an IF that directly impacts on the degradation but as an external action that affects the state of the other IFs. By way of an example regarding the propagation of a crack in a water-feeding turbo-pump of a nuclear power plant, the approach is shown to properly model the maintenance actions based on information that can be more easily elicited from experts

Two methods to approximate the superposition of imperfect failure processes

Suppose a series system is composed of a number of repairable components. If a component fails, it is repaired immediately and the effectiveness of the repair may be imperfect. Then the failure process of the component can be modelled by an imperfect failure process and the failure process of the system is the superposition of the failure processes of all components. In the literature, there is a bulk of research on the superimposed renewal process (SRP) for the case where the repair on each component is assumed perfect. For the case that the component causing the system to fail is unknown and that repair on a failed component is imperfect, however, there is little research on modelling the failure process of the system. Typically, the likelihood functions for the superposition of imperfect failure processes cannot be given explicitly. Approximation-based models have to be sought. This paper proposes two methods to model the failure process of a series system in which the failure process of each component is assumed an arithmetic reduction of intensity and an arithmetic reduction of age model, respectively. The likelihood method of parameter estimation is given. Numerical examples and real-world data are used to illustrate the applicability of the proposed models

Modeling of The Effect of Corrective and Preventive Maintenance with Bathtub Failure Intensity

The aim of this paper is to propose a general model to illustrate the joint effect of corrective and preventive maintenance on repairable systems. The intensity of the failure process without maintenance is characterized in bathtub form. The maintenance effect is expressed by the change induced on the failure intensity before and after maintenance. It takes into account the possibility of dependent maintenance times with different effects. The likelihood functions are derived, so parameter estimations and assessment of the maintenance efficiency are possible. The properties of the parameters estimators have to be theoretically studied. Finally, results are applied to a real maintenance data set

Reliability Analysis And Optimal Maintenance Planning For Repairable Multi-Component Systems Subject To Dependent Competing Risks

Modern engineering systems generally consist of multiple components that interact in a complex manner. Reliability analysis of multi-component repairable systems plays a critical role for system safety and cost reduction. Establishing reliability models and scheduling optimal maintenance plans for multi-component repairable systems, however, is still a big challenge when considering the dependency of component failures. Existing models commonly make prior assumptions, without statistical verification, as to whether different component failures are independent or not. In this dissertation, data-driven systematic methodologies to characterize component failure dependency of complex systems are proposed. In CHAPTER 2, a parametric reliability model is proposed to capture the statistical dependency among different component failures under partially perfect repair assumption. Based on the proposed model, statistical hypothesis tests are developed to test the dependency of component failures. In CHAPTER 3, two reliability models for multi-component systems with dependent competing risks under imperfect assumptions are proposed, i.e., generalized dependent latent age model and copula-based trend-renewal process model. The generalized dependent latent age model generalizes the partially perfect repair model by involving the extended virtual age concept. And the copula-based trend renewal process model utilizes multiple trend functions to transform the failure times from original time domain to a transformed time domain, in which the repair conditions can be treated as partially perfect. Parameter estimation methods for both models are developed. In CHAPTER 4, based on the generalized dependent latent age model, two periodic inspection-based maintenance polices are developed for a multi-component repairable system subject to dependent competing risks. The first maintenance policy assumes all the components are restored to as good as new once a failure detected, i.e., the whole system is replaced. The second maintenance policy considers the partially perfect repair, i.e., only the failed component can be replaced after detection of failures. Both the maintenance policies are optimized with the aim to minimize the expected average maintenance cost per unit time. The developed methodologies are demonstrated by using applications of real engineering systems

Modeling multivariate degradation processes with time‐variant covariates and imperfect maintenance effects

International audienceThis article proposes two types of degradation models that are suitable for describing multivariate degrading systems subject to time‐variant covariates and imperfect maintenance activities. A multivariate Wiener process is constructed as a baseline model, on top of which two types of models are developed to meaningfully characterize the time‐variant covariates and imperfect maintenance effects. The underlying difference between the two models lies in the way of capturing the influences of covariates and maintenance: The first model reflects these impacts in the degradation rates/paths directly, whereas the second one describes the impacts by modifying the time scales governing the degradation processes. In each model, two particular imperfect maintenance models are presented, which differ in the extent of reduction in degradation level or virtual age. The two degradation models are then compared in certain special cases. The proposed multivariate degradation models pertain to complex industrial systems whose health deterioration can be characterized by multiple performance characteristics and can be altered or affected by maintenance activities and operating/environmental conditions

Alternative scales in reliability models for a repairable system

In an industry, the lifetime of a technical system is often assessed according to its accumulated throughput/usage e.g., the performance of a Blast Furnace in terms of accumulated quantity of its product, the lifetime of a vehicle in terms of accumulated number of miles it has travelled. Most of these systems are repairable systems. The failure process of a repairable system is conventionally measured in the time domain also termed as a time scale in the literature. Nevertheless, the lifetime of some repairable systems and their failures may be measured in terms of their throughput/usage. Therefore, it makes sense to quantify their failure processes in terms of throughput/ usage which may be better indicators than time, of system failure and reliability. Time, usage or a combination of both time and usage may be used as alternative domains/scales of measurement for modelling the failure process of a repairable system. This paper proposes such alternative scales in reliability models for a repairable system. A method is devised in the paper to identify the better alternative scale to model the failure process and thus identify the appropriate scale to assess the system reliability. Industrial failure data are used to illustrate the proposed method

A failure process model with the exponential smoothing of intensity functions

This paper proposes a new model and investigates its special case model, both of which model the failure process of a series system composed of multiple components. We make the following assumption: (1) once the system fails, the failed component can be immediately identified and replaced with a new identical one, and (2) once the system fails, only the time of the failure is recorded; but the component that causes the system to fail is not known. The paper derives a parameter estimation method and compares the performance of the proposed models with nine other models on artificially generated data and fifteen real-world datasets. The results show that the two new models outperform the nine models in terms of the three most commonly used penalised model selection criteria, the Akaike's information criterion (AIC), corrected Akaike's information criterion (AICc) and Bayesian information criterion (BIC), respectively

Two new stochastic models of the failure process of a series system

Consider a series system consisting of sockets into each of which a component is inserted: if a component fails, it is replaced with a new identical one immediately and system operation resumes. An interesting question is: how to model the failure process of the system as a whole when the lifetime distribution of each component is unknown? This paper attempts to answer this question by developing two new models, for the cases of a specified and an unspecified number of sockets, respectively. It introduces the concept of a virtual component, and in this sense, we suppose that the effect of repair corresponds to replacement of the most reliable component in the system. It then discusses the probabilistic properties of the models and methods for parameter estimation. Based on six datasets of artificially generated system failures and a real-world dataset, the paper compares the performance of the proposed models with four other commonly used models: the renewal process, the geometric process, Kijima's generalised renewal process, and the power law process. The results show that the proposed models outperform these comparators on the datasets, based on the Akaike information criterion