On the Statistical Modeling and Analysis of Repairable Systems

We review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the nonhomogeneous Poisson process and the renewal process. In the case where several systems of the same kind are observed, we show how observed covariates and unobserved heterogeneity can be included in the models. We also consider various approaches to trend testing. Modern reliability data bases usually contain information on the type of failure, the type of maintenance and so forth in addition to the failure times themselves. Basing our work on recent literature we present a framework where the observed events are modeled as marked point processes, with marks labeling the types of events. Throughout the paper the emphasis is more on modeling than on statistical inference.Comment: Published at http://dx.doi.org/10.1214/088342306000000448 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parametric inference for multiple repairable systems under dependent competing risks

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/115899/1/asmb2079.pd

Two simple control policies for a multicomponent maintenance system

Control Systems;Maintenance;controle-systemen

Towards a generic prognostic function of technical multi-component systems taking into account the uncertainties of the predictions of their components

This article presents the first elements of a generic function that assesses the capacity of technical multi-component systems to accomplish the assigned productive tasks from production planning. This assessment is based on the prognostics of their components. It must so be able to process inaccuracies and uncertainties of these prognostics. For its implementation the aimed function combines the Dempster-Shafer theory combined and Bayesian inferences. The paper presents the multi-component system modeling and the inferences for the different identified structures as well as a general algorithm. The final aim of the proposed generic function is to compute decision supports for cooperative maintenance and production management

A design and a code invariant under the simple group Co3

Mathematics;mathematics

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation Columns

In this chapter, the analysis and design of a fuzzy observer based on a Takagi-Sugeno model of a batch distillation column are presented. The observer estimates the molar compositions and temperatures of the light component in the distillation column considering a binary mixture. This estimation aims to allow monitoring the physical variables in the process to improve the quality of the distillated product as well as to detect failures that could affect the system performance. The Takagi-Sugeno fuzzy model is based on eight linear subsystems determined by three premise variables: the opening percentage of the reflux valve and the liquid molar composition of the light element of the binary mixture in the boiler and in the condenser. The stability analysis and the observer gains are obtained by linear matrix inequalities (LMIs). The observer is validated by MATLAB® simulations using real data obtained from a distillation column to verify the observer’s convergence and analyze its response under system disturbances

Assessment method of the multicomponent systems future ability to achieve productive tasks from local prognoses

Conditioned-based maintenance and prognostics and health management enable to optimize maintenance by scheduling the necessary repairs and replacements of technical system components according to their present and future health states. The assessment of future health states is the prognostics and health management keystone. Many technical production systems are made of numerous components implementing their functions. A method to assess the ability of multicomponent systems to carry out future production tasks is proposed to provide decision supports for production and maintenance planning for a better compromise between their objectives. It is based on components prognoses. To handle inherent uncertainties of these prognoses, the method is based on the Dempster Shafer theory and Bayesian networks inferences. Local prognoses are categorized and transformed to be compliant to Dempster Shafer theory. Patterns of systems are identified for which inferences are defined. The patterns are then used to model systems and to assess their abilities to achieve future tasks. An identification of components that should first undergo maintenance is proposed. An example implementing a fictitious complex systems is presented to show how the provided decision supports can be used for production and maintenance planning purposes