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

BOUNDS FOR THE RELIABILITY OF MULTISTATE SYSTEMS WITH PARTIALLY ORDERED STATE SPACES AND STOCHASTICALLY MONOTONE MARKOV TRANSITIONS

Bounds for the reliability of multistate systems with partially ordered state spaces and stochastically monotone Markov transitions b

A Class of Tests for Trend in Time Censored Recurrent Event Data

This is an Accepted Manuscript of an article published by Taylor & Francis in Technometrics on April 25, 2019, available online: http://www.tandfonline.com/10.1080/00401706.2019.1605936.Statistical tests for trend in recurrent event data not following a Poisson process are generally constructed for event censored data. However, time censored data are more frequently encountered in practice. In this paper we contribute to filling an important gap in the literature on trend testing by presenting a class of statistical tests for trend in time censored recurrent event data, based on the null hypothesis of a renewal process. The class of tests is constructed by an adaption of a functional central limit theorem for renewal processes. By this approach a number of tests for time censored recurrent event data can be constructed, including among others a version of the classical LewisRobinson trend test and an Anderson-Darling type test. The latter test turns out to have attractive properties for general use by having good power properties against both monotonic and non-monotonic trends. Extensions to situations with several processes are considered. Properties of the tests are studied by simulations and some asymptotic calculations, and the approach is illustrated in data examples.acceptedVersio

A Maintenance Model For Components Exposed To Several Failure Mechanisms And Imperfect Repair

this paper we employ a model for components which fail due to one of a series of "competing" failure mechanisms, each acting independently on the system. The components under consideration are repaired upon failure, but are also preventively maintained. The preventive maintenance (PM) is performed periodically with some fixed period # , but PM can also be performed out of schedule due to casual observation of an evolving failure. The maintenance need not be perfect; we use a modified version of the imperfect repair model by Brown and Proschan to allow a flexible yet simple maintenance model. Our motivation for this model is to estimate quantities which describe the "goodness" of the maintenance crew; their ability to prevent failures by performing thorough maintenance at the correct time. The data required to estimate the parameters in the model we propose are the intermediate failure times, the "winning" failure mechanism associated with each failure (i.e. the failure mechanism leading to the failure), as well as the maintenance activity. This data is found in most modern reliability data bank