Statistical Modeling and Analysis of Repairable Systems

Lindqvist, Bo Henry

doi:10.1007/978-1-4612-1782-4_1

Cited by 30 publications

(37 citation statements)

References 43 publications

(40 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since our estimator (5) in effect is a weighted kernel estimator, it might be worthwhile to search for better weights than the ones suggested by (5). It is then tempting to try to maximize the log likelihood (3) simultaneously with respect to θ and the weights w = (w i ; i = 1, 2, .…”

Section: Maximum Likelihood Kernel Estimationmentioning

confidence: 99%

See 1 more Smart Citation

Nonparametric Estimation of Time Trend for Repairable Systems Data

Lindqvist

2010

Mathematical and Statistical Models and Methods in Reliability

Self Cite

View full text Add to dashboard Cite

The trend-renewal-process (TRP) is defined to be a time-transformed renewal process, where the time transformation is given by a trend function λ(·) which is similar to the intensity of a nonhomogeneous Poisson process (NHPP). A nonparametric maximum likelihood estimator of the trend function of a TRP can be obtained much in the same manner as for the NHPP using kernel smoothing. But for a TRP one must consider the simultaneous estimation of the renewal distribution, which is here assumed to belong to a parametric class such as the Weibull-distribution. A weighted kernel estimator for λ(·) is derived using a general approach for kernel smoothing in counting processes.

show abstract

Section: Maximum Likelihood Kernel Estimationmentioning

confidence: 99%

“…A class of models of this kind is the trend-renewal process (TRP), which was defined and studied by Lindqvist, Elvebakk and Heggland (2003), see also Lindqvist (2006). This model contains the RP and NHPP as special cases, and in a simple manner the TRP fills some of the gap between the two extreme repair models.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Estimation of Time Trend for Repairable Systems Data

Lindqvist

2010

Mathematical and Statistical Models and Methods in Reliability

Self Cite

View full text Add to dashboard Cite

show abstract

“…The TRP was introduced and investigated first by Lindqvist (1993) and by Lindqvist et al (1994) (see also Lindqvist and Doksum (2003), and Lindqvist (2006)). Parametric inference on the parameters of the TRP was considered in the paper of Lindqvist et al (2003), where the authors also proposed corresponding models, called heterogeneous trend-renewal processes, that extend the TRP to cases involving unobserved heterogeneity.…”

Section: Introductionmentioning

confidence: 99%

Estimation of parameters for trend-renewal processes

Jokiel-Rokita

Magiera

2011

Stat Comput

View full text Add to dashboard Cite

Methods of estimating unknown parameters of a trend function for trend-renewal processes are investigated in the case when the renewal distribution function is unknown. If the renewal distribution is unknown, then the likelihood function of the trend-renewal process is unknown and consequently the maximum likelihood method cannot be used. In such a situation we propose three other methods of estimating the trend parameters. The methods proposed can also be used to predict future occurrence times. The performance of the estimators based on these methods is illustrated numerically for some trend-renewal processes for which the statistical inference is analytically intractable.

show abstract

“…A general setup for this kind of processes is furthermore suggested by Lindqvist in the review paper [20].…”

Section: A General Setupmentioning

confidence: 99%

“…Recent review articles concerning repairable systems and maintenance include Pena [27] and Lindqvist [20]. A review of methods for analysis of recurrent events with a medical bias is given by Cook and Lawless [7].…”

Section: Introductionmentioning

confidence: 99%

Maintenance of Repairable Systems

Lindqvist

Springer Series in Reliability Engineering

Self Cite

View full text Add to dashboard Cite

A commonly used definition of a repairable system (Ascher and Feingold [3]) states that this is a system which, after failing to perform one or more of its functions satisfactorily, can be restored to fully satisfactory performance by any method other than replacement of the entire system. In order to cover more realistic applications, and to cover much recent literature on the subject, we need to extend this definition to include the possibility of additional maintenance actions which aim at servicing the system for better performance. This is referred to as preventive maintenance (PM), where one may further distinguish between condition based PM and planned PM. The former type of maintenance is due when the system exhibits inferior performance while the latter is performed at predetermined points in time.Traditionally, the literature on repairable systems is concerned with modelling of the failure times only, using point process theory. A classical reference here is Ascher and Feingold [3]. The most commonly used models for the failure process of a repairable system are renewal processes (RP), including the homogeneous Poisson processes (HPP), and nonhomogeneous Poisson processes (NHPP). While such models often are sufficient for simple reliability studies, the need for more complex models is clear. In this chapter we consider some generalizations and extensions of the basic models, with the aim to arrive at more realistic models which give better fit to data. First we consider the Trend Renewal Process (TRP) introduced and studied in Lindqvist, Elvebakk and Heggland [22]. The TRP includes NHPP and RP as special cases, and the main new feature is to allow a trend in processes of non-Poisson (renewal) type.As exemplified by some real data, in the case where several systems of the same kind are considered, there may be unobserved heterogeneity between the systems which, if overlooked, may lead to non-optimal or possibly completely wrong decisions. We will consider this in the framework of the TRP process, which in Lindqvist et al. [22] is extended to the so called HTRP model which includes the possibility of heterogeneity. Heterogeneity can be thought of as an effect of an unobserved covariate.Another extension of the basic models is to allow the systems to be preventively maintained. We review some recent research in this direction, where this 1

show abstract

Statistical Modeling and Analysis of Repairable Systems

Cited by 30 publications

References 43 publications

Nonparametric Estimation of Time Trend for Repairable Systems Data

Nonparametric Estimation of Time Trend for Repairable Systems Data

Estimation of parameters for trend-renewal processes

Maintenance of Repairable Systems

Contact Info

Product

Resources

About