Topic
Renewal theory
About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.
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TL;DR: These linear programming models are practical for the maintenance of a road network having a large number of road segments and that they are convenient to incorporate various constraints on the decision process, for example, performance requirements and available budgets.
50 citations
TL;DR: In this paper, a stochastic model is developed to study the success of a search by what is termed a predator for randomly or contagiously located points, called prey, which is specified by giving the distribution of the searching time to locate a prey, school or cluster of prey and the joint distribution of handling time and numbers caught from each cluster sighted.
Abstract: SUMMARY Stochastic models are developed to study the success of a search by what is termed a predator for randomly or contagiously located points, called prey. The model is specified by giving the distribution of the searching time to locate a prey, school or cluster of prey and the joint distribution of handling time and numbers caught from each cluster sighted. If a stationary distribution of prey is assumed and their removal is ignored, then the process is analogous to a cumulative renewal process. The mean numbers of prey or clusters of prey and their variances are readily obtained by use of limit theorems of renewal theory.
50 citations
TL;DR: In this paper, a new stochastic process, i.e., an extended Poisson process, is introduced for repairable systems where the failure intensity shows a bathtub-type nonmonotonic behaviour.
Abstract: Commonly used repair rate models for repairable systems in the reliability literature are renewal processes, generalised renewal processes or non-homogeneous Poisson processes. In addition to these models, geometric processes (GP) are studied occasionally. The GP, however, can only model systems with monotonously changing (increasing, decreasing or constant) failure intensities. This paper deals with the reliability modelling of failure processes for repairable systems where the failure intensity shows a bathtub-type non-monotonic behaviour. A new stochastic process, i.e. an extended Poisson process, is introduced in this paper. Reliability indices are presented, and the parameters of the new process are estimated. Experimental results on a data set demonstrate the validity of the new process.
49 citations
49 citations
TL;DR: In this article, a nonparametric estimator for the renewal function is proposed and its properties, including consistency, asymptotic normality, and asyptotic validity of bootstrap confidence regions are discussed.
Abstract: We introduce a nonparametric estimator for the renewal function and discuss its properties, including consistency, asymptotic normality and asymptotic validity of bootstrap confidence regions. The underlying theme is that stochastic models can be regarded as functionals or nonlinear operators. This view leads to nonparametric estimators in a natural way and statistical properties of the estimators can be related to the local behaviour of the functionals.
47 citations