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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01 Nov 2010
TL;DR: Warranty cost models are presented based on the quasi-renewal processes and exponential distribution, including repairable products with a given warranty period considering conditional probabilities and renewal theory.
Abstract: In this paper, warranty cost models are presented based on the quasi-renewal processes and exponential distribution. Cost analyses are conducted for various systems under the basic assumption that a repair service is imperfect. We develop warranty cost models, reliability, and other measures for several systems, including multicomponent systems. This paper focuses on warranty cost analysis, including repairable products with a given warranty period considering conditional probabilities and renewal theory. The exponential distribution is used to analyze and obtain the warranty cost. Numerical examples are discussed to demonstrate the applicability of the methodology derived in this paper.
51 citations
TL;DR: In this article, a proper treatment of the continuous-time random-walk problem leads to a frequency-dependent conductivity in agreement with our earlier work, which is similar to this article.
Abstract: A proper treatment of the continuous-time random-walk problem leads to a frequency-dependent conductivity in agreement with our earlier work.
51 citations
TL;DR: In this paper, Arc-sine laws in the sense of renewal theory are proved for return time processes generated by transformations with infinite invariant measure on sets satisfying a type of Darling-Kac condition.
Abstract: Arc-sine laws in the sense of renewal theory are proved for return time processes generated by transformations with infinite invariant measure on sets satisfying a type of Darling-Kac condition, and an application to real transformations with indifferent fixed points is discussed.
50 citations
TL;DR: In this article, the authors generalized discrete renewal theory to study the occurrence of a collection of patterns in random sequences, where a renewal is defined to be an occurrence of one of the patterns in the collection which does not overlap an earlier renewal.
Abstract: Discrete renewal theory is generalized to study the occurrence of a collection of patterns in random sequences, where a renewal is defined to be the occurrence of one of the patterns in the collection which does not overlap an earlier renewal. The action of restriction enzymes on DNA sequences provided motivation for this work. Related results of Guibas and Odlyzko are discussed.
50 citations
28 Aug 2011
TL;DR: In this paper, it was shown that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional poisson process with Mittag-Leffler waiting times.
Abstract: The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve
a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a
traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a
fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional
diffusion equations. The equivalence extends to a broad class of renewal processes that include models for tempered
fractional diffusion, and distributed-order (e.g., ultraslow) fractional diffusion. The paper also {discusses the relation between} the fractional Poisson process and Brownian time.
50 citations