Renewal theory

About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.

Transport properties of the one-dimensional stochastic Lorentz model: I. Velocity autocorrelation function

Abstract: Point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables (stationary renewal process). For a fixed configuration of scatterers a particle performs the following random walk: The particle starts at the pointx with velocityυ, ¦υ¦=1. In between scatterers the particle moves freely. At a scatterer the particle is either transmitted or reflected, both with probability 1/2. For given initial conditions of the particle the velocity autocorrelation function is a random variable on the scatterer configurations. If this variable is averaged over the distribution of scatterers, it decays not faster thant −3/2.

Extremes for shot noise processes with heavy tailed amplitudes

Abstract: Extreme value results for a class of shot noise processes with heavy tailed amplitudes are considered. For a process of the form, , where { τ k } are the points of a renewal process and { A k } are i.i.d. with d.f. having a regularly varying tail, the limiting behavior of the maximum is determined. The extremal index is computed and any value in (0, 1) is possible. Two-dimensional point processes of the form are shown to converge to a compound Poisson point process limit. As a corollary to this result, the joint limiting distribution of high local maxima is obtained.

On the convexity of loss probabilities

Abstract: For the M/G/c loss system, it is well known that Erlang's loss probability is convex in the number of servers. We extend this result firstly to renewal arrivals and exponential service, then to regenerative arrivals and exponential service, and finally to an arbitrary arrival process with i.i.d. service times that are independent of the arrival process.

Reliability analysis in railway repairable systems

Abstract: Purpose The purpose of this paper is to present the results of the application of various models to estimate the reliability in railway repairable systems. Design/methodology/approach The methodology proposed by the International Electrotechnical Commission (IEC), using homogeneous Poisson process (HPP) and non-homogeneous Poisson process (NHPP) models, is adopted. Additionally, renewal process (RP) models, not covered by the IEC, are used, with a complementary analysis to characterize the failure intensity thereby obtained. Findings The findings show the impact of the recurrent failures in the times between failures (TBF) for rejection of the HPP and NHPP models. For systems not exhibiting a trend, RP models are presented, with TBF described by three-parameter lognormal or generalized logistic distributions, together with a methodology for generating clusters. Research limitations/implications For those systems that do not exhibit a trend, TBF is assumed to be independent and identically distributed (i.i.d.), and therefore, RP models of “perfect repair” have to be used. Practical implications Maintenance managers must refocus their efforts to study the reliability of individual repairable systems and their recurrent failures, instead of collections, in order to customize maintenance to the needs of each system. Originality/value The stochastic process models were applied for the first time to electric traction systems in 23 trains and to 40 escalators with ten years of operating data in a railway company. A practical application of the IEC models is presented for the first time.