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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: This work characterize mean time to failure and system availability under the maximal repair policy where the whole system is replaced by a brand new after successfully completing a phase before the next phase starts.
46 citations
TL;DR: In this paper, a strong approximation of renewal processes in terms of partial sums has been developed and the consequences of this approximation are laws of the iterated logarithm and a Bahadur-Kiefer representation of the renewal process.
46 citations
TL;DR: In this article, a new method is presented which describes the behavior of an (N + 1) th-order tacking system in which the nonlinearity is either periodic [phase-locked loop (PLL) type] or a nonperiodic [delay-locked loops (DLL] type].
Abstract: A new method is presented which describes the behavior of an (N + 1) th-order tacking system in which the nonlinearity is either periodic [phase-locked loop (PLL) type] or a nonperiodic [delay-locked loop (DLL) type]. The cycle slipping of such systems is modeled by means of renewal Markov processes. A fundamental relation between the probability density function (pdf) of the single process and the renewal process is derived which holds in the transient as well as in the stationary state. Based on this relation it is shown that the stationary pdf, the mean time between two cycle slips, and the average number of cycles to the right (left) can be obtained by solving a single Fokker-Planck equation of the renewal process. The method is applied to the special case of a PLL and compared with the so-called periodic-extension (PE) approach. It is shown that the pdf obtained via the renewal-process approach can be reduced to agree with the PE solution for the first-order loop in the steady state only. The reasoning and its implications are discussed. In fact, it is shown that the approach based upon renewal-process theory yields more information about the system's behavior than does the PE solution.
45 citations
TL;DR: In this paper, the authors present explicit formulas for calculating the variance of the discounted costs over an unbounded time horizon, which can be easily implemented in software to optimise structural design and maintenance management.
45 citations
TL;DR: In this article, the authors investigated the Duffing oscillator under external non-Gaussian excitations by means of statistical linearization, where the input process is modelled as a polynomial of a Gaussian process or as a renewal-driven impulse process.
45 citations