Time Distribution Of Occurrence Research Articles

A non-homogeneous alternating renewal process model for interval censoring

Abstract Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant. In this work, we introduce a model which allows for non-homogeneous behaviour in both cases. In particular, we outline a censoring mechanism based on a non-homogeneous alternating renewal process in which interval generation is assumed to be time-dependent, and we propose a Markov point process model for the underlying occurrence time distribution. We prove the existence of this process and derive the conditional distribution of the occurrence times given the intervals. We provide a framework within which the process can be accurately modelled, and subsequently compare our model to the homogeneous approach through a number of illustrative examples.

Occurrence time distribution fitting and encounter probability analysis of extreme precipitation in the Huaihe River Basin

Occurrence time distribution fitting and encounter probability analysis of extreme precipitation in the Huaihe River Basin

Estimating the Occurrence Rate for Alpha-Series Process in Rayleigh Distribution

The geometric process is sometimes appropriate for reliability and scheduling problems. Some previous studies suggested a possible alternative process that is alpha-series as to the geometric process when it decreases with time, as the decreasing geometric process shows that the expected number of events at an arbitrary time does not exist. In contrast, the expected number of events of the alpha-series process (ASP) exists at an arbitrary time under some conditions. In this paper, we assumed that the first arrival followed the Rayleigh distribution (RD). The modified moment estimator was proposed to estimate the alpha-series process parameters in the Rayleigh distribution and compare it with the maximum likelihood estimators. A simulation was conducted to compare the two estimators. The real-data application of intervals between successive failures of the Mosul Dam power station in Nineveh governorate in Iraq is provided to illustrate the results. When the initial occurrence time distribution is indicated to be RD, an estimate of the occurrence rate of an ASP is investigated in this study. Estimators are generated using modified moment (MM), and maximum likelihood (ML) approaches. According to the simulation study's findings, the MM estimator outperforms the ML estimator. In all cases, ASP with RD provides better data than the renewal process (RP) in real data sets. A test statistic has been devised to determine if the data conforms to an ASP.

Quantifying the structural and temporal characteristics of negative links in signed citation networks

Although the citation relationships among papers can help in tracking and understanding the development of knowledge, few studies have noted that the content and sentiments of citations of a paper differ. Here, we use sentiment-labeled citation data to construct a directed signed citation network, in which an author may agree with or criticize the cited paper and these represent different ways of inheriting knowledge. The dataset we use consists of 9,038 papers in the field of Computational Linguistics, including 25,275 citations, with 20.8% positive citations, 8.6% negative citations and 70.6% neutral citations. We systematically quantify the structural patterns of negative citations, impact assortativity of involved papers, occurrence time distribution and consequences of receiving negative attention. Remarkably, we find that papers with different impacts have a similar probability of receiving negative citations, and highly cited papers tend to give negative citations to low-impact papers around but avoid giving negative citations to high-impact papers. Our research also reveals the random occurrence rules and colocation patterns of negative citation distribution. In addition, we show that, in the short term, around 60% of multiple negative citations is positively related to the impact of the cited paper while more than 80% are negatively related to the impact in the long run. Our findings explain the pattern by which negative citations occur and deepen the understanding of negative citations.

Digital Twin-driven framework for fatigue lifecycle management of steel bridges

This paper presents a Digital Twin-driven framework for fatigue lifecycle management of steel bridges. A probabilistic multi-scale fatigue deterioration model is proposed to predict the entire fatigue process of steel bridges. Bayesian inference of the deterioration parameters realizes the real-time updating of the predicted lifecycle fatigue evolution process, which provides a good basis for lifecycle optimization. To avoid an empirically predefined repair crack size for maintenance, an optimization process for maintenance strategies is included. The relationship of the extended lifetime and the design repair crack size is constructed by numerical experimental design and surrogate modeling. The solution for optimum repair crack size is obtained while maximizing the extended fatigue life and minimizing the maintenance costs. Based on the occurrence time distribution of the optimum repair crack size, the inspection/monitoring planning is determined from a probabilistic optimization process based on the minimization of the expected damage detection delay and the lifecycle costs. The uncertainties associated with the damage occurrence and detection ability are considered during the formulation of the expected damage detection delay by decision tree analysis. Based on Digital Twin concept, the predicted deterioration process, derived maintenance, and inspection/monitoring planning are timely updated until a defined stopping rule is met.

A multiplicative model of software defect repair times

We hypothesize that software defect repair times can be characterized by the Laplace Transform of the Lognormal (LTLN) distribution. This hypothesis is rooted in the observation that software defect repair times are influenced by the multiplicative interplay of several factors, and the lognormal distribution is a natural choice to model rates of occurrence of such phenomenon. Conversion of the lognormal rate distribution to an occurrence time distribution yields the LTLN. We analyzed a total of more than 10,000 software defect repair times collected over nine products at Cisco Systems to confirm our LTLN hypothesis. Our results also demonstrate that the LTLN distribution provides a statistically better fit to the observed repair times than either of the two most widely used repair time distributions, namely, the lognormal and the exponential. Moreover, we show that the repair times of subsets of defects, partitioned according to the Orthogonal Defect Classification (ODC) scheme also follow the LTLN distribution. Finally, we describe how the insights that lead to the LTLN repair time model allow us to consider and evaluate alternative process improvement strategies.

Spectral estimator for dynamic-test data from turbine-blade vibrations

This paper presents an analysis of the distribution of occurrence times for pulse trains which can arise in the measurement of turbine-blade vibrations. The problem arises where a proximity probe, mounted in the casing, detects the passing of a rotor-blade tip and generates a pulse. Since the pulse timing depends on the magnitude of the blade vibration an irregular distribution of time intervals arises, and here the properties of the pulse-occurrence distribution are related to the blade-vibration statistics. In particular, a spectral estimator is considered and its errors are evaluated. The analysis provides a solution to a general problem in the estimation of the power-spectral-density function of a Gaussian process from observations of crossings at an arbitrary barrier.