Alternating Renewal Process Model 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.

Anomalous Grain Boundary Diffusion: Fractional Calculus Approach

Grain boundary (GB) diffusion in engineering materials at elevated temperatures often determines the evolution of microstructure, phase transformations, and certain regimes of plastic deformation and fracture. Interpreting experimental data with the use of the classical Fisher model sometimes encounters contradictions that can be related to violation of Fick’s law. Here, we generalize the Fisher model to the case of non-Fickian (anomalous) diffusion ubiquitous in disordered materials. The process is formulated in terms of the subdiffusion equations with time-fractional derivatives of order α∈(0,1] and β∈(0,1] for grain volume and GB, respectively. It is shown that propagation along GB for the case of a localized instantaneous source and weak localization in GB (β>α/2) is approximately described by distributed-order subdiffusion with exponents α/2 and β. The mean square displacement is calculated with the use of the alternating renewal process model. The tail of the impurity concentration profiles along the z axis is approximately described by the dependence ∝exp(-Az6/5) for all 0<α≤1, as in the case of normal GB diffusion, so the 6/5-law itself can serve as an identifier of a more general phenomenon, namely, anomalous GB diffusion.

Spatio-Temporal Synthesis of Continuous Precipitation Series Using Vine Copulas

Long and continuous series of precipitation in a high temporal resolution are required for several purposes, namely, urban hydrological applications, design of flash flood control structures, etc. As data of the temporally required resolution is often available for short period, it is advantageous to develop a precipitation model to allow for the generation of long synthetic series. A stochastic model is applied for this purpose, involving an alternating renewal process (ARP) describing a system consisting of spells that can take two possible states: wet or dry. Stochastic generation of rainfall time series using ARP models is straight forward for single site simulation. The aim of this work is to present an extension of the model to spatio-temporal simulations. The proposed methodology combines an occurrence model to define in which locations rainfall events occur simultaneously with a multivariate copula to generate synthetic events. Rainfall series registered in different regions of Germany are used to develop and test the methodology. Results are compared with an existing method in which long independent time series of rainfall events are transformed to spatially dependent ones by permutation of their order. The proposed model shows to perform as a satisfactory extension of the ARP model for multiple sites simulations.

Limits of Risk Predictability in a Cascading Alternating Renewal Process Model

Most risk analysis models systematically underestimate the probability and impact of catastrophic events (e.g., economic crises, natural disasters, and terrorism) by not taking into account interconnectivity and interdependence of risks. To address this weakness, we propose the Cascading Alternating Renewal Process (CARP) to forecast interconnected global risks. However, assessments of the model’s prediction precision are limited by lack of sufficient ground truth data. Here, we establish prediction precision as a function of input data size by using alternative long ground truth data generated by simulations of the CARP model with known parameters. We illustrate the approach on a model of fires in artificial cities assembled from basic city blocks with diverse housing. The results confirm that parameter recovery variance exhibits power law decay as a function of the length of available ground truth data. Using CARP, we also demonstrate estimation using a disparate dataset that also has dependencies: real-world prediction precision for the global risk model based on the World Economic Forum Global Risk Report. We conclude that the CARP model is an efficient method for predicting catastrophic cascading events with potential applications to emerging local and global interconnected risks.

Four Methods for Analyzing Partial Interval Recording Data, with Application to Single-Case Research

Partial interval recording (PIR) is a procedure for collecting measurements during direct observation of behavior. It is used in several areas of educational and psychological research, particularly in connection with single-case research. Measurements collected using partial interval recording suffer from construct invalidity because they are not readily interpretable in terms of the underlying characteristics of the behavior. Using an alternating renewal process model for the behavior under observation, we demonstrate that ignoring the construct invalidity of PIR data can produce misleading inferences, such as inferring that an intervention reduces the prevalence of an undesirable behavior when in fact it has the opposite effect. We then propose four different methods for analyzing PIR summary measurements, each of which can be used to draw inferences about interpretable behavioral parameters. We demonstrate the methods by applying them to data from two single-case studies of problem behavior.

A stochastic alternating renewal process model for unavailability analysis of standby safety equipment

The paper presents a stochastic approach to analyze instantaneous unavailability of standby safety equipment caused by latent failures. The problem of unavailability analysis is formulated as a stochastic alternating renewal process without any restrictions on the form of the probability distribution assigned to time to failure and repair duration. An integral equation for point unavailability is derived and numerically solved for a given maintenance policy. The paper also incorporates an age-based preventive maintenance policy with random repair time. In case of aging equipment, the asymptotic limit or average unavailability should be used with a caution, because it cannot model an increasing trend in unavailability as a result of increasing hazard rate (i.e. aging) of the time to failure distribution.

Measurement-comparable effect sizes for single-case studies of free-operant behavior.

Single-case research comprises a set of designs and methods for evaluating the effects of interventions, practices, or programs on individual cases, through comparison of outcomes measured at different points in time. Although there has long been interest in meta-analytic techniques for synthesizing single-case research, there has been little scrutiny of whether proposed effect sizes remain on a directly comparable metric when outcomes are measured using different operational procedures. Much of single-case research focuses on behavioral outcomes in free-operant contexts, which may be measured using a variety of different direct observation procedures. This article describes a suite of effect sizes for quantifying changes in free-operant behavior, motivated by an alternating renewal process model that allows measurement comparability to be established in precise terms. These effect size metrics have the advantage of comporting with how direct observation data are actually collected and summarized. Effect size estimators are proposed that are applicable when the behavior being measured remains stable within a given treatment condition. The methods are illustrated by 2 examples, including a re-analysis of a systematic review of the effects of choice-making opportunities on problem behavior.

Alternating Renewal Process Models for Behavioral Observation: Simulation Methods, Software, and Validity Illustrations

Direct observation recording procedures produce reductive summary measurements of an underlying stream of behavior. Previous methodological studies of these recording procedures have employed simulation methods for generating random behavior streams, many of which amount to special cases of a statistical model known as the alternating renewal process. This paper describes the alternating renewal process model in its general form, demonstrates how it provides an organizing framework for most past simulation research on direct observation procedures, and introduces a freely available software package that implements the model. The software can be used to simulate behavior streams as well as data from many common recording procedures, including continuous recording, momentary time sampling, event counting, and interval recording procedures. Several examples illustrate how the software can be used to study the validity and reliability of direct observation data and to develop measurement strategies during the planning phases of empirical studies.

최소절단집합과 최소경로집합을 이용한 구조 및 신뢰성 중요도 척도의 개발 및 적용

The research discusses interrelationship of structural and reliability importance measures which used in the probabilistic safety assessment. The most frequently used component importance measures, such as Birnbaum`s Importance (BI), Risk Reduction (RR), Risk Reduction Worth (RRW), RA (Risk Achievement), Risk Achievement Worth (RAW), Fussel Vesely (FV) and Critically Importance (CI) can be derived from two structure importance measures that are developed based on the size and the number of Minimal Path Set (MPS) and Minimal Cut Set (MCS). In order to show an effectiveness of importance measures which is developed in this paper, the three representative functional structures, such as series-parallel, k out of n and bridge are used to compare with Birnbaum`s Importance measure. In addition, the study presents the implementation examples of Total Productive Maintenance (TPM) metrics and alternating renewal process models with exponential distribution to calculate the availability and unavailability of component facility for improving system performances. System state structure functions in terms of component states can be converted into the system availability (unavailability) functions by substituting the component reliabilities (unavailabilities) for the component states. The applicable examples are presented in order to help the understanding of practitioners.

Alternating renewal process models for electric power system loads

Results are derived for a class of stochastic processes called alternating renewal processes that appear particularly suitable for modeling air-conditioning loads on electrical power systems. Expressions for the Laplace transforms of the nonstationary mean and the stationary autocorrelation function are obtained. If the on-duration and off-duration random variables have gamma distributions of the particular type known as Erlang-n, then the transforms will turn out to be rational functions. Therefore, this class of air-conditioning loads can be characterized by the poles and zeros of these functions. Moreover, pole and zero locations determined empirically under quasi-equilibrium conditions can be used to predict the payback transient. How these results permit the prediction of transient behavior after an outage based on measurements taken under nominal conditions is explained. >

Econometric Analysis of CPS-Type Unemployment Data

Analysts studying the unemployment experiences of population members often have access to data collected from a sample of individuals at a point in time which contain the length of the ongoing spell of unemployment for sample members currently unemployed. No information regarding the lengths of ongoing employment spells is collected. This paper considers how such information may be utilized in the estimation of parameters of alternating renewal process models of labor market attachment, in the presence of both observed and unobserved population heterogeneity. A number of models are presented, and estimation is carried out using a CPS-type data set from Italy