Probability Distribution Of Duration Research Articles

Choice of Probability Distributions for Activity Durations in Project Networks with Limited Sample Size

Choice of Probability Distributions for Activity Durations in Project Networks with Limited Sample Size

Non-Mixture Cure Model Estimation in Bladder Cancer Patients: A Novel Approach with Exponentiated Weibull Exponential Distribution.

Cure models are frequently used in survival analysis to account for a cured fraction in the data. When there is a cure rate present, researchers often prefer cure models over parametric models to analyse the survival data. These models enable the ability to define the probability distribution of survival durations for patients who are at risk. Various distributions can be considered for the survival times, such as Exponentiated Weibull Exponential (EWE), Exponential Exponential (EE), Weibull and lognormal distribution. The objective of this research is to choose the most appropriate distribution that accurately represents the survival times of patients who have not been cured. This will be accomplished by comparing various non-mixture cure models that are based on the EWE distribution with its sub-distributions, and distributions distinct from those belonging to the EWE distribution family. A sample of 85 patients diagnosed with superficial bladder tumours was selected to be used in fitting the non-mixture cure model. In order to estimate the parameters of the suggested model, which takes into account the presence of a cure rate, censored data, and covariates, we utilized the maximum likelihood estimation technique using R software version 3.5.7. Upon conducting a comparison of various parametric models fitted to the data, both with and without considering the cure fraction and without incorporating any predictors, the EE distribution yields the lowest AIC, BIC, and HQIC values among all the distributions considered in this study, (1191.921/1198.502, 1201.692/1203.387, 1195.851/1200.467). Furthermore, when considering a non-mixture cure model utilizing the EE distribution along with covariates, an estimated ratio was obtained between the probabilities of being cured for placebo and thiotepa groups (and its 95% confidence intervals) were 0.76130 (0.13914, 6.81863). The findings of this study indicate that EE distribution is the optimal selection for determining the duration of survival in individuals diagnosed with bladder cancer.

Duration and extent of solar X-ray flares and shortwave fadeouts likely to impact high frequency radio wave propagation based on an evaluation of absorption at 30 MHz

High frequency (HF; 3–30 MHz) radio wave propagation can be impacted by absorption that results from enhanced photoionization in the dayside D-region following a solar X-ray flare. A database of >25,000 solar X-ray flares was evaluated to characterize the relationship between flare duration and the peak of the 0.1–0.8 nm solar X-ray flux. Expressions describing the mean and 90th percentile duration were developed. Based on these models, mean durations of 13, 18, 27, and 39 min and 90th percentile durations of 30, 48, 77, and 123 min are expected for C1, M1, X1 and X10 solar X-ray flares, respectively. A probability distribution of flare durations was developed to describe the probability of flare duration lasting 0–15, 15–30, 30–45, 45–60, 60–90, >90 min. In addition to flare duration, the duration of the expected impact to HF radio waves was evaluated. By considering examples where HF radio wave propagation in the 5–15 MHz range was impacted by space weather, a 0.5 dB threshold at 30 MHz was observed in samples of riometer data. Absorption modelled at 1-min increments from 1986 to 2017 was evaluated to create a probability distribution of impact duration, defined as the length of time the modelled 30 MHz absorption exceeded 0.5 dB during a single event. Modelled absorption was further evaluated to demonstrate the geographic extent of enhanced absorption, and to determine the minimum solar X-ray flux required to exceed the 0.5 dB impact threshold at a given latitude as a function of solar zenith angle and time of year. The results of this paper provide a better understanding of the impact of solar X-ray flares on high frequency radio wave propagation and aid in the development of tools and services for mitigating space weather impacts to systems that rely on HF radio wave propagation.

A Hidden Semi-Markov Model for Predicting Production Cycle Time Using Bluetooth Low Energy Data

This study proposes a statistical model to characterize the temporal characteristics of an entire production process. The model utilizes received signal strength indicator (RSSI) data obtained from a Bluetooth low energy (BLE) network. A hidden semi-Markov model (HSMM) is formulated based on the characteristics of the production process, and the forward-backward algorithm is employed to re-estimate the probability distribution of state durations. The proposed method is validated through numerical, simulation, and real-world experiments, yielding promising results. The results show that the Kullback-Leibler divergence (KLD) score of 0.1843, while the simulation achieves an average vector distance score of 0.9740. The real-time experiment also shows a reasonable accuracy, with an average HSMM estimated throughput time of 30.48 epochs, compared to the average real throughput time of 33.99 epochs. Overall, the model serves as a valuable tool for predicting the cycle time and throughput time of a production line.

Copula-Based Severity–Duration–Frequency (SDF) Analysis of Streamflow Drought in the Source Area of the Yellow River, China

In classical severity–duration–frequency (SDF) analysis, the dependence between drought characteristics is not effectively considered. The present study aims to propose the SDF relationships of streamflow drought in the source area of the Yellow River (SAYR) using a copula-based approach. Comparison of multiple time-varying threshold levels and the integration and elimination of drought events were considered. Selection of marginal probability distribution and copula-based joint probability distribution was properly conducted with multiple means. Copula-based joint and conditional probabilities were computed. The findings support carrying out integration and elimination processing on the preliminarily identified streamflow droughts through a run analysis with a time-varying threshold level of the 80% quantile of daily streamflow. The Gaussian copula was selected as the optimal model for constructing bivariate joint probability distribution, with generalized extreme value and log-normal as the suitable marginal probability distributions of streamflow drought duration and severity. The proposed copula-based SDF relationships of streamflow drought events can provide more critical information in addition to univariate frequency analysis, benefitting from the joint and conditional probabilities. The multivariate probabilistic analyses can effectively consider the connection and interaction between drought characteristics, while conditional probability distribution allows analyzing the impact of one drought characteristic on another. The results also indicate a relatively high risk of streamflow drought with short duration and low severity in the region, requiring effective drought-mitigation strategies and measures.

Periodic Transmissions in Random Access Networks: Stressed Period and Delay

Most IoT systems use random access protocols for wireless communication. This paper considers an IoT node that generates periodic traffic to be delivered to a destination over a random access network; each packet of the node is expected to be delivered before its deadline. We say that the node is in a stressed period if, within a time interval, its successive packets miss their deadlines. In many systems, the worst-case performance is significantly affected by stressed periods. Characterizing the stochastic properties of stressed periods is thus of fundamental importance. In this paper, we use a fluid flow model to approximate the evolution of the buffer occupancy (i.e., backlog) at the transmitting node. We derive a relationship between buffer occupancy and delay and formally define a stressed period via a time interval in which the buffer occupancy exceeds a certain threshold. With this model, we analyze the dynamics of the buffer occupancy evolution and obtain the probability distributions of stressed period duration and delay. Real network experiments show that our model can well approximate the distributions of stressed period duration and delay in practical WiFi networks. The theoretical results of this paper can be used to analyze the robustness and worst-case performance of IoT monitoring and control systems built on random access networks.

Maximum entropy copula for bivariate drought analysis

Copula functions are widely used to derive multivariate probability distributions in hydrometeorology. One of the key steps in the copula method is the derivation of marginal distributions of individual variables which can be accomplished using the principle of maximum entropy where the distribution parameters are estimated from the specified constraints. This study, investigated two drought variables (severity and duration) by coupling the principle of maximum entropy with parametric and empirical copulas. So, homogeneous climatic zones were first identified by applying the fuzzy clustering method to data from 39 synoptic stations in Iran and then drought severity and duration were determined with the standardized precipitation index. These two variables were scaled and their marginal probability distribution functions were derived using the principle of maximum entropy as well as empirically. Then, the joint probability distribution of drought severity and duration was determined using maximum entropy-copula, and parametric and empirical copulas. Thereafter, bivariate conditional return periods were determined for each homogeneous region. Results showed that 1) univariate and bivariate distributions can be obtained by maximizing entropy; 2) the dependence structure via Spearman's rho, which directly affects the Lagrange parameters of entropy copula, was a controlling factor to optimize the objective function; 3) for a given set of constraints, the maximum entropy copula is independent of the types of marginals; 4)The entropy-entropy copula (with entropy marginals) is considered a better method than alternatives, because it has a similar result to the parametric methods while it only needs to fit a single model.

Statistical properties of group energy and group duration for unidirectional ocean wave groups

The statistical properties of ocean wave groups play an important role in determining the design of marine structures and in analyzing of hydrodynamic phenomena. Unlike the definition of wave groups based on continuous large waves under the assumption of a narrow band in previous studies, the paper investigates the characteristics of all unidirectional wave groups that may lead to responses of structures in not only narrow but also wide spectra. Both marginal and joint distributions of group energy and duration for wave groups with various peak periods and spectral widths are analyzed. It is found that Generalized Extreme Value (GEV) distributions can provide excellent fits for both the marginal probability distributions of group energy and group duration. Moreover, a Gaussian Copula function can best fit the joint distribution of group energy and group duration. Last, formulae to predict the univariate and bivariate possibility distributions of group energy and group duration are constructed by giving a peak period and a spectral width of a sea state. After testing numerous wave cases, it is found that the formulations predict statistical properties of wave groups accurately in both narrow and wide spectral width as a peak period varying from 6.0 to 17.0 s.

ECG segmentation algorithm based on bidirectional hidden semi-Markov model

Accurate segmentation of electrocardiogram (ECG) waves is crucial for cardiovascular diseases (CVDs). In this study, a bidirectional hidden semi-Markov model (BI-HSMM) based on the probability distributions of ECG waveform duration was proposed for ECG wave segmentation. Four feature-vectors of ECG signals were extracted as the observation sequence of the hidden Markov model (HMM), and the statistical probability distribution of each waveform duration was counted. Logistic regression (LR) was used to train model parameters. The starting and ending positions of the QRS wave were first detected, and thereafter, bidirectional prediction was employed for the other waves. Forwardly, ST segment, T wave, and TP segment were predicted. Backwardly, P wave and PQ segments were detected. The Viterbi algorithm was improved by integrating the recursive formula of the forward prediction and backward backtracking algorithms. In the QT database, the proposed method demonstrated excellent performance (Acc = 97.98%, F1 score of P wave = 98.37%, F1 score of QRS wave = 97.60%, F1 score of T wave = 97.79%). For the wearable dynamic electrocardiography (DCG) signals collected by the Shandong Provincial Hospital (SPH), the detection accuracy was 99.71% and the F1 of each waveform was above 99%. The experimental results and real DCG signal validation confirmed that the proposed new BI-HSMM method exhibits significant ability to segment the resting and DCG signals; this is conducive to the detection and monitoring of CVDs.

Dynamic and Interpretable Hazard-Based Models of Traffic Incident Durations

Understanding and predicting the duration or “return-to-normal” time of traffic incidents is important for system-level management and optimization of road transportation networks. Increasing real-time availability of multiple data sources characterizing the state of urban traffic networks, together with advances in machine learning offer the opportunity for new and improved approaches to this problem that go beyond static statistical analyses of incident duration. In this paper we consider two such improvements: dynamic update of incident duration predictions as new information about incidents becomes available and automated interpretation of the factors responsible for these predictions. For our use case, we take one year of incident data and traffic state time-series data from the M25 motorway in London. We use it to train models that predict the probability distribution of incident durations, utilizing both time-invariant and time-varying features of the data. The latter allow predictions to be updated as an incident progresses, and more information becomes available. For dynamic predictions, time-series features are fed into the Match-Net algorithm, a temporal convolutional hitting-time network, recently developed for dynamical survival analysis in clinical applications. The predictions are benchmarked against static regression models for survival analysis and against an established dynamic technique known as landmarking and found to perform favourably by several standard comparison measures. To provide interpretability, we utilize the concept of Shapley values recently developed in the domain of interpretable artificial intelligence to rank the features most relevant to the model predictions at different time horizons. For example, the time of day is always a significantly influential time-invariant feature, whereas the time-series features strongly influence predictions at 5 and 60-min horizons. Although we focus here on traffic incidents, the methodology we describe can be applied to many survival analysis problems where time-series data is to be combined with time-invariant features.

Project scheduling and performance prediction: a fuzzy-Bayesian network approach

PurposeDespite the extensive research in project risk management and availability of several techniques and tools, quantifying uncertainty in project schedules remains a challenge. Current risk analysis models suffer from several shortcomings that need to be addressed to provide more reliable and valid schedules. This paper aims to present a dynamic decision support system with the purpose of providing project managers with necessary tool for making real-time informed decisions.Design/methodology/approachThe proposed approach incorporates the widely accepted critical path method (CPM) calculations in a Bayesian network (BN). BN is employed to conduct inferencing and causal analysis and provide probabilistic results, which can improve the decision-making process. Time parameters of each activity in the CPM network is modeled by a set of simulation nodes in the BN. Prior probability distribution of activities duration is extracted from experts using a fuzzy analytical solution.FindingsThe model proposed in this paper is able to address some key outstanding issues of current project scheduling techniques through: (1) modeling the causality among different sources of schedule uncertainty, (2) minimizing uncertainty in experts' evaluations, (3) assessing effects of unknown risk factors and (4) using actual activity data for learning the behavior of project and predicting crew productivity.Originality/valueThe purposed methodology provides a framework for the new generation of project schedule analysis tools that are better informed by available knowledge and data, and hence, more reliable and useful.

The RED scheme: Rate-constant estimation from pre-steady state weighted ensemble simulations.

We present the Rate from Event Durations (RED) scheme, a new scheme that more efficiently calculates rate constants using the weighted ensemble path sampling strategy. This scheme enables rate-constant estimation from shorter trajectories by incorporating the probability distribution of event durations, or barrier-crossing times, from a simulation. We have applied the RED scheme to weighted ensemble simulations of a variety of rare-event processes that range in complexity: residue-level simulations of protein conformational switching, atomistic simulations of Na+/Cl- association in explicit solvent, and atomistic simulations of protein-protein association in explicit solvent. Rate constants were estimated with up to 50% greater efficiency than the original weighted ensemble scheme. Importantly, our scheme accounts for the systematic error that results from statistical bias toward the observation of events with short durations and reweights the event duration distribution accordingly. The RED scheme is relevant to any simulation strategy that involves unbiased trajectories of similar length to the most probable event duration, including weighted ensemble, milestoning, and standard simulations as well as the construction of Markov state models.

Intensity of Respiratory Cortical Arousals Is a Distinct Pathophysiologic Feature and Is Associated with Disease Severity in Obstructive Sleep Apnea Patients.

Background: We investigated whether the number, duration and intensity of respiratory arousals (RA) on C3-electroencephalographic (EEG) recordings correlate with polysomnography (PSG)-related disease severity in obstructive sleep apnea (OSA) patients. We also investigated if every patient might have an individual RA microstructure pattern, independent from OSA-severity. Methods: PSG recordings of 20 OSA patients (9 female; age 27–80 years) were analyzed retrospectively. Correlation coefficients were calculated between RA microstructure (duration, EEG-intensity) and RA number and respiratory disturbance index (RDI), oxygen desaturation index (ODI) and arousal index (AI). Intraclass correlations (ICC) for both RA duration and intensity were calculated. Sleep stage-specific and apnea- and hypopnea-specific analyses were also done. The probability distributions of duration and intensity were plotted, interpolated with a kernel which fits the distribution. A Bayesian posterior distribution analysis and pair-wise comparisons of each patient with all other 19 patients were performed. Results: Of the analyzed 2600 RA, strong positive correlations were found between average RA intensity and both RDI and AI. The number of PSG-recorded RA was strongly positively correlated with RDI. Significant correlations between average RA intensity in REM, NREM2 and NREM3 sleep stages and total ODI were identified. No sleep stage-specific correlations of arousal microstructure with age, sex, RDI or AI were identified. Although between-subjects ICC values were <0.25, within-subject ICC values were all >0.7 (all p < 0.05). While apnea-related RA duration did not differ from hypopnea-related RA duration, RA intensity was significantly higher (p = 0.00135) in hypopneas than in apneas. A clear individual pattern of arousal duration for each patient was made distinct. For arousal intensity, a Gaussian distribution was identified in most patients. The Bayesian statistics regarding the arousal microstructure showed significant differences between each pair of patients. Conclusions: Each individual patient with OSA might have an individual pattern of RA intensity and duration indicating a distinct individual pathophysiological feature. Arousal intensity was significantly higher in hypopneic than in apneic events and may be related causally to the diminished (compared to apneas) respiratory distress associated with hypopneas. RA intensity in REM, NREM2 and NREM3 strongly correlated with ODI.

Estimating horizontal movement performance of patient beds and the impact on emergency evacuation time

Emergency evacuation of patients from a hospital can be challenging in the event of a fire. Most emergency evacuation studies are based on the assumption that pedestrians are ambulant and can egress by themselves. However, this is often not the case during emergency evacuations in healthcare facilities such as hospitals and nursing homes. To investigate emergency evacuations in such healthcare facilities, we performed a series of controlled experiments to study the dynamics of patient beds in horizontal movement. We considered a patient bed because it is one of the commonly used devices to transport patients within healthcare facilities. Through a series of controlled experiments, we examined the change of velocity in corner turning movements and speed reductions in multiple trips between both ends of a straight corridor. Based on the experimental results, we then developed a mathematical model of total evacuation time prediction for a patient bed horizontally moving in a healthcare facility. Factoring uncertainty in the horizontal movement, we produced the probability distribution of movement duration and estimated the probability that an evacuation can be safely performed within certain amount of time. In addition, we predicted that the evacuation time would be longer than the prediction results from an existing model which assumes constant movement speed. Our results from the model demonstrated good agreement with our experimental results.

Probabilistic forecasting of surgical case duration using machine learning: model development and validation.

Accurate estimations of surgical case durations can lead to the cost-effective utilization of operating rooms. We developed a novel machine learning approach, using both structured and unstructured features as input, to predict a continuous probability distribution of surgical case durations. The data set consisted of 53783 surgical cases performed over 4 years at a tertiary-care pediatric hospital. Features extracted included categorical (American Society of Anesthesiologists [ASA] Physical Status, inpatient status, day of week), continuous (scheduled surgery duration, patient age), and unstructured text (procedure name, surgical diagnosis) variables. A mixture density network (MDN) was trained and compared to multiple tree-based methods and a Bayesian statistical method. A continuous ranked probability score (CRPS), a generalized extension of mean absolute error, was the primary performance measure. Pinball loss (PL) was calculated to assess accuracy at specific quantiles. Performance measures were additionally evaluated on common and rare surgical procedures. Permutation feature importance was measured for the best performing model. MDN had the best performance, with a CRPS of 18.1 minutes, compared to tree-based methods (19.5-22.1 minutes) and the Bayesian method (21.2 minutes). MDN had the best PL at all quantiles, and the best CRPS and PL for both common and rare procedures. Scheduled duration and procedure name were the most important features in the MDN. Using natural language processing of surgical descriptors, we demonstrated the use of ML approaches to predict the continuous probability distribution of surgical case durations. The more discerning forecast of the ML-based MDN approach affords opportunities for guiding intelligent schedule design and day-of-surgery operational decisions.

Hybrid fuzzy-Bayesian decision support tool for dynamic project scheduling and control under uncertainty

Construction projects are complex and highly uncertain due to their special characteristics. Considering the incapability of current project scheduling methods in addressing the associated uncertainty, there is an emerging need for a dynamic scheduling and monitoring tool during project implementation. This paper addresses this need by proposing a dynamic decision support tool which employs fuzzy set theory to assess the combinatory effect of multiple risk factors on activities duration and Bayesian network to control and predict productivity under uncertainty. Advantages of proposed decision support tool comparing to existing approaches are: (1) calculating the fuzzy weighted average through an exact analytical solution which avoids creating incorrect fuzzy membership functions; (2) employing Type-2 interval-valued fuzzy numbers to model the uncertainty in expert evaluations, and (3) utilizing the advantages of Bayesian network in updating prior probability distributions of duration and predict productivity with actual activity data. Proposed model contributes to knowledge that could help minimize the schedule overrun and improve overall project performance. To elaborate the methodology, modelling and updating procedures of a group of activities in a simulated bridge project is presented as a case study.

Using stochastic programming to solve an outpatient appointment scheduling problem with random service and arrival times

AbstractWe study a stochastic outpatient appointment scheduling problem (SOASP) in which we need to design a schedule and an adaptive rescheduling (i.e., resequencing or declining) policy for a set of patients. Each patient has a known type and associated probability distributions of random service duration and random arrival time. Finding a provably optimal solution to this problem requires solving a multistage stochastic mixed‐integer program (MSMIP) with a schedule optimization problem solved at each stage, determining the optimal rescheduling policy over the various random service durations and arrival times. In recognition that this MSMIP is intractable, we first consider a two‐stage model (TSM) that relaxes the nonanticipativity constraints of MSMIP and so yields a lower bound. Second, we derive a set of valid inequalities to strengthen and improve the solvability of the TSM formulation. Third, we obtain an upper bound for the MSMIP by solving the TSM under the feasible (and easily implementable) appointment order (AO) policy, which requires that patients are served in the order of their scheduled appointments, independent of their actual arrival times. Fourth, we propose a Monte Carlo approach to evaluate the relative gap between the MSMIP upper and lower bounds. Finally, in a series of numerical experiments, we show that these two bounds are very close in a wide range of SOASP instances, demonstrating the near‐optimality of the AO policy. We also identify parameter settings that result in a large gap in between these two bounds. Accordingly, we propose an alternative policy based on neighbor‐swapping. We demonstrate that this alternative policy leads to a much tighter upper bound and significantly shrinks the gap.

Change in the heatwave statistical characteristics over China during the climate warming slowdown

Heatwaves are multi-day periods of extremely high-temperature weather relative to a region's average conditions and are among the deadliest natural disasters. This study was designed to evaluate changes in the characteristics of heatwaves during the periods of warming acceleration versus warming slowdown using the multivariate joint probability distributions of heatwave duration and severity. The results revealed that: (1) From the warming acceleration period (1961–1997) to the warming slowdown period (1998–2017), the return levels of heatwave duration increased by <1.0 d as the return period increased. As the return period lengthened, the return level of heatwave severity rose as well; (2) The joint occurrence probability of heatwaves with both variables exceeding the 20-yr, 50-yr, and 100-yr return levels exhibited relative increases of 3%, 8%, and 16% across China, respectively. There were greater than the joint probability of heatwaves with only 1 variable exceeding the return levels; (3) The number of heatwaves with both duration and severity exceeding the 50-yr joint return period increased in China, and this increase was dominated by heatwaves with joint return periods of 50–100 years, leading to a strengthening of heatwave severity.

Completeness of the known graptoloid palaeontological record

Using a high-resolution chronology of graptoloid first and last appearances, we apply mathematical models that allow the simultaneous inference of the probability distribution of species durations and the effective sampling rate relating those durations to the observed stratigraphic ranges. This approach allows the completeness of the documented palaeontological record of graptoloids to be assessed. We estimate that c. 75% of species in the geographical regions that contribute to the stratigraphic data have been sampled and that, of those species known from more than a single stratigraphic horizon, c. 85% of their original durations, on average, are represented by their global composite stratigraphic ranges. As expected in light of their biostratigraphic importance, graptoloids have one of the most completely documented records among groups of fossil organisms. We expect that application of the methods used herein will show comparably complete records for other biostratigraphically relevant groups. Supplementary material: The R code and data are available at https://doi.org/10.6084/m9.figshare.c.4547174

Analysis of models for the Stochastic Outpatient Procedure Scheduling Problem

In this paper, we present a new stochastic mixed-integer linear programming model for the Stochastic Outpatient Procedure Scheduling Problem (SOPSP). In this problem, we schedule a day’s worth of procedures for a single provider, where each procedure has a known type and associated probability distribution of random duration. Our objective is to minimize the expectation of a weighted sum of patient waiting time, provider idling, and clinic overtime. We present computational results to show the size and characteristics of problem instances that can be solved with our model. We also compare this model to other formulations in the literature and analyze them both empirically and theoretically, demonstrating where significant improvements in performance can be gained with our proposed model. This work is motivated by our research on developing scheduling templates for endoscopic procedures at a major medical center. More broadly, however, the SOPSP is a stochastic single-resource sequencing and scheduling problem and therefore has applications both within and outside of healthcare operations.