scholarly journals Exponentially Weighted Moving Averages of Counting Processes When the Time between Events Is Weibull Distributed

2020 ◽  
Author(s):  
Ross Stewart Sparks ◽  
Hossein Hazrati-Marangaloo
Keyword(s):  
Control Charts ◽  
Negative Binomial ◽  
Counting Processes ◽  
Moving Averages ◽  
Control Distribution ◽  
Poisson Counts ◽  
Exponentially Weighted

There are control charts for Poisson counts, zero-inflated Poisson counts, and over dispersed Poisson counts (negative binomial counts) but nothing on counting processes when the time between events (TBEs) is Weibull distributed. In our experience the in-control distribution for time between events is often Weibull distributed in applications. Counting processes are not Poisson distributed or negative binomial distributed when the time between events is Weibull distributed. This is a gap in the literature meaning that there is no help for practitioners when this is the case. This book chapter is designed to close this gap and provide an approach that could be helpful to those applying control charts in such cases.

scholarly journals GLM-Based Flexible Monitoring Methods: An Application to Real-Time Highway Safety Surveillance

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 362
Author(s):  
Arshad Jamal ◽  
Tahir Mahmood ◽  
Muhamad Riaz ◽  
Hassan M. Al-Ahmadi
Keyword(s):  
Real Time ◽  
Control Charts ◽  
Negative Binomial ◽  
Highway Safety ◽  
Monitoring Methods ◽  
Count Data Models ◽  
Crash Data ◽  
Safety Surveillance ◽  
Study Results ◽  
Best Fit

Statistical modeling of historical crash data can provide essential insights to safety managers for proactive highway safety management. While numerous studies have contributed to the advancement from the statistical methodological front, minimal research efforts have been dedicated to real-time monitoring of highway safety situations. This study advocates the use of statistical monitoring methods for real-time highway safety surveillance using three years of crash data for rural highways in Saudi Arabia. First, three well-known count data models (Poisson, negative binomial, and Conway–Maxwell–Poisson) are applied to identify the best fit model for the number of crashes. Conway–Maxwell–Poisson was identified as the best fit model, which was used to find the significant explanatory variables for the number of crashes. The results revealed that the road type and road surface conditions significantly contribute to the number of crashes. From the perspective of real-time highway safety monitoring, generalized linear model (GLM)-based exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are proposed using the randomized quantile residuals and deviance residuals of Conway–Maxwell (COM)–Poisson regression. A detailed simulation-based study is designed for predictive performance evaluation of the proposed control charts with existing counterparts (i.e., Shewhart charts) in terms of the run-length properties. The study results showed that the EWMA type control charts have better detection ability compared with the CUSUM type and Shewhart control charts under small and/or moderate shift sizes. Finally, the proposed monitoring methods are successfully implemented on actual traffic crash data to highlight the efficacy of the proposed methods. The outcome of this study could provide the analysts with insights to plan sound policy recommendations for achieving desired safety goals.

scholarly journals Training Load and Baseline Characteristics Associated With New Injury/Pain Within an Endurance Sporting Population: A Prospective Study

2019 ◽  
Vol 14 (5) ◽  
pp. 590-597 ◽  
Author(s):  
Richard Johnston ◽  
Roisin Cahalan ◽  
Laura Bonnett ◽  
Matthew Maguire ◽  
Alan Nevill ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Frailty Model ◽  
Training Load ◽  
Moving Averages ◽  
Shared Frailty Model ◽  
Shared Frailty ◽  
History Of ◽  
Baseline Characteristics ◽  
A Prospective Study ◽  
Exponentially Weighted

Purpose: To determine the association between training-load (TL) factors, baseline characteristics, and new injury and/or pain (IP) risk in an endurance sporting population (ESP). Methods: Ninety-five ESP participants from running, triathlon, swimming, cycling, and rowing disciplines initially completed a questionnaire capturing baseline characteristics. TL and IP data were submitted weekly over a 52-wk study period. Cumulative TL factors, acute:chronic workload ratios, and exponentially weighted moving averages were calculated. A shared frailty model was used to explore time to new IP and association to TL factors and baseline characteristics. Results: 92.6% of the ESP completed all 52 wk of TL and IP data. The following factors were associated with the lowest risk of a new IP episode: (a) a low to moderate 7-d lag exponentially weighted moving averages (0.8–1.3: hazard ratio [HR] = 1.21; 95% confidence interval [CI], 1.01–1.44; P = .04); (b) a low to moderate 7-d lag weekly TL (1200–1700 AU: HR = 1.38; 95% CI, 1.15–1.65; P < .001); (c) a moderate to high 14-d lag 4-weekly cumulative TL (5200–8000 AU: HR = 0.33; 95% CI, 0.21–0.50; P < .001); and (d) a low number of previous IP episodes in the preceding 12 mo (1 previous IP episode: HR = 1.11; 95% CI, 1.04–1.17; P = .04). Conclusions: To minimize new IP risk, an ESP should avoid high spikes in acute TL while maintaining moderate to high chronic TLs. A history of previous IP should be considered when prescribing TLs. The demonstration of a lag between a TL factor and its impact on new IP risk may have important implications for future ESP TL analysis.

Various Workload Models and the Preseason Are Associated With Injuries in Professional Female Cyclists

2021 ◽  
pp. 1-6
Author(s):  
Teun van Erp ◽  
Taco van der Hoorn ◽  
Marco J.M. Hoozemans ◽  
Carl Foster ◽  
Jos J. de Koning
Keyword(s):  
Generalized Estimating Equations ◽  
Perceived Exertion ◽  
Estimating Equations ◽  
Rating Of Perceived Exertion ◽  
Moving Averages ◽  
The Third ◽  
Increased Risk ◽  
The Difference ◽  
Workload Models ◽  
Exponentially Weighted

Purpose: To determine if workload and seasonal periods (preseason vs in season) are associated with the incidence of injuries and illnesses in female professional cyclists. Methods: Session rating of perceived exertion was used to quantify internal workload and was collected from 15 professional female cyclists, from 33 athlete seasons. One week (acute) workload, 4 weeks (chronic) workload, and 3 acute:chronic workload models were analyzed. Two workload models are based on moving averages of the ratios, the acute:chronic workload ratio (ACWR), and the ACWR uncoupled (ACWRuncoup). The difference between both is the chronic load; in ACWR, the acute load is part of the chronic load, and in ACWRuncoup, the acute and chronic load are uncoupled. The third workload model is based on exponentially weighted moving averages of the ratios. In addition, the athlete season is divided into the preseason and in season. Results: Generalized estimating equations analysis was used to assess the associations between the workload ratios and the occurrence of injuries and illnesses. High values of acute workload (P = .048), ACWR (P = .02), ACWRuncoup (P = .02), exponentially weighted moving averages of the ratios (P = .01), and the in season (P = .0001) are significantly associated with the occurrence of injury. No significant associations were found between the workload models, the seasonal periods, and the occurrence of illnesses. Conclusions: These findings suggest the importance of monitoring workload and workload ratios in female professional cyclists to lower the risk of injuries and therefore improve their performances. Furthermore, these results indicate that, in the preseason, additional stressors occur, which could lead to an increased risk of injuries.

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