Exponentially Weighted Moving Averages Research Articles

Comparison of weekly training load and acute:chronic workload ratio methods to estimate change in training load in running.

Before examining the impact of training load on injury risk in runners, it is important to gain insight in the differences between methods that are used to measure change in training load. To investigate differences between four methods to calculate change in training load: (1) weekly training load; (2) acute:chronic workload ratio (ACWR), coupled rolling average (RA); (3) ACWR, uncoupled RA; (4) ACWR, exponentially weighted moving averages (EWMA). Descriptive epidemiology study. This study is part of a randomized-controlled trial on running injury prevention among recreational runners. Runners received a baseline questionnaire and a request to share GPS training data. Runners who registered for running events (distances 10-42.195 kilometers) in the Netherlands. Primary outcome measure was the predefined significant increase in training load (weekly training loads ≥30% progression and ACWRs ≥1.5), based on training distance. Proportional Venn diagrams visualized the differences between the methods. 430 participants (73.3% men; age 44.3 years) shared their GPS training data with in total 22,839 training sessions. For the weekly training load, coupled RA, uncoupled RA, and EWMA method, respectively 33.4% (95% CI 32.8-34.0), 16.2% (95% CI 15.7-16.6), 25.8% (95% CI 25.3-26.4), and 18.9% (95% CI 18.4-19.4) of the training sessions were classified as significant increase in training load. Of the training sessions with significant increase in training load, 43.0% expressed in the weekly training load method showed a difference with the coupled RA and EWMA method. Training sessions with significant increase in training load based on the coupled RA method showed 100% overlap with the uncoupled RA and EWMA method. The difference in change in training load measured by weekly training load and ACWR methods was high. To validate an appropriate measure of change in training load in runners, future research on the association between training loads and RRI risk is needed.

Compromised-Imputation and EWMA-Based Memory-Type Mean Estimators Using Quantile Regression

Survey sampling commonly faces the challenge of missing information, prompting the development of various imputation-based mean estimation methods to address this concern. Among these, ratio-type regression estimators have been devised to compute population parameters using only current sample data. However, recent pioneering research has revolutionized this approach by integrating both past and current sample information through the application of exponentially weighted moving averages (EWMA). This groundbreaking methodology has given rise to the creation of memory-type estimators tailored for surveys conducted over time. In this paper, we present novel imputation-based memory-type mean estimators that leverage EWMA and quantile regression to handle missing observations. For the performance assessment between traditional, adapted and proposed estimators, real-life time-scaled datasets related to the stock market and humidity are considered. Furthermore, we conduct a simulation study using an asymmetric dataset to further validate the effectiveness of the introduced estimators. The humidity data results show that the proposed estimators (Tpq(0.25), Tpq(0.45), Tpq(0.25)′, Tpq(0.45)′, Tpq(0.25)″, Tpq(0.45)″) have the minimum MSE. The stock market data results show that the proposed estimators (Tpq(0.85), Tpq(0.85)′, Tpq(0.85)″) also have the minimum MSE. Additionally, the simulation results demonstrate that the proposed estimators (Tpq(0.45), Tpq(0.45)′, Tpq(0.45)″) have the minimum MSE when compared to traditional and adapted estimators. Therefore, in conclusion, the use of the proposed estimators is recommended over traditional and adapted ones.

Control Charts for Monitoring the Mean of Skew-Normal Samples

The presence of asymmetric data in production processes or service operations has prompted the development of new monitoring schemes. In this article, an adapted version of the exponentially weighted moving averages (EWMA) control chart with dynamic limits is proposed to monitor the mean of samples from the skew-normal distribution. The detection ability of the proposed control chart in online monitoring was investigated by simulating the average run length (ARL) performance for different out-of-control scenarios. The results of the simulation study suggest that the proposed scheme overcomes the main drawback of the recently developed Shewhart-type control scheme. As shown in this article, the existing Shewhart-type procedure exhibits the undesirable property of taking longer to detect changes in the mean value of skewed normal observations due to increases in the shape parameter of the basic distribution than in stable conditions. The proposed control chart was shown to work fairly acceptably in all considered out-of-control scenarios.

Efficient algorithms for real-time syndromic surveillance

ObjectiveOutbreaks of influenza-like diseases often cause spikes in the demand for hospital beds. Early detection of these outbreaks can enable improved management of hospital resources. The objective of this study was to test whether surveillance algorithms designed to be responsive to a wide range of anomalous decreases in the time between emergency department (ED) presentations with influenza-like illnesses provide efficient early detection of these outbreaks. MethodsOur study used data on ED presentations to major public hospitals in Queensland, Australia across 2017–2020. We developed surveillance algorithms for each hospital that flag potential outbreaks when the average time between successive ED presentations with influenza-like illnesses becomes anomalously small. We designed one set of algorithms to be responsive to a wide range of anomalous decreases in the time between presentations. These algorithms concurrently monitor three exponentially weighted moving averages (EWMAs) of the time between presentations and flag an outbreak when at least one EWMA falls below its control limit. We designed another set of algorithms to be highly responsive to narrower ranges of anomalous decreases in the time between presentations. These algorithms monitor one EWMA of the time between presentations and flag an outbreak when the EWMA falls below its control limit. Our algorithms use dynamic control limits to reflect that the average time between presentations depends on the time of year, time of day, and day of the week. ResultsWe compared the performance of the algorithms in detecting the start of two epidemic events at the hospital-level: the 2019 seasonal influenza outbreak and the early-2020 COVID-19 outbreak. The algorithm that concurrently monitors three EWMAs provided significantly earlier detection of these outbreaks than the algorithms that monitor one EWMA. ConclusionSurveillance algorithms designed to be responsive to a wide range of anomalous decreases in the time between ED presentations are highly efficient at detecting outbreaks of influenza-like diseases at the hospital level.

Assessing the Relationship Between External Workloads and Noncontact Injuries During Summer Conditioning and Preseason Practice in National Collegiate Athletic Association Division 1 Football Players.

Burghardt, WP, Pfeiffer, KA, and Kuenze, C. Assessing the relationship between external workloads and noncontact injuries during summer conditioning and preseason practice in National Collegiate Athletic Association Division 1 football players. J Strength Cond Res 37(4): 816-822, 2023-The purpose of this study was to prospectively investigate the relationship between noncontact injuries and workload in collegiate football during summer conditioning and preseason training. Workload and noncontact injury data were collected over the summer conditioning and preseason practice periods for a Division 1 National Collegiate Athletic Association football team ( n = 34). Seven- and 21-day exponentially weighted moving averages (EWMA) were calculated daily for each athlete. The acute:chronic ratio (A:C ratio) of these 2 measures was also calculated daily. Injury rates for noncontact injuries were calculated for both periods. Continuous variable modeling (panel logistic regression and restricted cubic spline) was used to assess the relationship of EWMA A:C ratio and noncontact injury using a 3-day lag period. Athletic exposures (AEs) were defined as individual sport training, practice, or competition sessions. Nine injuries were observed (6.97/1,000 AEs), with 4 injuries resulting in lost time (3.09/1,000 AEs). The mean EWMA A:C ratio was 0.92 ± 0.41 (95% confidence interval: 0.03-2.09). Both the panel logistic regression and the restricted cubic spline models showed a significant relationship between EWMA A:C ratio and noncontact injuries. However, the odds ratio (14.16) in the logistic regression had a very large standard error (14.51) and a wide 95% confidence interval (1.90-105.49). The restricted cubic spline model had a pseudo R2 of 0.136. Injury occurrence at given EWMA ratio values was lower than reported in previous research. Although both continuous models demonstrated a significant relationship between the EWMA A:C ratio and subsequent noncontact injuries over the next 3 days, neither model had sufficient goodness of fit to warrant adoption at this time.

Forecasting international equity market volatility: A new approach

AbstractWe propose a new heterogeneous autoregressive (HAR) model to investigate whether the novel HAR‐RV model we design exhibits superior predictive ability compared with the classical HAR‐RV model in forecasting the realized volatility (RV) of international equity markets. We reconstruct the weekly and monthly HAR components by using the exponentially weighted moving averages (EWMA) method, and the new model is therefore termed EWMA‐HAR‐RV. The in‐sample results and the out‐of‐sample analyses suggest that the EWMA‐HAR‐RV model exhibits stronger predictive power in predicting most international equity market RVs. We further analyze the source of additional predictive power for the EWMA‐HAR‐RV model and find that giving more weight to recent information and using more historical information are helpful for the predictions.

Paper 22: Increased Lower Extremity Injury Associated with Player Load and Distance in Collegiate Women’s Soccer

Objectives:High cumulative workloads and spikes in player workloads have been associated with an increased risk of injury in soccer and other sports. These studies, however, have all been conducted with data from male soccer players or male athletes in other sports, with few studies investigating female athletes. Using metrics collected from GPS units to monitor cumulative load and distance may be valuable for injury prevention. The purpose of this study was to examine the relationship between injury risk and workload as collected from wearable GPS units in NCAA Division I women’s soccer players.Methods:Lower extremity injury incidence and GPS workload data (player load, total distance, and high-speed distance) of 65 NCAA Division I women’s soccer players were collected over 3 seasons. Accumulated 1-, 2-, 3- and 4-weekly loads and acute: chronic workload ratios (ACWR) were classified into discrete ranges by z-scores. ACWR was calculated using rolling averages and exponentially weighted moving averages (EWMA) models. Binary logistic regression models were used to compare the 7:28 rolling average and EWMA ACWRs between injured and non-injured players for all GPS/accelerometer variables. The prior 1-, 2-, 3-, and 4-weekly accumulated loads for all GPS/accelerometer variables were compared between the injured and uninjured cohorts using two-sample t-tests with an alpha level of 0.05 set as significant.Results:There were a total of 53 lower extremity injuries that resulted in lost time recorded (5.76/1000 hours ‘on-field’ exposure time; 34 non-contact and 19 contact injuries). The prior 2-week (7,242 vs 6,613; p=0.02), 3-week (10,533 vs 9,718; p=0.02), and 4-week (13,819 vs 12,892; p=0.04) accumulated player loads and 2-week (62.40 vs 57.25 km; p=0.04), 3-week (90.97 vs 84.10 km; p=0.03), and 4-week (119.31 vs 111.38 km; p=0.05) accumulated total distances were significantly higher for injured players compared to non-injured players during the same timeframes. There were no significant differences in player load, total distance, or high-speed distance ACWR between injured and non-injured players for both the rolling averages and EWMA calculations.Conclusions:Higher accumulated player load and total distance, but not ACWR, are associated with injury in women’s soccer players.

Memory-type ratio and product estimators for population variance using exponentially weighted moving averages for time-scaled surveys

In this study, we have proposed memory-type ratio and product estimators for the estimation of population variance based on exponentially weighted moving averages (EWMA) statistic. The EWMA statistic simultaneously utilizes the current and previous information in time-scaled surveys. The equations of approximate mean square errors are established for proposed memory-type ratio and product estimators. The performance of the proposed estimators is evaluated mathematically by deriving the conditions in which memory-type ratio and product estimators are better than the conventional ratio and product estimators. The results of simulation study and real data application revealed that the use of previous sampled information excels the efficiency of the proposed estimators for time-scaled surveys.

Increased Lower Extremity Injury Risk Associated With Player Load and Distance in Collegiate Women's Soccer.

Background:There is limited research regarding the impact of workload on injury risk specific to women’s soccer. Wearable global positioning system (GPS) units can track workload metrics such as total distance traveled and player load during games and training sessions. These metrics can be useful in predicting injury risk.Purpose:To examine the relationship between injury risk and player workload as collected from wearable GPS units in National Collegiate Athletic Association (NCAA) Division I women’s soccer players.Study Design:Case-control study; Level of evidence, 3.Methods:Lower extremity injury incidence and GPS workload data (player load, total distance, and high-speed distance) for 65 NCAA Division I women’s soccer players were collected over 3 seasons. Accumulated 1-, 2-, 3-, and 4-week loads and acute-to-chronic workload ratios (ACWR) were classified into discrete ranges by z-scores. ACWR was calculated using rolling averages and exponentially weighted moving averages (EWMA) models. Binary logistic regression models were used to compare the 7:28 rolling average and EWMA ACWRs between injured and noninjured players for all GPS/accelerometer variables. The prior 1-, 2-, 3-, and 4-week accumulated loads for all GPS/accelerometer variables were compared between the injured and uninjured cohorts using 2-sample t tests.Results:There were a total of 53 lower extremity injuries that resulted in lost time recorded (5.76/1000 hours “on-legs” exposure time; 34 noncontact and 19 contact injuries). The prior 2-week (7242 vs 6613 m/s2; P = .02), 3-week (10,533 vs 9718 m/s2; P = .02), and 4-week (13,819 vs 12,892 m/s2; P = .04) accumulated player loads and 2-week (62.40 vs 57.25 km; P = .04), 3-week (90.97 vs 84.10 km; P = .03), and 4-week (119.31 vs 111.38 km; P = .05) accumulated total distances were significantly higher for injured players compared with noninjured players during the same time frames. There were no significant differences in player load, total distance, or high-speed distance ACWR between injured and noninjured players for both the rolling averages and EWMA calculations.Conclusion:Higher accumulated player load and total distance, but not ACWR, were associated with injury in women’s soccer players.

The association between training load indices and upper respiratory tract infections (URTIs) in elite soccer players

This study aimed to investigate the association between training load indices and Upper Respiratory Tract Infection (URTI) across different lag periods in elite soccer players. Internal training load was collected from 15 elite soccer players over one full season (40 weeks). Acute, chronic, Acute:Chronic Workload Ratio (ACWR), Exponentially Weighted Moving Averages (EWMA) ACWR, 2, 3 and 4-week cumulative load, training strain and training monotony were calculated on a rolling weekly basis. Players completed a daily illness log, documenting any signs and symptoms, to help determine an URTI. Multilevel logistic regression was used to analyze the associations between training load indices and URTIs across different lag periods (1 to 7-days). The results found a significant association between 2-week cumulative load and an increased likelihood of a player contracting an URTI 3 days later (Odds Ratio, 95% Confidence Interval: OR = 2.07, 95% CI = 0.026-1.431). Additionally, a significant association was found between 3-week cumulative load and a players’ increased risk of contracting an URTI 4 days later (OR = 1.66, 95% CI = 0.013–1.006). These results indicate that accumulated periods of high training load (2- and 3-week) associated with an increased risk of a player contracting an URTI, which may lead to performance decrements, missed training sessions or even competitions.

Improving intensity-modulated radiation therapy quality assurance by adopting statistical process control

PurposeTo use statistical process control for intensity-modulated radiation therapy (IMRT) quality assurance (QA) and improve tolerance limits and action limits. MethodsAn electronic portal imaging device (EPID) was selected to verify IMRT QA. The I-chart and the exponentially weighted moving averages (EWMA) chart were used to analyze the corresponding results. ResultsTwenty samples were used to enable the sampling requirements for building the control limits to be met. The I-chart showed that isolated data points beyond the control limits were mainly derived from complex plans. The EWMA made predictions of systematic errors earlier than the I-chart. Systematic errors primarily originated from the dose calibration on the EPID, and recalibrating the EPID could eliminate such errors. ConclusionStatistical process control is an effective tool to detect controllable and can be used in IMRT QA. After calibrating the EPID, the tolerance and action limits all improved and satisfied the requirements/recommended values of the AAPM TG-218 report.

The Association Between the Acute:Chronic Workload Ratio and Running-Related Injuries in Dutch Runners: A Prospective Cohort Study.

To investigate the association between the acute:chronic workload ratio (ACWR) and running-related injuries (RRI). This is a secondary analysis using a database composed of data from three studies conducted with the same RRI surveillance system. Longitudinal data comprising running exposure (workload) and RRI were collected biweekly during the respective cohorts' follow-up (18-65 weeks). ACWR was calculated as the most recent (i.e., acute) external workload (last 2 weeks) divided by the average external (i.e., chronic) workload of the last 4, 6, 8, 10 and 12 weeks. Three methods were used to calculate the ACWR: uncoupled, coupled and exponentially weighted moving averages (EWMA). Bayesian logistic mixed models were used to analyse the data. The sample was composed of 435 runners. Runners whose ACWR was under 0.70 had about 10% predicted probability of sustaining RRI (9.6%; 95% credible interval [CrI] 7.5-12.4), while those whose ACWR was higher than 1.38 had about 1% predicted probability of sustaining RRI (1.3%; 95% CrI 0.7-1.7). The association between the ACWR and RRI was significant, varying from a small to a moderate association (1-10%). The higher the ACWR, the lower the RRI risk. The ACWR showed an inversely proportional association with RRI risk that can be represented by a smooth L-shaped, second-order, polynomial decay curve. The ACWR using hours or kilometres yielded similar results. The coupled and uncoupled methods revealed similar associations with RRIs. The uncoupled method presented the best discrimination for ACWR strata. The EWMA method yielded sparse and non-significant results.

The Association Between Training Load Indices and Injuries in Elite Soccer Players.

Tiernan, C, Comyns, T, Lyons, M, Nevill, AM, and Warrington, G. The association between training load indices and injuries in elite soccer players. J Strength Cond Res 36(11): 3143-3150, 2022-To investigate the association between contact injuries, noncontact injuries, and training load indices, across different lag periods in elite soccer players. Internal load (session rate of perceived exertion) was collected from 15 elite soccer players over 1 season (40-weeks). Acute (7 days), chronic (28 days), acute:chronic workload ratio (ACWR) (uncoupled), exponentially weighted moving averages (EWMA) ACWR, and 2-, 3-, and 4-week cumulative load were calculated on a rolling weekly basis. Multilevel logistic regression was used to analyze the associations between contact, noncontact injuries, and training load indices, across different lag periods (5 and 7 days). A player was at a significantly higher risk of a noncontact injury 5 days later, if week-to-week acute load changes increased (odds ratio [OR] = 1.97). An increase in EWMA ACWR was associated with an increased risk of both a contact (OR = 1.30) and noncontact injury (OR = 1.35), 5 days later. An increase in 2-week cumulative load (OR = 1.77) was associated with an increased risk of a contact injury 7 days later and 3-week cumulative load (OR = 1.55) 5 days later. These findings suggest that to reduce the potential risk of a noncontact injury, training load should be gradually increased, avoiding an increase in week-to-week acute load change (≥9%) or EWMA ACWR (>1.20). Findings indicated that EWMA ACWR may be a more sensitive measure for detecting a player at a higher risk of an injury than ACWR. Furthermore, a high 2- and 3-week cumulative load was associated with an increased risk of a contact injury, which may indicate accumulated fatigue. Practitioners must note that this study investigated associations with injury risk and not injury prediction.

Does an Optimal Relationship Between Injury Risk and Workload Represented by the "Sweet Spot" Really Exist? An Example From Elite French Soccer Players and Pentathletes.

ObjectiveTo examine the relationships between the occurrence and severity of injuries using three workload ratios (ACWR, EWMA, REDI) in elite female soccer players and international male and female pentathletes.Materials and MethodsFemale soccer players in the U16 to U18 national French teams (n = 24) and international athletes (n = 12, 4 women and 8 men) in the French modern pentathlon team were monitored throughout an entire season. The Acute Chronic Workload Ratio (ACWR), the Exponentially Weighted Moving Averages (EWMA), and the Robust Exponential Decreasing Index (REDI) were calculated for internal load by the ROE method in soccer and external load in pentathlon. The occurrence and severity of injuries (determined according to time-loss) were quantified in the sweet spot zone [0.8; 1.3] and compared to the other zones of load variation: [0; 0.8], [1.3; 1.5], [1.5; +8], using the three ratios.ResultsOver the study period, a total of sixty-six injuries (2.75 per athlete) were reported in the soccer players and twelve in pentathletes (1 per athlete). The cumulative severity of all injuries was 788 days lost in soccer and 36 in pentathlon: respectively, 11.9 days lost per injury in soccer player and 3.0 per pentathlete. The mean values across the three methods in soccer showed a higher number of injuries detected in the [0; 0.8] workload ratio zone: 22.3 ± 6.4. They were 17.3 ± 3.5 in the sweet spot ([0.8–1.3] zone) and 17.6 ± 5.5 in the [1.5; +8] zone. In comparison to the [1.5; +8] zone, soccer players reported a higher number of days lost to injuries in the presumed sweet spot and in the [0–0.8] zone: 204.7 ± 28.7 and 275.0 ± 120.7 days, respectively. In pentathletes, ten of the twelve injuries (83.3%) occurred in the presumed sweet spot. REDI was the only method capable of tracking workloads over all-time series.ConclusionIn the present cohort of elite soccer players and pentathletes, acute chronic workload calculations showed an association with injury occurrence and severity but did not provide evidence supporting existence of a sweet spot diminishing injury risk.

EWMA and DEWMA repetitive control charts under non-normal processes

In this paper, we present a repetitive sampling method to construct control charts using exponentially weighted moving averages (EWMA) and double exponentially weighted moving averages (DEWMA) to monitor shift in the process. For non-normal processes, t-distribution with various degrees of freedom (i.e. ) is used as symmetric distribution, gamma distribution with unit scale parameter and various shape parameters (i.e. ) is used as positively skewed distribution and Weibull distribution with unit scale parameter and various shape parameters (i.e. 10 and 20) is used as negatively skewed distribution. We use Monte Carlo simulations to check whether the process is out of control. We use average run length as a tool to find the ability of proposed control charts to identify a shift earlier in a process, as compared to other control charts currently used to monitor the same type of process. The proposed control charts are applied to two real datasets.

Memory type estimators of population mean using exponentially weighted moving averages for time scaled surveys

Exponentially weighted moving average (EWMA) statistic is a memory type statistic that used present and past information to estimate the population parameter. This study utilizes EWMA statistic to propose a ratio and product estimator for the surveys based on time scale. The usual ratio and product estimators consist of only current sample information, whereas the proposed estimators consist of current as well as past sample information. The mean square error expressions of the proposed estimators are derived and mathematical conditions are established to prove the efficiency of proposed estimators. It is revealed from the results of simulation study that utilization of the past samples information excels the performance of estimator in terms of efficiency. Two real life examples are presented to demonstrate the use of proposed estimators.

An enhanced approach for the progressive mean control charts

AbstractTo maintain and improve the quality of the processes, control charts play an important role for reduction of variation. To detect large shifts in the process parameters, Shewhart control charts are commonly applied but for small shifts, exponentially weighted moving averages (EWMA), cumulative sum (CUSUM), double exponentially weighted moving average (DEWMA), double CUSUM, moving average (MA), double moving average (DMA), and progressive mean (PM) control charts, are used. This study proposes double progressive mean (DPM) and optimal DPM control charts to enhance the performance of the PM chart. As the proposed DPM control charts use information sequentially, hence their performance is compared with natural competitors EWMA, CUSUM, DEWMA, double CUSUM, MA, DMA, and PM control charts. Run length and its different properties are evaluated to compare the performance of the proposed charts and counterparts. Results reveal that proposed optimal DPM outperforms the other charts. An example related to voltage on fixed capacitance level is also provided to illustrate the proposed charts.

Injury risk-workload associations in NCAA American college football

ObjectivesTo determine injury risk-workload associations in collegiate American Football. DesignRetrospective analysis. MethodsWorkload and injury data was recorded from 52 players during a full NCAA football season. Acute, chronic, and a range of acute:chronic workload ratios (ACWR: 7:14, 7:21 and 7:28 day) calculated using rolling and exponentially weighted moving averages (EWMA) were plotted against non-contact injuries (regardless of time lost or not) sustained within 3- and 7-days. Injury risks were also determined relative to position and experience. Results105 non-contact injuries (18 game- and 87 training-related) were observed with almost 40% sustained during the pre-season. 7–21 day EWMA ACWR’s with a 3-day injury lag were most closely associated with injury (R2=0.54). Relative injury risks were >3× greater with high compared to moderate and low ratios and magnified when combined with low 21-day chronic workloads (injury probability=92.1%). Injury risks were similar across positions. ‘Juniors’ presented likely and possibly increased overall injury risk compared to ‘Freshman’ (RR: 1.94, CI 1.07–3.52) and ‘Seniors’ (RR: 1.7, CI 0.92–3.14), yet no specific ACWR – experience or – position interactions were identified. ConclusionsHigh injury rates during college football pre-season training may be associated with high acute loads. In-season injury risks were greatest with high ACWR and evident even when including (more common and less serious) non-time loss injuries. Substantially increased injury risks when low 21-day chronic workloads and concurrently high EWMA ACWR highlights the importance of load management for individuals with chronic game- (non-involved on game day) and or training (following injury) absences.

Statistical process control and quality of service at seaports

This paper focuses on statistical process control as a strategic tool for the improvement of service at seaports. The aim of this paper is to examine the variable Time of container ships at port. A methodology based on the exponentially weighted moving average (EWMA) statistic is proposed in order to monitor each container vessel that arrives at the Port of Valencia. The EWMA chart is a time-weighted control chart that plots the exponentially weighted moving averages of a process. In the future, this model can be used by terminal managers of Valencia Port to implement better control techniques and thus improve the quality of service. Moreover, the methodological procedure presented in this paper is general enough to be applied by any other port as well.

Statistical process control and quality of service at seaports

This paper focuses on statistical process control as a strategic tool for the improvement of service at seaports. The aim of this paper is to examine the variable Time of container ships at port. A methodology based on the exponentially weighted moving average (EWMA) statistic is proposed in order to monitor each container vessel that arrives at the Port of Valencia. The EWMA chart is a time-weighted control chart that plots the exponentially weighted moving averages of a process. In the future, this model can be used by terminal managers of Valencia Port to implement better control techniques and thus improve the quality of service. Moreover, the methodological procedure presented in this paper is general enough to be applied by any other port as well.