Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5, 2535-2548 2025 Publisher: Learning Gate DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate © 2025 by the authors; licensee Learning Gate History: Received: 18 March 2025; Revised: 30 April 2025; Accepted: 5 May 2025; Published: 24 May 2025 * Correspondence: raimondadervishi@yahoo.com Novel application of time-weighted statistical techniques for trend analysis in roadway accident fatalities: A case study from Albania Raimonda Dervishi1*, Sander Kovaci1, Agbata Benedict Celestine2, Eshetu Dadi Gurmu3, Homan Emadifar4,5,6 1Department of Mathematical Engineering, Polytechnic University of Tirana, Tirana, Albania; raimondadervishi@yahoo.com (R.D.). 2Department of Mathematics and Statistics, Confluence University of Science and Technology, Osara, Nigeria. 3Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia. 4Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai-602 105, Tamil Nadu, India. 5MEU Research Unit, Middle East University, Amman, Jordan. 6Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran. Abstract: Road transportation in developing countries is a rapidly growing industry, leading to an increased risk of roadway accidents, which pose significant challenges across social, economic, health, justice, and security dimensions. Fatalities resulting from road accidents remain a global concern, and in Albania, despite a reduction in the number of accidents in recent years, the fatalities per 100,000 population have shown a significant rise compared to previous years. This study presents a novel application of three time-weighted statistical techniques, commonly used in quality control processes, to detect sustained changes in fatality trends due to roadway accidents over a 120-month period. The study not only compares the performance of the three designed control chart schemes but also highlights their sensitivity in detecting small shifts from the mean levels, with the Moving Average Technique being the most sensitive. Moreover, the points of process change are clearly identified and effectively located by all three techniques. The findings demonstrate the utility of these methods as diagnostic tools for identifying critical trends and evaluating the effectiveness of interventions aimed at reducing roadway fatalities in Albania. This research introduces an innovative approach to trend analysis in roadway accident fatalities and provides a framework for enhancing road safety management strategies in developing countries. Keywords: Albania, Roadway accidents, Time-Weighted Techniques, Trend fatalities. 1. Introduction The road transport sector is expanding rapidly in developing nations, contributing to a rise in traffic accidents, which pose significant challenges across multiple dimensions, including social, economic, health, legal, and security concerns [1, 2]. As an integral component of the national transportation network, the road transport industry must enhance its capacity to ensure safety, efficiency, and seamless operations, supporting economic and regional development. The increasing population has led to a surge in vehicle ownership, a rise in road accidents [3, 4] and, in recent years, a decline in fatality rates, particularly in developing nations [5-7]. Although these countries account for nearly 60% of the world’s vehicles, they experience 93% of global road accident fatalities [8]. To mitigate accident rates, it is essential to improve road infrastructure design and integrate safety measures into transportation planning [9]. Road traffic incidents should be treated as an urgent issue requiring immediate action to minimize adverse impacts on health, society, and the economy [10]. 2536 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate Fatalities and injuries resulting from roadway accidents present a serious problem for both developed and developing nations. Current trends indicate that by 2030, road accidents could become the fifth leading cause of death worldwide [11, 12]. The World Health Organization (WHO) reports that nearly 90% of road traffic deaths occur in low- and middle-income countries, even though these regions own only half of the world’s motor vehicles. The economic consequences of such accidents are severe. Data further reveal that approximately 1.3 million individuals die annually due to road accidents, while an additional 20 to 50 million suffer injuries across the globe [12, 13]. Addressing the challenges of forecasting traffic accidents is crucial for public safety, and research has emphasized various contributing factors. Tackling these issues plays a fundamental role in promoting road safety and fostering a more sustainable transport sector in developing nations beyond 2030 [14, 15]. Many traffic collisions are preventable, as they stem from specific risk factors associated with driver behavior, vehicle conditions, road design, and environmental elements [16, 17]. Key causes of road accidents include speeding, impaired driving due to alcohol, and non-compliance with safety measures like seatbelt use, helmets, and child restraints [18-21]. Other influential factors include driver age, time of travel, and geographical location, all of which significantly affect accident rates [18, 21]. Regardless of a country's level of development, traffic crashes remain one of the leading causes of mortality [22, 23]. Given the inevitability of road accidents, economic projections suggest that global losses due to fatal and non-fatal traffic incidents could reach approximately $1.8 trillion USD between 2015 and 2030, underscoring the magnitude of this global issue [24, 25]. Road traffic fatalities result from a combination of complex factors, making it difficult to attribute them to a singular cause. However, refining accident prediction models is crucial for strengthening traffic safety strategies [26, 27]. In Europe, Albania has exhibited a rising trend in fatal traffic collisions [28]. Recent statistics position the country eighth in terms of road traffic mortality rates per 100,000 people [29]. The Albanian Statistical Institute [30] indicates that while the overall number of accidents has declined in 2024, the fatality rate per 100,000 individuals has significantly increased. Male fatalities surpass female fatalities, and drivers are more frequently involved in fatal crashes than pedestrians. The age group most susceptible to accidents falls between 25 and 34 years, with drivers being the primary contributors to collisions [31]. This study aims to evaluate trends in road accident fatalities in Albania, which will support future projections and the formulation of effective preventive policies. Numerous studies worldwide have examined road traffic fatality patterns and assessed the success of various intervention strategies. Time series models have been widely employed for these analyses [32-36]. Nevertheless, long-term data collection is necessary to improve the accuracy of time series models [37]. Consequently, some researchers have utilized Time-Weighted statistical techniques to refine projections of traffic-related fatalities [38-40]. These methods are also extensively applied in modern industries for monitoring and controlling service and manufacturing processes Zhao, et al. [41]; Chamalwa, et al. [42] and Aslam, et al. [43]. Jamal, et al. [38] and Adekeye and Aluko [39] implemented statistical monitoring approaches for real-time highway safety surveillance using three years of crash data from rural highways in Saudi Arabia. Through an extensive simulation-based study, they compared the performance of various control charts, focusing on run-length characteristics. Their findings demonstrated that EWMA-type control charts provided superior detection capabilities compared to CUSUM and Shewhart control charts, especially for small and moderate shifts. Furthermore, these monitoring techniques were successfully applied to real-world crash data to validate their effectiveness. A related study by Adekeye and Aluko [39] employed CUSUM control charts to examine fatal traffic accidents in a state in western Nigeria. The control chart successfully identified periods with the highest fatality occurrences, particularly during festive seasons, highlighting the necessity for road authorities to enhance safety measures during these critical times. Braimah, et al. [44] and Shewhart [45] developed and compared CUSUM, EWMA, and Moving Average control charts to detect fluctuations in roadway accident data in Nigeria. The study revealed that CUSUM charts were the most effective in identifying minor deviations in the process mean, surpassing both 2537 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate EWMA and Moving Average charts. Similarly, Olanrewaju, et al. [40] applied EWMA and CUSUM techniques over a 120-month period to assess daily crash casualties in Osun State, Nigeria. A comparative analysis confirmed that while both methods effectively identified deviations, CUSUM exhibited greater sensitivity. Additionally, both charts accurately detected and highlighted shifts in accident trends. In this study, CUSUM, EWMA, and Moving Average statistical techniques—commonly employed in quality control processes—were utilized to monitor sustained variations in fatality trends following roadway accident interventions over a 120-month period. This methodology enabled a comprehensive analysis of accident patterns and intervention effectiveness. Table 1 displays the recorded fatality data throughout the study period. The performance assessment of the three control charts confirmed their efficacy in detecting minor deviations from the mean, with the Moving Average technique demonstrating the highest sensitivity. Furthermore, all methods successfully identified and highlighted critical change points in accident trends. These insights provide valuable information for designing strategies to manage and reduce roadway accident fatalities in Albania. Table 1. Data on fatalities over the study period. Months/Years 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 January 19 17 22 13 15 17 22 16 13 11 February 23 21 17 20 9 12 18 16 14 8 March 21 16 16 14 24 10 18 14 19 14 April 27 27 22 14 14 10 12 10 13 20 May 27 26 26 17 14 9 20 19 13 9 June 21 23 12 20 26 16 15 14 18 12 July 18 27 22 18 13 14 13 6 20 9 August 22 25 22 27 22 26 26 14 11 16 September 24 19 17 9 20 24 7 13 18 14 October 18 27 20 16 25 15 14 12 13 19 November 23 15 20 22 21 15 11 9 25 16 December 27 26 16 23 24 13 21 21 15 26 2. Methodology A critical component of Time-Weighted Control Charts is the use of control limits, which define the acceptable range of variations in the dataset. These limits are not static but instead fluctuate based on the number of subgroups included in the analysis. Subgroups, which represent specific time intervals (e.g., monthly or quarterly accident records), allow for a more refined investigation of trends. The manner in which control limits adjust across different charts depends on how they change in relation to the number of subgroups. This flexibility enables the identification of statistically significant deviations in accident fatality trends over time [46]. By analyzing subgroups, the study seeks to detect periods where fatalities exhibit significant increases or decreases, which may indicate the success or failure of safety interventions. Seasonal variations, such as higher accident rates during holiday periods, are also considered to determine recurring patterns. Furthermore, the analysis assesses whether reductions in fatalities following road safety policies are sustained over time or whether they represent only short- term improvements. Understanding these patterns is crucial for developing long-term strategies to enhance road safety and reduce accident-related deaths. The data for this study were sourced from the Albanian Statistical Institute (INSTAT), which maintains official records on public safety and transportation. The dataset includes annual and monthly counts of roadway accident fatalities, along with demographic details of accident victims such as age, gender, and location. Additionally, the dataset contains records of traffic safety interventions, including law enforcement measures, infrastructure improvements, and public awareness campaigns. This information provides a comprehensive foundation for analyzing fatality trends and assessing the effectiveness of intervention strategies. 2538 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate To ensure the accuracy and reliability of the dataset, the study incorporated several preprocessing steps before conducting the statistical analysis. Data cleaning was performed to remove inconsistencies and missing values, ensuring that the dataset remained robust and free from errors. Normalization techniques were applied to standardize values across different time periods, making comparisons between years more reliable. Lastly, categorization was used to classify accidents based on factors such as severity, location, and the presence of safety interventions. These preprocessing steps help refine the dataset and ensure that the statistical models produce accurate and meaningful results. 2.1. The CUSUM Statistical Technique ‘’Cumulative Sum control models were first proposed by Page [47]. The Cumulative Sum control chart is a good alternative when small shifts are important. It is a graphical representation of the trend in the outcome of a series of consecutive procedures performed over time’’ [39, 47]. Moreover, the CUSUM control chart can be adapted for different states in the country, the entire country, and all countries of the world [39, 44]. Suppose that X represents a process characteristic variable of concern and that it obeys a normal distribution N(µ,σ2), with known mean µ, and standard deviation σ. Without loss of generality, we may suppose that µ = 0 and σ = 1.5, with µ = δ for an out-of-control process. Let { 1x , 2x , ..., nx , …} a series of observations for the process variable, X [48]. In particular, the CUSUM statistics are defined as: 0 1 ( ) i i i j C x  = = − (1) 0 1max 0, ( )i i iC x K C+ + −  = − + +  (2) 0 1max 0,( )i i iC K x C− − −  = − − +  (3) where, the starting values for the statistics are 0 0 0C C+ −= = . ‘’The CUSUM control chart is determined by K and H, and an out-of-control signal is triggered if either one of the two CUSUM charts, 𝐶𝑖 + and 𝐶𝑖 −, signals. K is usually called the reference value (or the allowance, or the slack value), and it is often chosen about halfway between the target 0 and the out- of-control value of the mean 1 that we are interested in detecting quickly. The process is considered to be out of control if 𝐶𝑖 +>H for an upward shift or 𝐶𝑖 −< -H for a downward shift [49]. The values of 0 and 1 are the mean numbers of counts per sampling interval. The reference value K for the CUSUM chart should be chosen close to:’’ 1 0 1 0ln ln K     − = − (4) ‘’The proper selection of these two parameters is quite important, as it has a substantial impact on the performance of the CUSUM. A reasonable value for H is four or five times the process standard deviation σ. A two-sided CUSUM control chart is encouraged because its properties can easily be obtained by combining the results of the respective one-sided charts used to detect significant increases or decreases, while this approach allows for flexibility in detecting change [39, 50]. If the process remains in control at the target value 0 the cumulative sum defined in equation (1) is a random walk with mean zero. However, if the mean shifts upward to some value 1 > 0 an upward or positive drift will develop in the Cumulative Sum Ci. Conversely, if the mean shifts downward to some 1 [50]’’. The Upper Control Limit and the Lower Control Limit for the CUSUM control chart are given by Eq. 2539 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate 1 0max 0, i iUCL C x H+ −  = + −   (5) 1 1min 0, i iLCL C x H− −  = + −  −  (6) 2.2. The Exponentially Weighted Moving Average Statistical Technique ‘’The Exponentially Weighted Moving Average (EWMA) model was derived by JP Morgan in 1989 from a Gaussian distribution, for their risk metrics framework [51]. The EWMA chart is easy to plot and interpret, and its control limits are easy to obtain. Further, the EWMA leads naturally to an empirical dynamic control equation [52]. The EWMA statistic is defined as:  1(1 )i i iZ wX w Z −= − − (7) where 020. The points of change in the process are identified and located on the CUSUM chart in Figure 1. The months when high incidence of roadway accident fatalities is evidenced should be used as a reference point to pay more attention or take precautions on the roads to reduce or eliminate high cases of roadway accident fatalities [44]. The values of CUSUM statistics are computed similarly using Equation (1) over a 120 months period and are presented in Table 2 — Table 11. Using Equation (5) and Equation (6), we computed 𝑈𝐶𝐿 = 21.4 and 𝐿𝐶𝐿 = − 21.4. From calculated values, the road accident fatalities were out of control from the 18th month to the 29th month’’. Table 2. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2015. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 19 -2 -2 0 17.9 19.0 February 23 2 0 0 18.9 21.0 March 21 0 0 0 19.3 21.0 April 27 6 6 6 20.9 22.5* May 27 6 12 12 22.1 23.4* June 21 0 12 12 21.9 23.0* July 18 -3 9 9 21.1 22.3 August 22 1 10 10 21.3 22.3 September 24 3 13 13 21.8 22.4 October 18 -3 10 10 21.1 22.0 November 23 2 12 12 21.4 22.1 December 27 6 18 18 22.6* 22.5* Table 3. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2016. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 17 -4 14 14 21.4 22.1 February 21 0 14 14 21.4 22.0 March 16 -5 9 9 21.4 21.6 April 27 6 15 15 20.3 22.0 May 26 5 20 20 21.6 22.2 June 23 2 22 22* 22.5* 22.5* July 27 6 28 28* 22.6* 22.6* August 25 4 32 32* 23.5* 22.4 September 19 -2 30 30* 23.8* 22.4 October 27 6 36 36* 22.8* 22.6* November 15 -6 30 30* 23.7* 22.3 December 26 5 35 35* 21.9 22.5* 2541 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate Table 4. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2017. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 22 1 36 36* 22.7* 22.4 February 17 -4 32 32* 22.6* 22.3 March 16 -5 27 27* 21.5 22.0 April 22 1 28 28* 20.4 22.0 May 16 -5 23 23* 20.7 21.8 June 12 -9 14 14 19.8 21.5 July 22 1 15 15 21.5 21.5 August 22 1 16 16 19.0 21.4 September 17 -4 12 12 19.6 21.3 October 20 -1 11 11 19.1 21.3 November 20 -1 10 10 19.2 22.3 December 16 -5 5 5 19.4 21.1 Table 5. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2018. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 13 -8 -3 0 18.7 20.9 February 20 -1 -4 0 17.6 20.8 March 14 -7 -11 0 18.1 20.7 April 14 -7 -18 0 17.2 20.5 May 17 -4 -22 0 16.6 20.5 June 20 -1 -23 0 16.7 20.4 July 18 -3 -26 0 17.3 20.4 August 27 6 -20 0 17.5 20.5 September 9 -12 -32 0 19.4 20.3 October 16 -5 -37 0 17.3 20.2 November 22 1 -36 0 17.0 20.2 December 23 2 -34 0 18.0 20.3 Table 6. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2019. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 15 -6 -40 0 19.0 20.2 February 9 -12 -52 0 18.2 19.9 March 24 3 -49 0 16.4 20.0 April 14 -7 -56 0 17.9 19.9 May 14 -7 -63 0 17.1 19.8 June 26 5 -58 0 16.5 19.9 July 13 -8 -66 0 18.4 19.8 August 22 1 -65 0 17.3 19.8 September 20 -1 -66 0 18.3 19.8 October 25 4 -62 0 18.6 19.9 November 21 0 -62 0 19.9 19.9 December 24 3 -59 0 20.1 20.0 2542 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate Table 7. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2020. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 17 -4 -63 0 20.9 19.9 February 12 -9 -72 0 20.1 19.8 March 10 -11 -83 0 18.5 19.7 April 10 -11 -94 0 16.8 19.5 May 9 -12 -106 0 15.4 19.3 June 16 -5 -111 0 14.1 19.3 July 14 -7 -118 0 14.5 19.2 August 26 5 -113 0 14.4 19.3 September 24 3 -110 0 16.7 19.4 October 15 -6 -116 0 18.2 19.3 November 15 -6 -122 0 17.5 19.9 December 13 -8 -130 0 17.0 19.2 Table 8. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2021. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 22 21 -109 0 16.2 19.2 February 18 -3 -112 0 17.4 19.2 March 18 -3 -115 0 17.5 19.2 April 12 -9 -124 0 17.6 19.1 May 20 -1 -125 0 16.5 19.1 June 15 -6 -131 0 17.2 18.9 July 13 -8 -139 0 16.8 19.0 August 26 5 -134 0 16.0 18.9 September 7 -14 -148 0 18.0 18.8 October 14 -7 -155 0 15.8 18.8 November 11 -10 -165 0 15.4 18.8 December 21 0 -165 0 14.6 18.7 Table 9. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2022. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 16 -5 -170 0 15.8 18.7 February 16 -5 -175 0 15.9 18.7 March 14 -7 -182 0 15.9 18.6 April 10 -10 -190 0 15.5 20.8 May 19 -2 -192 0 14.4 18.5 June 14 -7 -199 0 15.3 18.5 July 6 -15 -214 0 15.1 18.4 August 14 -7 -221 0 13.3 18.3 September 13 -8 -229 0 13.4 18.3 October 12 -9 -238 0 13.3 18.2 November 9 -12 -250 0 13.1 18.1 December 21 0 -250 0 12.2 18.2 2543 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate Table 10. Computed Cusum, and EWMA, AM Statistics in fatalities of roadway accidents for the year 2023. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 13 -8 -258 0 14.0 18.1 February 14 -7 -265 0 13.8 18.0 March 19 -2 -267 0 13.8 18.0 April 13 -8 -275 0 14.9 18.0 May 13 -8 -283 0 14.5 17.9 June 18 -3 -286 0 14.2 17.9 July 20 -1 -287 0 15.0 17.9 August 11 -10 -297 0 16.0 17.9 September 18 -3 -300 0 15.0 17.9 October 13 -8 -308 0 15.6 17.8 November 25 4 -304 0 15.1 17.9 December 15 -6 -310 0 17.1 17.9 Table 11. Computed Cusum, EWMA, and AM Statistics in fatalities of roadway accidents for the year 2024. Months(i) Xi Xi-K Ci=(Xi-K) 𝐂𝐢 Zi= wXi+ (1 - w)Zi-1 Mi = 𝐗𝐢+𝐗𝐢−𝟏+⋯+𝐗𝐢−𝐰+𝟏 𝐰 January 11 -10 -320 0 16.6 17.9 February 8 -13 -333 0 15.5 17.8 March 15 -6 -339 0 14.0 17.7 April 20 -1 -340 0 14.2 17.8 May 9 -12 -352 0 15.4 17.7 June 12 -9 -361 0 14.1 17.6 July 9 -12 -373 0 13.7 17.5 August 16 -5 -378 0 12.7 17.5 September 14 -7 -385 0 13.4 17.5 October 19 -2 -387 0 13.5 17.5 November 16 -5 -392 0 14.6 17.5 December 26 5 -387 0 14.9 17.6 Figure 1. Graphical representation of the CUSUM chart on fatalities of roadway accidents over the period 2015-2024. 2544 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate 3.2. Intervention of Analysis Performed by Exponentially Weighted Moving Average ‘’The starting value of EWMA is 0 0Z = =17, and Z is the exponential weighted moving average of the value. In this study, we use w=0.2. The other values of EWMA statistics are computed similarly using Equation (7) over a 120-month period and are presented in Table 2 — Table 11. Using Equation (8) and Equation (9), we computed 𝑈𝐶𝐿 = 22.4 and 𝐿𝐶𝐿 = 12.8, where L is the width of the control limit assumed as 3. From calculated values, the road accident fatalities were out of control in the 12th month, and later it was out of control from the 18th month to the 26th month’’. The points of change in the process are identified and located on the EWMA chart in Figure 2. Figure 2. Graphical representation of the EWMA chart on fatalities of roadway accidents over the period 2015-2024. 3.3. Intervention of Analysis Performed by Moving Average ‘’The values of Moving Average statistics are computed using Equation (10) over a 120 months period and are presented in Table 2 — Table 11. Using Equation (11) and Equation (12), we computed 𝑈𝐶𝐿 = 19.7 and 𝐿𝐶𝐿 = 15.5. Road accident fatalities, from calculated values, were out of control from the 4th month to the 6th month in the 12th month, later it was out of control from the 19th month to the 20th month, and in the 22th and 24th months.’’ The points of change in the process are identified and located on the Moving Average chart in Figure 3. UCL 22.4 CL 17.6 LCL 12.8 10.9 12.9 14.9 16.9 18.9 20.9 22.9 24.9 1 5 9 1 3 1 7 2 1 2 5 2 9 3 3 3 7 4 1 4 5 4 9 5 3 5 7 6 1 6 5 6 9 7 3 7 7 8 1 8 5 8 9 9 3 9 7 1 0 1 1 0 5 1 0 9 1 1 3 1 1 7 EW M A C h ar t 1 - 120 2545 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate Figure3. Graphical representation of the Moving Average chart on fatalities of roadway accidents over the period 2015-2024. 4. Discussion Time-weighted statistical techniques, including Cumulative Sum (CUSUM), Exponentially Weighted Moving Average (EWMA), and Moving Average, are highly effective in detecting small process changes, particularly shifts in the mean of 1.5 sigma, as applied in this study. These techniques are widely recognized for their ability to identify subtle variations that may not be immediately apparent in conventional statistical analyses. Over the 120-month study period, the results indicate that among the three techniques, the Moving Average method provides the fastest response in detecting shifts in roadway accident fatalities. The computed values of roadway accident fatalities, as presented in Tables 2 to 11, revealed distinct differences in the detection times of each control chart method. The Moving Average chart signaled the first deviation at the 4th observation point, followed by the EWMA chart at the 12th point, and the CUSUM chart at the 18th point. This demonstrates that the Moving Average method is the most responsive in identifying small yet significant changes in the dataset. The earlier detection of shifts suggests that the Moving Average technique could be a more effective choice for monitoring sudden variations in accident fatality trends. Given its faster response time, the Moving Average control chart may be particularly advantageous for real-time traffic safety monitoring, where early detection of changes can enable authorities to implement timely interventions. The ability to detect shifts quickly is essential in developing proactive road safety policies, adjusting enforcement strategies, and mitigating accident risks. While EWMA and CUSUM techniques remain valuable for their ability to track long-term trends and cumulative variations, the Moving Average method’s superior speed in signaling shifts makes it more suitable for datasets requiring immediate attention. Our findings suggest that control chart selection should be tailored to the specific objectives of traffic safety monitoring. If the goal is early intervention and rapid response, the Moving Average technique is the preferred option. However, for a more comprehensive analysis of long-term trends, integrating EWMA and CUSUM methods could provide additional insights into accident patterns and intervention effectiveness. Future studies may explore the combined use of multiple control charts to optimize roadway accident monitoring and enhance predictive accuracy. 5. Conclusion Worldwide, road accidents are one of the leading causes of fatalities, affecting individuals of all ages, depriving them of their futures and dreams [53]. In this study, Cumulative Sum (CUSUM), Exponentially Weighted Moving Average (EWMA), and Moving Average statistical techniques— commonly used in quality control—were applied to detect sustained changes in roadway accident UCL 19.7 CL 17.6 LCL 15.5 0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000 1 5 9 1 3 1 7 2 1 2 5 2 9 3 3 3 7 4 1 4 5 4 9 5 3 5 7 6 1 6 5 6 9 7 3 7 7 8 1 8 5 8 9 9 3 9 7 1 0 1 1 0 5 1 0 9 1 1 3 1 1 7 M o vi n g A ve ra ge C h ar t 1 - 120 2546 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 9, No. 5: 2535-2548, 2025 DOI: 10.55214/25768484.v9i5.7516 © 2025 by the authors; licensee Learning Gate fatality trends over a 120-month period. This approach allowed for a thorough intervention and trend analysis, evaluating the impact of traffic safety measures over time. The comparative analysis of the three designed control charts demonstrated that all techniques were effective in detecting minor shifts from the mean. However, the Moving Average technique proved to be the most responsive, triggering alerts at a faster rate than the others. Additionally, all three methods successfully identified key points of change in the process, making them valuable tools for monitoring fatality trends. Among the control charts assessed, the Moving Average control chart emerged as the most efficient in detecting small process variations. Research suggests that it offers a more straightforward implementation compared to CUSUM and EWMA charts, while also being superior to the Shewhart chart in capturing subtle shifts in process behavior [48]. These findings provide a diagnostic framework for reducing roadway accident fatalities in Albania, contributing to enhanced monitoring and safety management strategies. Furthermore, our results hold significant value for transportation authorities and public safety policymakers, offering insights that can guide the formulation of effective safety policies. The results highlight the importance of using data-driven decision-making to achieve long-term traffic safety improvements. Future research could explore the integration of multiple advanced control chart techniques to enhance detection accuracy and optimize intervention strategies for accident prevention. Funding: The publication of this article has been financially supported by the Scientific Research Fund of the Polytechnic University of Tirana. Transparency: The authors confirm that the manuscript is an honest, accurate, and transparent account of the study; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. This study followed all ethical practices during writing. Acknowledgment: The authors acknowledge the Polytechnic University of Tirana for financially supporting the publication of this article. Copyright: © 2025 by the authors. 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