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Journal articles on the topic 'Average run length (ARL)'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

B. C. Khoo, Michael, S. Y. Teh, X. Y. Chew, and W. L. Teoh. "Standard Deviation of the Run Length (SDRL) and Average Run Length (ARL) Performances of EWMA and Synthetic Charts." International Journal of Engineering and Technology 7, no. 6 (2015): 513–17. http://dx.doi.org/10.7763/ijet.2015.v7.847.

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Mongkoltawat, Phunsa, Yupaporn Areepong, and Saowanit Sukparungsee. "Average Run Length Computations of Autoregressive and Moving Average Process using the Extended EWMA Procedure." WSEAS TRANSACTIONS ON MATHEMATICS 23 (May 20, 2024): 371–84. http://dx.doi.org/10.37394/23206.2024.23.40.

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In the past, the control chart served as a statistical tool for detecting process changes. The Exponentially Weighted Moving Average (EWMA) control chart is highly effective for detecting small changes. This research introduces the Extended Exponentially Weighted Moving Average (Extended EWMA) control chart for the Autoregressive and Moving average process with order p = 1 and q = 1 (ARMA(1,1)) The Extended EWMA control chart incorporates two smoothing parameters ( λ1 and λ2 ) derived from the EWMA control chart. A comparative analysis of the performance of the EWMA control chart. The Average

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Sunthornwat, Rapin, Yupaporn Areepong, and Saowanit Sukparungsee. "Analytical Explicit Formulas of Average Run Length of DEWMA Control Chart based on Seasonal Moving Average Process." WSEAS TRANSACTIONS ON SYSTEMS 24 (October 7, 2024): 1–15. https://doi.org/10.37394/23202.2025.24.1.

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The primary objective of this research is to propose explicit formulas for the Average Run Length (ARL) of the Double Exponentially Weighted Moving Average control chart (DEWMA) for the Seasonal Moving Average process (SMA (Q)L) with exponential white noise. The Numerical Integral Equation by the midpoint rule is employed to compare the results derived from the formulas and evaluate their accuracy using the percentage of accuracy (%Acc). The DEWMA control chart's efficacy is measured by calculating the average run length (ARL), median run length (MRL), and standard deviation of run length (SDR

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4

Talordphop, Khanittha, Saowanit Sukparungsee, and Yupaporn Areepong. "Performance of new nonparametric Tukey modified exponentially weighted moving average—Moving average control chart." PLOS ONE 17, no. 9 (2022): e0275260. http://dx.doi.org/10.1371/journal.pone.0275260.

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Control charts are an amazing and essential statistical process control (SPC) instrument that is commonly used in monitoring systems to detect a specific defect in the procedure. The mixed Tukey modified exponentially weighted moving average - moving average control chart (MMEM-TCC) with motivation detection ability for fewer shifts in the process mean under symmetric and non-symmetric distributions is proposed in this paper. Average run length (ARL), standard deviation of run length (SDRL), and median run length (MRL) were used as efficiency criteria in the Monte Carlo simulation, and their e

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Mongkoltawat, Phunsa, Yupaporn Areepong, and Saowanit Sukparungsee. "Exact Average Run Length Evaluation on a Two-Sided Extended EWMA Control Chart for the Moving Average Process." WSEAS TRANSACTIONS ON SYSTEMS 24 (April 1, 2025): 142–55. https://doi.org/10.37394/23202.2025.24.16.

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The Extended Exponentially Weighted Moving Average (Extended EWMA) control chart is a type of control chart that is effective in promptly identifying minor deviations. The evaluation of control charts can be conducted using the average run length (ARL). Finding the explicit formulas for the ARL on a two-sided Extended EWMA control chart for the moving average process (MA(q)) has not been reported previously and the purpose of this research. The processes considered the MA(2) and MA(3) processes, all with exponential white noise. The accuracy of the analytical solution was assessed using the Ex

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LEE, M. H., and MICHAEL B. C. KHOO. "OPTIMAL STATISTICAL DESIGNS OF A MULTIVARIATE CUSUM CHART BASED ON ARL AND MRL." International Journal of Reliability, Quality and Safety Engineering 13, no. 05 (2006): 479–97. http://dx.doi.org/10.1142/s0218539306002380.

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Optimal statistical designs of the multivariate CUSUM (MCUSUM) chart for multivariate individual observations based on ARL and MRL are proposed. Statistical design procedures refer to choices of the reference value, k and the control limit, H to ensure that the MCUSUM chart's performance meets certain statistical criteria. The primary criterion is the average run length (ARL) which is the most commonly used measure of a control chart's performance, while the median run length (MRL) which is the 50th percentage point of the run length distribution is suggested to be used as a potential alternat

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7

Sunthornwat, Rapin, Yupaporn Areepong, and Saowanit Sukparungsee. "Performance Evaluation of HWMA Control Chart based on AR(p) with Trend Model to Detect Shift Process Mean." WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS 21 (January 26, 2024): 603–16. http://dx.doi.org/10.37394/23207.2024.21.50.

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The main goal of this study is to establish explicit solutions for the average run length (ARL) of the Homogenously Weighted Moving Average control chart when subjected to autoregressive with trend process. The accuracy of the explicit formula for the ARL is evaluated in comparison to the numerical integral equation method. To evaluate the two approaches, the accuracy percentage was employed. A determination is carried out of the HWMA control chart’s effectiveness using the median run length (MRL), the standard deviation of run length (SDRL), and the average run length (ARL). A comprehensive c

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8

Yahaya, Masthura, Sok Li Lim, Adriana Irawati Ibrahim, Wai Chung Yeong, and Michael Boon Chong Khoo. "A VARIABLE SAMPLE SIZE SYNTHETIC CHART FOR THE COEFFICIENT OF VARIATION." South African Journal of Industrial Engineering 33, no. 1 (2022): 16–24. http://dx.doi.org/10.7166/32-4-2545.

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A variable sample size (VSS) synthetic chart to monitor the coefficient of variation is proposed in this paper to improve the performance of the existing synthetic chart. A description of how the chart operates, as well as the formulae for various performance measures (i.e., the average run length (ARL), standard deviation of the run length (SDRL), average sample size (ASS), and expected average run length (EARL)) are proposed. The algorithms that optimise the out-of-control ARL (ARL1) and EARL (EARL1), subject to the constraints in the in-control ARL (ARL0) and ASS (ASS0), are also proposed.

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9

You, Huay Woon. "Performance of Synthetic Double Sampling Chart with Estimated Parameters Based on Expected Average Run Length." Journal of Probability and Statistics 2018 (May 31, 2018): 1–6. http://dx.doi.org/10.1155/2018/7583610.

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A synthetic double sampling (SDS) chart is commonly evaluated based on the assumption that process parameters (namely, mean and standard deviation) are known. However, the process parameters are usually unknown and must be estimated from an in-control Phase-I dataset. This will lead to deterioration in the performance of a control chart. The average run length (ARL) has been implemented as the common performance measure in process monitoring of the SDS chart. Computation of ARL requires practitioners to determine shift size in advance. However, this requirement is too restricted as practitione

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Areepong, Yupaporn, and Saowanit Sukparungsee. "Integral Equation Method for ARL on New Modified EWMA Chart in Change-Point Detection Problems." WSEAS TRANSACTIONS ON MATHEMATICS 24 (April 10, 2025): 268–88. https://doi.org/10.37394/23206.2025.24.26.

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This research proposes an explicit formula for the Average Run Length (ARL) on a new modified EWMA (new MEWMA) control chart. This study proposes a mathematical algorithm for determining the ARL of a new MEWMA control chart for detecting autocorrelated processes for zero-state. The integral equation method is called Fredholm Integral Equations of the second kind can be effectively employed to calculate ARL. Banach’s fixed point theorem is utilized to demonstrate the existence and uniqueness of the ARL solution. A process for constructing one-sided and two-sided new MEWMA control charts is pres

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Ng, Jing Wen, Voon Hee Wong, and Sook Theng Pang. "A synthetic exponentially weighted moving average control chart to monitor process median based on ranked set sampling." ITM Web of Conferences 36 (2021): 01002. http://dx.doi.org/10.1051/itmconf/20213601002.

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Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situati

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You, Huay Woon, Michael Khoo Boon Chong, Chong Zhi Lin, and Teoh Wei Lin. "The Expected Average Run Length of the EWMA Median Chart with Estimated Process Parameters." Austrian Journal of Statistics 49, no. 3 (2020): 19–24. http://dx.doi.org/10.17713/ajs.v49i3.1020.

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The performance of a control chart is commonly investigated based on the assumption of known process parameters. Nevertheless, in most manufacturing and service applications, the process parameters are usually unknown to practitioners. Hence, they are estimated from an in-control Phase-I samples. As such, the performance of the control chart with estimated process parameters will behave differently from the corresponding chart with known process parameters. To study this issue, the exponentially weighted moving average (EWMA) median chart is examined in this article. The EWMA median chart is t

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Sunthornwat, Rapin, Saowanit Sukparungsee, and Yupaporn Areepong. "Analytical Explicit Formulas of Average Run Length of Homogenously Weighted Moving Average Control Chart Based on a MAX Process." Symmetry 15, no. 12 (2023): 2112. http://dx.doi.org/10.3390/sym15122112.

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Statistical process control (SPC) is used for monitoring and detecting anomalies in processes in the areas of manufacturing, environmental studies, economics, and healthcare, among others. Herein, we introduce an innovative SPC approach via mathematical modeling and report on its application via simulation studies to examine its suitability for monitoring processes involving correlated data running on advanced control charts. Specifically, an approach for detecting small to moderate shifts in the mean of a process running on a homogenously weighted moving average (HWMA) control chart, which is

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14

Yeong, Waie Chung, Ping Yin Lee, Sok Li Lim, Peh Sang Ng, and Khai Wah Khaw. "Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length." PLOS ONE 16, no. 7 (2021): e0255366. http://dx.doi.org/10.1371/journal.pone.0255366.

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The side sensitive synthetic chart was proposed to improve the performance of the synthetic chart to monitor shifts in the coefficient of variation (γ), by incorporating the side sensitivity feature where successive non-conforming samples must fall on the same side of the control limits. The existing side sensitive synthetic- γ chart is only evaluated in terms of the average run length (ARL) and expected average run length (EARL). However, the run length distribution is skewed to the right, hence the actual performance of the chart may be frequently different from what is shown by the ARL and

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Karoon, Kotchaporn, and Yupaporn Areepong. "Improving Sensitivity of the DEWMA Chart with Exact ARL Solution under the Trend AR(p) Model and Its Applications." Emerging Science Journal 7, no. 6 (2023): 1875–91. http://dx.doi.org/10.28991/esj-2023-07-06-03.

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The double exponentially weighted moving average (DEWMA) chart is a control chart that is a vital analytical tool for keeping track of the quality of a process, and the sensitivity of the control chart to the process is evaluated using the average run length (ARL). Herein, the aim of this study is to derive the explicit formula of the ARL on the DEWMA chart with the autoregressive with trend model and its residual, which is exponential white noise. This study shows that this proposed method was compared to the ARL derived using the numerical integral equation (NIE) approach, and the explicit A

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Sunthornwat, Rapin, Saowanit Sukparungsee, and Yupaporn Areepong. "The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process." HighTech and Innovation Journal 5, no. 1 (2024): 16–35. http://dx.doi.org/10.28991/hij-2024-05-01-02.

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This research aims to investigate a Homogenously Weighted Moving Average (HWMA) control chart for detecting minor and moderate shifts in the process mean. A mathematical model for the explicit formulae of the average run length (ARL) of the HWMA control chart based on the autoregressive (AR) process is presented. The efficacy of the HWMA control chart is evaluated based on the average run length, the standard deviation of run length (SDRL), and the median run length (MRL). As illustrations of the design and implementation of the HWMA control chart, numerical examples are provided. In numerous

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17

Huang, Wei-Heng. "The Performance of S Control Charts for the Lognormal Distribution with Estimated Parameters." Sustainability 14, no. 24 (2022): 16582. http://dx.doi.org/10.3390/su142416582.

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Control charts, one of the powerful tools in statistical process control (SPC), are widely used to monitor and detect out-of-control processes in the manufacturing industry. Many researchers have pointed out the effects of using estimated parameters on the average run length (ARL) performance metric. Most of the previous literature has studied the expected value of the average run length (AARL) and the standard deviation of the average run length (SDARL) to evaluate the performance of control charts. In this article, we study the performance of three S control charts, the Shewhart S-chart, the

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Rosaiah, K., G. Srinivasa Rao, and S. V. S. V. S. V. Prasad. "A control chart for time truncated life tests using type-ii generalized log logistic distribution." Biometrics & Biostatistics International Journal 10, no. 4 (2021): 138–43. http://dx.doi.org/10.15406/bbij.2021.10.00340.

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In this paper, an attribute control chart is aimed when the lifetime of the item follows Type-II generalized log-logistic distribution (TGLLD) under a time truncated life test assuming that the common scale parameter is known. Average run length (ARL) is used to assess the performance of the aimed control chart. Simulation technique is developed to present the performance of the control charts at a specified average run length (ARL), shift constant and for different parametric values of shape and scale parameters, sample size. The results are illustrated with live data example.

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Resti, Aulia, Tatik Widiharih, and Rukun Santoso. "GRAFIK PENGENDALI MIXED EXPONENTIALLY WEIGHTED MOVING AVERAGE – CUMULATIVE SUM (MEC) DALAM ANALISIS PENGAWASAN PROSES PRODUKSI (Studi Kasus : Wingko Babat Cap “Moel”)." Jurnal Gaussian 10, no. 1 (2021): 114–24. http://dx.doi.org/10.14710/j.gauss.v10i1.30938.

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Quality control is an important role in industry for maintain quality stability. Statistical process control can quickly investigate the occurrence of unforeseen causes or process shifts using control charts. Mixed Exponentially Weighted Moving Average - Cumulative Sum (MEC) control chart is a tool used to monitor and evaluate whether the production process is in control or not. The MEC control chart method is a combination of the Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) charts. Combining the two charts aims to increase the sensitivity of the control chart in det

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Suvimol, P., and C. Chananet. "Moving Average Control Chart for Generalized Poisson Distribution." Journal of Physics: Conference Series 2346, no. 1 (2022): 012004. http://dx.doi.org/10.1088/1742-6596/2346/1/012004.

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Abstract This study aim to propose a moving average control chart explicit formula based on the Generalized Poisson distribution (MAGP ) and to compare the performance of the MAGP control chart with that of the Shewhart control chart (CGP ). The average run length (ARL) is used to consider the performance. The ARL results indicated that the MAGP control chart is superior to the CGP control chart based on the Generalized Poisson distribution for detecting small shifts. Practitioners will find this explicit formula to be accurate as well as simple to apply and use.

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Sunthornwat, Rapin, and Yupaporn Areepong. "Average Run Length on CUSUM Control Chart for Seasonal and Non-Seasonal Moving Average Processes with Exogenous Variables." Symmetry 12, no. 1 (2020): 173. http://dx.doi.org/10.3390/sym12010173.

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The aim of this study was to derive explicit formulas of the average run length (ARL) of a cumulative sum (CUSUM) control chart for seasonal and non-seasonal moving average processes with exogenous variables, and then evaluate it against the numerical integral equation (NIE) method. Both methods had similarly excellent agreement, with an absolute percentage error of less than 0.50%. When compared to other methods, the explicit formula method is extremely useful for finding optimal parameters when other methods cannot. In this work, the procedure for obtaining optimal parameters—which are the r

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Sarfraz, Maryam, Najam ul Hassan, and Ateeba Atir. "COEFFICIENT OF VARIATION CONTROL CHART BASED ON CONDITIONAL EXPECTED VALUES FOR THE MONITORING OF CENSORED RAYLEIGH LIFETIMES." Pakistan Journal of Social Research 04, no. 03 (2022): 1058–74. http://dx.doi.org/10.52567/pjsr.v4i03.1285.

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This article deals with the monitoring of type-I censored data using coefficient of variation (CV) control chart based on conditional expected values (CEVs) for Rayleigh lifetimes under type-I censoring. In particular, the censored data is replaced by the CEV to develop an efficient design structure. The main focus is to detect shifts in the mean of Rayleigh lifetimes assuming censored data. The performance of the proposed CEV based CV chart is evaluated by the average run length (ARL). Besides the simulation study, monitoring of a real-life dataset of 30 average daily wind speeds (in kilomete

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Yu, Wang Hai. "The Performance Assessment and Optimal Design of EWMA Charts Based on Average Product Length." Advanced Materials Research 383-390 (November 2011): 2573–77. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.2573.

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ARL (Average Run Length) is used as a tool to measure the performance of control chart. But it isn’t very accurate. In this paper, a Markov chain method is proposed to calculate the APL (Average Product Length) of EWMA chart, and APL is used as a criterion of performance assessment to decide optimal design of this chart. By comparing with traditional EWMA design method, we can find that this method can detect little shifts in processes more quickly.

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Aslam, Muhammad, G. Srinivasa Rao, Muhammad Saleem, Rehan Ahmad Khan Sherwani, and Chi-Hyuck Jun. "Monitoring Mortality Caused by COVID-19 Using Gamma-Distributed Variables Based on Generalized Multiple Dependent State Sampling." Computational and Mathematical Methods in Medicine 2021 (April 22, 2021): 1–17. http://dx.doi.org/10.1155/2021/6634887.

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More recently in statistical quality control studies, researchers are paying more attention to quality characteristics having nonnormal distributions. In the present article, a generalized multiple dependent state (GMDS) sampling control chart is proposed based on the transformation of gamma quality characteristics into a normal distribution. The parameters for the proposed control charts are obtained using in-control average run length (ARL) at specified shape parametric values for different specified average run lengths. The out-of-control ARL of the proposed gamma control chart using GMDS s

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Mongkoltawat, Phunsa, Yupaporn Areepong, and Saowanit Sukparungsee. "Exact Average Run Length Evaluation on One-Sided and Two-Sided Extended EWMA Control Chart with Correlated Data." WSEAS TRANSACTIONS ON MATHEMATICS 22 (November 9, 2023): 819–30. http://dx.doi.org/10.37394/23206.2023.22.90.

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The Extended Exponentially Weighted Moving Average (Extended EWMA) control chart is one of the control charts that can rapidly detect a minor shift. Using the average run length (ARL), the control charts' effectiveness can be evaluated. This research aims to derive the explicit formulations for the ARL on one-sided and two-sided Extend EWMA control charts for the MA(1) model with exponential white noise, as they have not been previously presented. The analytical solution accuracy was determined and compared to the numerical integral equation (NIE) method. The results indicate that the ARL calc

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Itrat, Batool Naqvi, and Aslam Muhammad. "Quantile Function for Rayleigh and Scaled Half Logistic: Application in Missing Data." Journal of Progressive Research in Mathematics 15, no. 2 (2019): 2641–53. https://doi.org/10.5281/zenodo.3974072.

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In this research paper quantile Functions for Scaled half logistic and Rayleigh distributions has been constructed. Data generated through the quantile Functions and then different limits for the full and missing data set have been developed with scale parameter. A number of such mean control limits could be constructed through purposed method but for analysis purpose few of them have discussed. The missing data limits broadened than the full data in each case, which was expected to be. The average run length (ARL) was also calculated for different sample sizes (50,100,150). The general decrea

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Peerajit, Wilasinee. "Gauss–Legendre Numerical Integrations for Average Run Length Running on EWMA Control Chart with Fractionally Integrated MAX Process." WSEAS TRANSACTIONS ON MATHEMATICS 23 (September 27, 2024): 579–90. http://dx.doi.org/10.37394/23206.2024.23.61.

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The performance of a process running on an exponentially weighted moving average (EWMA) control chart is contingent upon the ability to detect changes in the process mean rapidly. This entails determining the shortest average run length (ARL) for when a process becomes out-of-control (ARL1). Herein, we propose a numerical integral equation (NIE) method to approximate the ARL for a long-memory fractionally integrated moving-average process with an exogenous variable with underlying exponential white noise running on an EWMA control chart using the Gauss-Legendre quadrature. In a numerical evalu

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Bhat, Sharada V., and Shradha S. Patil. "Shewhart Type Control Chart Based on Median for Location Parameter." INTERNATIONAL JOURNAL OF AGRICULTURAL AND STATISTICAL SCIENCES 20, no. 01 (2024): 275. http://dx.doi.org/10.59467/ijass.2024.20.275.

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Control charts are prominent tools in monitoring various variables of manufacturing processes. In this paper, the control chart based on sample median is proposed for process location parameter using Shewhart?s approach. The proposed control chart is developed under some distributions including normal distribution. Its performance is studied in terms of power, average run length (ARL) and standard deviation of run length (SDRL). Also, the effect of non normality on this control chart is discussed.. KEYWORDS :ARL, Control limits, Location parameter, Median, Non-normality, Power.

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Polyeam, Dollaporn, and Suvimol Phanyeam. "Enhancing Average Run Length Efficiency of the Exponentially Weighted Moving Average Control Chart under the SAR(1)L Model with Quadratic Trend." Malaysian Journal of Fundamental and Applied Sciences 21, no. 3 (2025): 2174–93. https://doi.org/10.11113/mjfas.v21n3.4290.

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This study proposes an explicit formula for finding the Average Run Length (ARL) of Exponentially Weighted Moving Average (EWMA) control charts when applied to seasonal autoregressive processes with a quadratic trend. The ARL values derived from the proposed explicit formula were evaluated for accuracy by comparing them with results from the numerical integral equation (NIE) approach utilizing the Midpoint rule. These methods were assessed using real-world applications in the medical field, along with comprehensive simulations. The results demonstrate that the proposed explicit formula and the

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Areepong, Yupaporn, and Wilasinee Peerajit. "Enhancing the Ability of the EWMA Control Chart to Detect Changes in the Mean of a Time-Series Model." Malaysian Journal of Fundamental and Applied Sciences 20, no. 6 (2024): 1420–39. https://doi.org/10.11113/mjfas.v20n6.3851.

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We improved the ability of the exponentially weighted moving average (EWMA) control chart to detect small shifts in the mean of a long-memory fractionally integrated autoregressive process with an exogenous variable under exponential white noise. We first designed the structure of the control chart and then evaluated its performance in terms of the average run length (ARL) via a simulation study. We first derived an analytical ARL using explicit formulas by solving integral equations and an approximated ARL derived by utilizing the numerical integral equation approach. Banach's fixed-point the

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Raza, Muhammad Ali, Farah Tariq, Abdullah A. Zaagan, Gideon Mensah Engmann, Ali M. Mahnashi, and Mutum Zico Meetei. "A nonparametric mixed exponentially weighted moving average-moving average control chart with an application to gas turbines." PLOS ONE 19, no. 8 (2024): e0307559. http://dx.doi.org/10.1371/journal.pone.0307559.

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This study aims to develop a nonparametric mixed exponentially weighted moving average-moving average (NPEWMA-MA) sign control chart for monitoring shifts in process location, particularly when the distribution of a critical quality characteristic is either unknown or non-normal. In literature, the variance expression of the mixed exponentially weighted moving average-moving average (EWMA-MA) statistic is calculated by allowing sequential moving averages to be independent, and thus the exclusion of covariance terms results in an inaccurate variance expression. Furthermore, the effectiveness of

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Qamar, Abdul Wahab, Najam ul Hassan, and Maqbool Hussain Sial. "HYBRID DOUBLE EXPONENTIALLY WEIGHTED MOVING AVERAGE (HDEWMA) CONTROL CHART FOR INVERSE RAYLEIGH DISTRIBUTION." Pakistan Journal of Social Research 05, no. 02 (2023): 1337–46. http://dx.doi.org/10.52567/pjsr.v5i02.1359.

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In this paper, we proposed a Hybrid Double Exponentially Weighted Moving Average HDEWMA control chart. The proposed control chart is based on Inverse Rayleigh Distributed lifetimes using simple random sampling (SRS) and ranked set sampling (RSS). Out-of-control-Average Run Length (ARL1) is used to evaluate the performance of the proposed control chart. The HDEWMA control chart is compared with traditional/simple EWMA and CUSUM control charts. The performance of the control chart is evaluated using out of control average run length (ARL1). A simulated example is used to compare the proposed HDE

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Iqbal, Taswar, Muhammad Zafar Iqbal, Muhammad Kashif, and Ghulam Farid. "Advancing Quality Assurance In Manufacturing: A Weighted Exponential Distribution Control Chart For Enhanced Production Monitoring." Migration Letters 21, S5 (2024): 1344–62. http://dx.doi.org/10.59670/ml.v21is5.8159.

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Over the last few decades, weighted distributions have received substantial attention from researchers due to their utility across a range of research fields. With an emphasis on the relevance of weighted distributions, a new control chart for a weighted exponentially distributed characteristic using an exponentially weighted moving average (EWMA) has been proposed in this manuscript. The average run length of both in-control and out-of-control processes has been derived. The efficiency of the proposed control chart has been compared with existing chart based on the unweighted exponential dist

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Peerajit, Wilasinee, and Yupaporn Areepong. "Alternative to Detecting Changes in the Mean of an Autoregressive Fractionally Integrated Process with Exponential White Noise Running on the Modified EWMA Control Chart." Processes 11, no. 2 (2023): 503. http://dx.doi.org/10.3390/pr11020503.

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The modified exponentially weighted moving-average (modified EWMA) control chart is an improvement on the traditional EWMA control chart. Herein, we provide more details about the modified EWMA control chart using various values of an additional design parameter for detecting small-to-moderate shifts in the process mean of an autoregressive fractionally integrated (ARFI(p, d)) process with exponential white noise running thereon. The statistical performances of the two charts were evaluated in terms of the average run length (ARL) obtained by solving integral equations (IEs). This provides an

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KHAW, KHAI WAH, XINYING CHEW, MING HA LEE, and WAI CHUNG YEONG. "An Optimal Adaptive Variable Sample Size Scheme for the Multivariate Coefficient of Variation." Statistics, Optimization & Information Computing 9, no. 3 (2021): 681–93. http://dx.doi.org/10.19139/soic-2310-5070-996.

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Development of an efficient process monitoring system has always received great attention. Previous studies revealed that the coefficient of variation (CV) is important in ensuring process quality, especially for monitoring a process where its process mean and variance are highly correlated. The fact that almost all industrial process monitoring involves a minimum of two or more related quality characteristics being monitored simultaneously, this paper incorporates the salient feature of the adaptive sample size VSS scheme into the standard multivariate CV (MCV) chart, called the VSS MCV chart

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Puengpapat, Phassarapon, Saowanit Sukparungsee, and Yupaporn Areepong. "An Approximation of ARL of the DHWMA Control Chart for MA(q) Process using the Numerical Integral Equation Method." WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS 22 (May 30, 2025): 1100–1110. https://doi.org/10.37394/23207.2025.22.90.

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Quality control of products and services is essential across various industries and sectors, including manufacturing, engineering, public health, economics, finance, and medicine. It is critical to ensure that product characteristics align with customer requirements while maintaining consistent quality and standards. Control charts are essential tools in Statistical Process Control (SPC), used to detect changes in process means or variability, and play a critical role in monitoring, controlling, and enhancing quality within production processes. This study evaluates the Average Run Length (ARL

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Peerajit, Wilasinee. "Accurate Average Run Length Analysis for Detecting Changes in a Long-Memory Fractionally Integrated MAX Process Running on EWMA Control Chart." WSEAS TRANSACTIONS ON MATHEMATICS 22 (July 24, 2023): 514–30. http://dx.doi.org/10.37394/23206.2023.22.58.

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Numerical evaluation of the average run length (ARL) when detecting changes in the mean of an autocorrelated process running on an exponentially weighted moving average (EWMA) control chart has received considerable attention. However, accurate computation of the ARL of changes in the mean of a long-memory model with an exogenous (X) variable, which often occurs in practice, is challenging. Herein, we provide an accurate determination of the ARL for long-memory models such as the fractionally integrated MAX processes (FIMAX) with exponential white noise running on an EWMA control chart by usin

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Herdiani, Erna Tri, and Mustabsyirah Mustabsyirah. "COMPARISON OF EXPONENTIALLY WEIGHTED MOVING AVERAGE CONTROL CHART WITH HOMOGENEOUSLY WEIGHTED MOVING AVERAGE CONTROL CHARTS AND ITS APPLICATION." BAREKENG: Jurnal Ilmu Matematika dan Terapan 19, no. 3 (2025): 2243–62. https://doi.org/10.30598/barekengvol19iss3pp2243-2262.

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The Exponentially Weighted Moving Average (EWMA) control chart is a widely used memory-type control chart known for detecting small shifts in process means. The recently developed Homogeneously Weighted Moving Average (HWMA) control chart modifies the weighting scheme of EWMA, giving more weight to the latest data and distributing smaller weights evenly to past data to further improve sensitivity. This paper compares the performance of EWMA and HWMA control charts on an iron pipe production process dataset. The methodology involves a two-phase analysis: Phase I for establishing in-control proc

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Sukparungsee, Saowanit, and Yupaporn Areepong. "The Exact Solution of ARL using an Integral Equation on the DMEWMA Chart for the SAR(P)L Process for Mean Shift Detection." WSEAS TRANSACTIONS ON SYSTEMS 24 (May 12, 2025): 388–402. https://doi.org/10.37394/23202.2025.24.34.

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The main objective of this investigation is to prove the explicit formula for the average run length (ARL) of the modified double exponentially weighted moving average (DMEWMA) control chart in the context of a seasonal regression process. The explicit formula is compared to the numerical integral equation (NIE) method, with the percentage of accuracy serving as the evaluation metric for both approaches. Furthermore, the performance of the DMEWMA control chart is assessed by calculating the standard deviation of the run length (SDRL) and the median run length (MRL). To demonstrate the design a

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Guo, Yi, Lei Gao, and Yan Zhu. "ARL Estimation of the Control Chart of Log Likelihood Ratios’ Sum for Markov Sequence." Journal of Mathematics 2021 (May 8, 2021): 1–10. http://dx.doi.org/10.1155/2021/6649949.

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To evaluate the surveillance performance of a control chart with the charting statistic of the sum of log likelihood ratios in the statistical process control (SPC), in this paper, we give the proof procedure based on Markov chains for the asymptotic estimation of the average run length (ARL) for this kind of chart. The out-of-control ARL 1 is approximately equal to 1 for any fixed in-control ARL 0 with a negative control limit. By the equivalence between limit distribution of a sum and that of a suprema sum of Markov chain, we derive the estimation of ARL 1 with a large enough positive contro

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Phantu, Suganya, Yupaporn Areepong, and Saowanit Sukparungsee. "Double Moving Average Control Chart for Time Series Data with Poisson INARCH(1)." WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS 21 (February 23, 2024): 694–707. http://dx.doi.org/10.37394/23207.2024.21.58.

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The objectives of this research are to find the explicit formulas of the average run length (ARL) of a double moving average (DMA) control chart for first-order integer-valued autoregressive conditional heteroscedasticity (INARCH1))) of Poisson count data. In addition, the numerical results obtained from the proposed explicit formulas are compared with those obtained from Monte Carlo simulations (MC) for the Poisson INARCH(1) counting process. An out-of-control ARL (ARL1) is the criteria for measuring the performance of control charts. The numerical results found that the values of both ARL0 a

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Wang, Hai Yu. "The Optimization Design Method of Multivariate Control Chart with Adaptive Sample Size." Advanced Materials Research 403-408 (November 2011): 4108–13. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.4108.

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ARL (Average Run Length) is used as a tool to measure the performance of control chart. But it isn’t very accurate. In this paper, APL (Average Product Length) is used as a criterion of multivariate control chart performance assessment and a multivariate chart with adaptive sample size is proposed. A Markov chain method is proposed to calculate the APL of multivariate chart with adaptive sample size and then the optimization design method of this chart is discussed. By comparing with traditional fixed sample size design method, we can find that this method have higher efficiency.

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Ali, Sajid, Shayaan Rajput, Ismail Shah, and Hassan Houmani. "Process Monitoring Using Truncated Gamma Distribution." Stats 6, no. 4 (2023): 1298–324. http://dx.doi.org/10.3390/stats6040080.

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The time-between-events idea is commonly used for monitoring high-quality processes. This study aims to monitor the increase and/or decrease in the process mean rapidly using a one-sided exponentially weighted moving average (EWMA) chart for the detection of upward or downward mean shifts using a truncated gamma distribution. The use of the truncation method helps to enhance and improve the sensitivity of the proposed chart. The performance of the proposed chart with known and estimated parameters is analyzed by using the run length properties, including the average run length (ARL) and standa

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Ali, Sajid, Muhammad Farhan Akram, and Ismail Shah. "Max-EWMA Chart Using Beta and Simplex Distributions for Time and Magnitude Monitoring." Mathematical Problems in Engineering 2022 (July 20, 2022): 1–12. http://dx.doi.org/10.1155/2022/7306775.

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Control charts are used to detect assignable causes in different manufacturing and nonmanufacturing processes. This study presents a new maximum exponentially weighted moving average (Max-EWMA) chart for joint unit interval time and magnitude monitoring. To this end, beta distribution is considered for time whereas simplex distribution is used for magnitude. Average run length (ARL), standard deviation of run length (SDRL), and different quantiles are used to evaluate the performance of the Max-EWMA chart. A real data example is also included in the study to show the application of the propose

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Sankle, R., J. R. Singh, and I. K. Mangal. "Cumulative sum control charts for truncated normal distribution under measurement error." Statistics in Transition new series 13, no. 1 (2013): 95–106. http://dx.doi.org/10.59170/stattrans-2012-007.

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In the present paper Cumulative Sum Control Chart (CSCC) for the truncated normal distribution under measurement error (r) is discussed. The sensitivity of the parameters of the V-Mask and the Average Run Length (ARL) is studied through numerical evaluation for different values of r.

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Tuh, Moi Hua, Cynthia Mui Lian Kon, Hong Siang Chua, Man Fai Lau, and Yee Hui Robin Chang. "Evaluating the Performance of Synthetic Double Sampling np Chart Based on Expected Median Run Length." Mathematics 11, no. 3 (2023): 595. http://dx.doi.org/10.3390/math11030595.

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To keep an eye on the status of high-quality processes for fraction nonconforming, the synthetic double sampling (SDS) np chart is a helpful tool. The SDS np chart is a hybrid between the double sampling (DS) np chart and the conforming run length (CRL) chart. The performance of a control chart is typically judged solely using the average run length (ARL). However, as the shape of the run length (RL) distribution varies with the magnitude of the shift in the process fraction nonconforming, the ARL no longer provides clear interpretation of a chart’s performance. Subsequently, enhanced DS np ch

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Wei Lin, Teoh, Goh Kai Le, Chong Zhi Lin, Chew XinYing, Lee Ming Ha, and Khaw Khai Wah. "Optimising Variable Sample Size Chart Through Median Run Length with Estimated Process Parameters." Sains Malaysiana 54, no. 4 (2025): 1187–207. https://doi.org/10.17576/jsm-2025-5404-18.

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The classic charting procedures for designing the estimated process parameters-based variable sample size (VSS) chart rely on the average run length (ARL) criterion. Nevertheless, variations in the number of Phase-I samples and sample size, as well as the magnitude of the process mean shift affect the skewness of the run-length distribution for a control chart. Hence, we claim that the ARL can be a misleading metric when adopted in the estimated process parameters-based control charts. Instead, examining percentiles of the run-length distribution, which focus on the run-length behaviour, are m

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Hassan, Najam ul, Maqbool Hussain Sial, and Javed Iqbal. "MONITORING INVERSE RAYLEIGH DISTRIBUTED LIFETIMES USING DEWMA CONTROL CHART." Pakistan Journal of Social Research 04, no. 03 (2022): 1143–50. http://dx.doi.org/10.52567/pjsr.v4i03.1294.

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In this paper, we proposed a Double Exponentially Weighted Moving Average DEWMA control chart. The proposed control chart is based on Inverse Rayleigh Distributed lifetimes using simple random sampling. Out-of-control-Average Run Length (ARL1) is used to evaluate the performance of the proposed control chart. The DEWMA control chart is compared with traditional/simple EWMA and CUSUM control charts. A simulated example is used to compare the proposed DEWMA, traditional/simple EWMA chart control chart. It is observed that the proposed DEWMA control chart performs simple EWMA control charts. The

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Phantu, Suganya, Yupaporn Areepong, and Saowanit Sukparungsee. "Analysis Process Dispersion Variation Tracked using a Mixed MA-EWMA Control Chart." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 19 (July 29, 2024): 217–26. http://dx.doi.org/10.37394/23203.2024.19.23.

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This study aims to develop a combined Moving Average - Exponentially Weighted Moving Average Control Chart with standard deviation based (MA-EWMAS chart) that can be used to identify changes in standard deviation in processes under a normal distribution. The average run length (ARL), standard deviation of run length (SRL), and median run length (MRL) are used to compare the performance of the proposed control chart with S, MAS, and EWMAS control charts. This benchmark is assessed using Monte Carlo (MC) simulations. Furthermore, actual data is used to apply the suggested control charts. For all

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Gadde, Srinivasa Rao, and Amer Ibrahim Al-Omari. "Attribute Control Charts Based on TLT for Length-Biased Weighted Lomax Distribution." Journal of Mathematics 2022 (April 22, 2022): 1–15. http://dx.doi.org/10.1155/2022/3091850.

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The length-biased weighted Lomax distribution (LBWD) is a novel continuous of two parameters lifetime distribution. In this article, we introduced an attribute control chart (CC) for the lifetime of a product that follows the LBWD in terms of the number of failure items before a fixed time period is investigated. The performance of the suggested charts is investigated using in term of the average run length (ARL). The necessary tables of shift sizes and various sample sizes are offered for numerous values of the distribution parameters as well as specified ARL and shift constants. Some numeric

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