{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T08:26:31Z","timestamp":1777710391540,"version":"3.51.4"},"reference-count":42,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,13]],"date-time":"2022-01-13T00:00:00Z","timestamp":1642032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71802110, 71801049, 11701437"],"award-info":[{"award-number":["71802110, 71801049, 11701437"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Research Base of Philosophy and Social Sciences 413 in Jiangsu-Information Industry Integration Innovation and Emergency Management Research 414 Center","award":["none"],"award-info":[{"award-number":["none"]}]},{"name":"The Excellent Innovation Teams of Philosophy and Social Science in Jiangsu Province","award":["2017ZSTD022"],"award-info":[{"award-number":["2017ZSTD022"]}]},{"name":"Postgraduate Research and Practice Innovation Program of 416 Jiangsu Province","award":["KYCX21_0840"],"award-info":[{"award-number":["KYCX21_0840"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Much research has been conducted on two-sided Exponentially Weighted Moving Average (EWMA) control charts, while less work has been devoted to the one-sided EWMA charts. Traditional one-sided EWMA charts involve resetting the EWMA statistic to the target whenever it falls below or above the target, or truncating the observations above or below the target and further applying the EWMA statistic to the truncated samples. In order to further improve the performance of traditional one-sided EWMA mean (X\u00af) charts, this paper studies the performance of the Modified One-sided EWMA (MOEWMA) X\u00af charts to monitor a normally distributed process. The Monte-Carlo simulation method is used to obtain the zero- and steady-state Run Length (RL) properties of the proposed control charts. Through extensive simulations and comparisons with other charts, it is shown that the proposed MOEWMA X\u00af charts compare favorably with some existing competing charts. Moreover, by attaching the variable sampling intervals (VSI) feature to the MOEWMA X\u00af charts, it is shown that the VSI MOEWMA charts outperform the corresponding charts without the VSI feature. Finally, a real data example from manufacturing process shows the implementation of the proposed one-sided charts.<\/jats:p>","DOI":"10.3390\/sym14010159","type":"journal-article","created":{"date-parts":[[2022,1,14]],"date-time":"2022-01-14T03:14:56Z","timestamp":1642130096000},"page":"159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Modified One-Sided EWMA Charts without- and with Variable Sampling Intervals for Monitoring a Normal Process"],"prefix":"10.3390","volume":"14","author":[{"given":"Xuelong","family":"Hu","sequence":"first","affiliation":[{"name":"School of Management, Nanjing University of Posts and Telecommunications, No. 66, Xinmofan Road, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suying","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Management, Nanjing University of Posts and Telecommunications, No. 66, Xinmofan Road, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guan","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Management, Nanjing University of Posts and Telecommunications, No. 66, Xinmofan Road, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianlan","family":"Zhong","sequence":"additional","affiliation":[{"name":"College of Management & College of Tourism, Fujian Agriculture and Forestry University, Fuzhou 350002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9175-892X","authenticated-orcid":false,"given":"Shu","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Logistics, Wuhan University of Technology, Wuhan 430063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1093\/biomet\/59.3.539","article-title":"An Approach to the Probability Distribution of CUSUM Run Length","volume":"59","author":"Brook","year":"1972","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1080\/00224065.1984.11978921","article-title":"The Shewhart Control Chart\u2013Tests for Special Causes","volume":"16","author":"Nelson","year":"1984","journal-title":"J. Qual. Technol."},{"key":"ref_3","first-page":"1","article-title":"Exponentially weighted moving average control schemes: Properties and enhancements","volume":"32","author":"Lucas","year":"1990","journal-title":"J. Qual. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Hawkins, D., and Olwell, D. (1999). Cumulative Sum Charts and Charting for Quality Improvement, Springer.","DOI":"10.1007\/978-1-4612-1686-5"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1779","DOI":"10.1080\/00949655.2013.766737","article-title":"The computation of average run length and average time to signal: An overview","volume":"84","author":"Li","year":"2014","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1080\/00224065.2018.1541387","article-title":"Some simultaneous progressive monitoring schemes for the two parameters of a zero-inflated Poisson process under unknown shifts","volume":"51","author":"Mukherjee","year":"2019","journal-title":"J. Qual. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1080\/08982112.2020.1788717","article-title":"Multivariate Time-Between-Events Monitoring\u2013An overview and some (overlooked) underlying complexities","volume":"33","author":"Zwetsloot","year":"2020","journal-title":"Qual. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1080\/00224065.2019.1571343","article-title":"An EWMA control chart for categorical processes with applications to social network monitoring","volume":"52","author":"Perry","year":"2020","journal-title":"J. Qual. Technol."},{"key":"ref_9","unstructured":"Montgomery, D.C. (2009). Intorduction to Ststistical Quality Control, Wiley. [7th ed.]."},{"key":"ref_10","first-page":"401","article-title":"A Simple Method for Studying Run-Length Distributions of Exponentially Weighted Moving Average Charts","volume":"29","author":"Crowder","year":"1987","journal-title":"Technometrics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1080\/00401706.1991.10484836","article-title":"Some Omnibus Exponentially Weighted Moving Average Statistical Process Monitoring Schemes","volume":"33","author":"Domangue","year":"1991","journal-title":"Technometrics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/00224065.1999.11979929","article-title":"Robustness of the EWMA Control Chart to Non-Normality","volume":"31","author":"Borror","year":"1999","journal-title":"J. Qual. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1080\/00224065.1999.11979913","article-title":"EWMA Control Charts for Monitoring the Mean of Autocorrelated Processes","volume":"31","author":"Lu","year":"1999","journal-title":"J. Qual. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1198\/004017001750386279","article-title":"The Performance of Exponentially Weighted Moving Average Charts With Estimated Parameters","volume":"43","author":"Jones","year":"2001","journal-title":"Technometrics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1002\/qre.1121","article-title":"Shewhart and EWMA t control charts for short production runs","volume":"27","author":"Celano","year":"2011","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1080\/16843703.2013.11673307","article-title":"The Synthetic t and Synthetic EWMA t Charts","volume":"10","author":"Calzada","year":"2013","journal-title":"Qual. Technol. Quant. Manag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1080\/03610926.2018.1429631","article-title":"An enhanced EWMA-t control chart for monitoring the process mean","volume":"48","author":"Haq","year":"2019","journal-title":"Commun. -Stat.-Theory Methods"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/00224065.2011.11917861","article-title":"Monitoring the Coefficient of Variation Using EWMA Charts","volume":"43","author":"Castagliola","year":"2011","journal-title":"J. Qual. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1002\/qre.1918","article-title":"Monitoring the Ratio of Two Normal Variables Using EWMA Type Control Charts","volume":"32","author":"Tran","year":"2016","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1002\/qre.2259","article-title":"Steady-state ARL analysis of ARL-unbiased EWMA-RZ control chart monitoring the ratio of two normal variables","volume":"34","author":"Tran","year":"2018","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.cie.2014.09.027","article-title":"A new exponentially weighted moving average control chart for monitoring the coefficient of variation","volume":"78","author":"Zhang","year":"2014","journal-title":"Comput. Ind. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.cie.2018.09.045","article-title":"Monitoring the coefficient of variation using a variable sample size EWMA chart","volume":"126","author":"Muhammad","year":"2018","journal-title":"Comput. Ind. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1002\/qre.2595","article-title":"CUSUM control charts with variable sampling interval for monitoring the ratio of two normal variables","volume":"36","author":"Nguyen","year":"2020","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"478","DOI":"10.1080\/00949655.2018.1555252","article-title":"Weighted adaptive multivariate CUSUM charts with variable sampling intervals","volume":"89","author":"Haq","year":"2018","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2181","DOI":"10.1002\/qre.2177","article-title":"Nonparametric signed-rank control charts with variable sampling intervals","volume":"33","author":"Coelho","year":"2017","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1016\/j.apm.2017.08.005","article-title":"Multivariate nonparametric control chart with variable sampling interval","volume":"52","author":"Yue","year":"2017","journal-title":"Appl. Math. Model."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1080\/00224065.2017.11918004","article-title":"Monitoring the Coefficient of Variation Using a Variable Sampling Interval EWMA Chart","volume":"49","author":"Yeong","year":"2017","journal-title":"J. Qual. Technol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5521","DOI":"10.1080\/00207543.2017.1285076","article-title":"A variable sampling interval Shewhart control chart for monitoring the coefficient of variation in short production runs","volume":"55","author":"Amdouni","year":"2017","journal-title":"Int. J. Prod. Res."},{"key":"ref_29","first-page":"230","article-title":"Multivariate Control Charts for Monitoring the Mean Vector and Covariance Matrix with Variable Sampling Intervals","volume":"30","author":"Matrix","year":"2011","journal-title":"Seq. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1080\/03610918.2013.796980","article-title":"Multivariate Synthetic |S| Control Chart with Variable Sampling Interval","volume":"44","author":"Lee","year":"2015","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.cie.2015.08.015","article-title":"The variable sampling interval run sum X\u00af control chart","volume":"90","author":"Chew","year":"2015","journal-title":"Comput. Ind. Eng."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1080\/00401706.1978.10489620","article-title":"Average Run Lengths of Geometric Moving Average Charts by Numerical Methods","volume":"20","author":"Robinson","year":"1978","journal-title":"Technometrics"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1080\/00224065.1992.11979373","article-title":"Average Run Lengths of EWMA Control Charts for Monitoring a Process Standard Deviation","volume":"24","author":"Hamilton","year":"1992","journal-title":"J. Qual. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00224065.1998.11979819","article-title":"Designs of one- and two-sided exponential EWMA charts","volume":"30","author":"Gan","year":"1998","journal-title":"J. Qual. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1080\/00224065.2008.11917737","article-title":"A New EWMA Chart for Monitoring Process Dispersion","volume":"40","author":"Shu","year":"2008","journal-title":"J. Qual. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1080\/03610910701418465","article-title":"A One-Sided EWMA Control Chart for Monitoring Process Means","volume":"36","author":"Shu","year":"2007","journal-title":"Commun.-Stat.-Simul. Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"699","DOI":"10.1080\/00949655.2019.1699926","article-title":"One-sided and two one-sided MEWMA charts for monitoring process mean","volume":"90","author":"Haq","year":"2020","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1080\/00224065.2014.11917976","article-title":"CUSUM Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes","volume":"46","author":"Dickinson","year":"2014","journal-title":"J. Qual. Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1080\/00224065.2000.11979987","article-title":"CUSUM Charts for Signalling Varying Location Shifts","volume":"32","author":"Sparks","year":"2000","journal-title":"J. Qual. Technol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1080\/00224065.2018.1436830","article-title":"Weighted EWMA charts for monitoring type I censored Weibull lifetimes","volume":"50","author":"Xu","year":"2018","journal-title":"J. Qual. Technol."},{"key":"ref_41","first-page":"181","article-title":"X\u00af Charts With Variable Sampling Intervals","volume":"30","author":"Reynolds","year":"1988","journal-title":"Technometrics"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1080\/00401706.1990.10484721","article-title":"CUSUM Charts with Variable Sampling Intervals","volume":"32","author":"Reynolds","year":"1990","journal-title":"Technometrics"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/1\/159\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:02:20Z","timestamp":1760364140000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/1\/159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,13]]},"references-count":42,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2022,1]]}},"alternative-id":["sym14010159"],"URL":"https:\/\/doi.org\/10.3390\/sym14010159","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,13]]}}}