{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T03:02:56Z","timestamp":1772766176022,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research (DSR) at the King Fahd University of Petroleum and Minerals (KFUPM) under Project Number SB191030\u201d (Muhammad Riaz).","award":["SB191030"],"award-info":[{"award-number":["SB191030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>To detect sustainable changes in the manufacturing processes, memory-type charting schemes are frequently functioning. The recently designed, homogenously weighted moving average (HWMA) technique is effective for identifying substantial changes in the processes. To make the HWMA chart more effective for persistent shifts in the industrial processes, a double HWMA (DHWMA) chart has been proposed recently. This study intends to develop a triple HWMA (THWMA) chart for efficient monitoring of the process mean under zero- and steady-state scenarios. The non-normal effects of monitoring characteristics under in-control situations for heavy-tailed highly skewed and contaminated normal environments are computed under both states. The relative efficiency of the proposed structure is compared with HWMA, DHWMA, exponentially weighted moving average (EWMA), double EWMA, and the more effective triple EWMA control charting schemes. The relative analysis reveals that the proposed THWMA design performs more efficiently than the existing counterparts. An illustrative application related to substrate manufacturing is also incorporated to demonstrate the proposal.<\/jats:p>","DOI":"10.3390\/sym13020360","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T20:19:36Z","timestamp":1614111576000},"page":"360","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["On the Development of Triple Homogeneously Weighted Moving Average Control Chart"],"prefix":"10.3390","volume":"13","author":[{"given":"Muhammad","family":"Riaz","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8122-082X","authenticated-orcid":false,"given":"Zameer","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Statistics, Government Ambala Muslim College Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hafiz Zafar","family":"Nazir","sequence":"additional","affiliation":[{"name":"Departemnt of Statistics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Abid","sequence":"additional","affiliation":[{"name":"Department of Statistics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1093\/biomet\/41.1-2.100","article-title":"Continuous inspection schemes","volume":"41","author":"Page","year":"1954","journal-title":"Biometrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1080\/00401706.1959.10489860","article-title":"Control chart tests based on geometric moving averages","volume":"42","author":"Roberts","year":"1959","journal-title":"Technometrics"},{"key":"ref_3","unstructured":"Montgomery, D.C. 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