{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:37:12Z","timestamp":1760240232917,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T00:00:00Z","timestamp":1555459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Variability or dispersion plays an important role in any process and provides insight into the spread of data from some central point, usually the mean. A process with less spread is preferred over a process in which values differ greatly from the mean. Various methods are available to estimate the process dispersion by using information on the variable of interest. Certain additional variables provide good insight to estimate the process dispersion. In this paper, we propose an efficient method for the estimation of process variability by using the exponential method. The properties of the proposed method were studied. We conducted simulation and empirical studies to compare the proposed method with some existing methods of estimation of variability. The results of the numerical study show that our proposed method is better than the other methods used in the study.<\/jats:p>","DOI":"10.3390\/sym11040554","type":"journal-article","created":{"date-parts":[[2019,4,17]],"date-time":"2019-04-17T07:58:09Z","timestamp":1555487889000},"page":"554","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["On Efficient Estimation of Process Variability"],"prefix":"10.3390","volume":"11","author":[{"given":"Tanveer","family":"Akhlaq","sequence":"first","affiliation":[{"name":"Department of Statistics, COMSATS University Islamabad, Lahore 54900, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Ismail","sequence":"additional","affiliation":[{"name":"Department of Statistics, COMSATS University Islamabad, Lahore 54900, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0695-1216","authenticated-orcid":false,"given":"Muhammad Qaiser","family":"Shahbaz","sequence":"additional","affiliation":[{"name":"Department of Statistics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1080\/01621459.1983.10477939","article-title":"Variance Estimation Using Auxiliary Information","volume":"78","author":"Isaki","year":"1983","journal-title":"J. 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Appl."},{"key":"ref_6","first-page":"29","article-title":"A Class of Ratio-Cum-Dual to Ratio Estimator of Population Variance","volume":"6","author":"Yadav","year":"2013","journal-title":"J. Reliab. Stat. Stud."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"213","DOI":"10.15446\/rce.v37n1.44368","article-title":"Generalized Exponential Type Estimator for Population Variance in Survey Sampling","volume":"37","author":"Asghar","year":"2014","journal-title":"Revista Colombiana de Estad\u00edstica"},{"key":"ref_8","unstructured":"Singh, R., Chauhan, P., Sawan, N., and Smarandache, F. (arXiv Preprint, 2009). Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables, arXiv Preprint."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1080\/03610926.2011.597921","article-title":"A Generalized Family of Transformed Ratio-Product Estimators for Variance in Sample Surveys","volume":"42","author":"Yadav","year":"2013","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_10","first-page":"27","article-title":"A New Ratio-Cum-Dual to Ratio Estimator of Finite Population Mean in Simple Random Sampling","volume":"10","author":"Sharma","year":"2010","journal-title":"Glob. J. Sci. Front. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1016\/j.amc.2013.10.088","article-title":"Generalized Exponential Chain Ratio Estimators under Stratified Two-Phase Random Sampling","volume":"226","author":"Sanaullah","year":"2014","journal-title":"Appl. Math. Comput."},{"key":"ref_12","unstructured":"Das, A.K. (1980). 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Theory and Methods of Survey Sampling, Prentice Hall."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/554\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:46:07Z","timestamp":1760186767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/4\/554"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,17]]},"references-count":18,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,4]]}},"alternative-id":["sym11040554"],"URL":"https:\/\/doi.org\/10.3390\/sym11040554","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,4,17]]}}}