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However, no research exists for processes under the combined effect of autocorrelation and measurement errors; thus, such adaptive Shewhart [Formula: see text] schemes are proposed. The Markov chain approach for adaptive designs are used to evaluate the run-length distribution properties with two special sampling strategies (i.e. s-skip and multiple measurements) incorporated to reduce the combined negative effect of autocorrelation and measurement inaccuracy. Using numerous run-length metrics, it is shown that the combination of the two sampling strategies with the VSSI design reduces this negative effect considerably and improves the detection ability of the [Formula: see text] scheme by a significant margin as compared with using the fixed sample size and sampling interval (FSSI), VSS and VSI designs. Autocorrelation level has a higher negative effect as compared with the measurement inaccuracy level. For high levels of autocorrelation ([Formula: see text]0.8), the s-skip strategy has little influence in reducing the negative effect; but the VSSI design maintains better performance than the other designs. Finally, a real-life example is used to illustrate its implementation.<\/jats:p>","DOI":"10.1177\/0142331220935293","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T03:26:00Z","timestamp":1595215560000},"page":"537-548","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Combined effect of autocorrelation and measurement errors on the adaptive X\u00af monitoring schemes"],"prefix":"10.1177","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2243-8196","authenticated-orcid":false,"given":"Sandile Charles","family":"Shongwe","sequence":"first","affiliation":[{"name":"Department of Statistics, College of Science, Engineering and Technology, University of South Africa, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean-Claude","family":"Malela-Majika","sequence":"additional","affiliation":[{"name":"Department of Statistics, 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