{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:29:53Z","timestamp":1759336193434,"version":"3.40.5"},"reference-count":25,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04621\/2020","UIDP\/04621\/2020"],"award-info":[{"award-number":["UIDB\/04621\/2020","UIDP\/04621\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Independence between successive counts is not a sensible premise while dealing, for instance, with very high sampling rates.\nAfter assessing the impact of falsely assuming independent binomial counts in the performance of <jats:italic>np<\/jats:italic>-charts, such as the one with 3-\u03c3 control limits, we propose a modified <jats:italic>np<\/jats:italic>-chart for monitoring first-order autoregressive counts with binomial marginals.\nThis simple chart has an in-control average run length (ARL) larger than any out-of-control ARL, i.e., it is ARL-unbiased.\nMoreover, the ARL-unbiased modified <jats:italic>np<\/jats:italic>-chart triggers a signal at sample <jats:italic>t<\/jats:italic> with\nprobability one if the observed value of the control statistic\nis beyond the lower and upper control limits <jats:italic>L<\/jats:italic> and <jats:italic>U<\/jats:italic>.\nIn addition to this, the chart emits a signal with probability <jats:inline-formula id=\"j_eqc-2022-0052_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\u03b3<\/m:mi>\n                              <m:mi>L<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_eqc-2022-0052_eq_0195.png\"\/>\n                        <jats:tex-math>{\\gamma_{L}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> (resp. <jats:inline-formula id=\"j_eqc-2022-0052_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\u03b3<\/m:mi>\n                              <m:mi>U<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_eqc-2022-0052_eq_0197.png\"\/>\n                        <jats:tex-math>{\\gamma_{U}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>) if that observed value coincides with <jats:italic>L<\/jats:italic> (resp. <jats:italic>U<\/jats:italic>).\nThis randomization allows us to set the control limits in such a way that the in-control ARL takes the desired value <jats:inline-formula id=\"j_eqc-2022-0052_ineq_9997\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>ARL<\/m:mi>\n                              <m:mn>0<\/m:mn>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_eqc-2022-0052_eq_0222.png\"\/>\n                        <jats:tex-math>{\\operatorname{ARL}_{0}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, in contrast to <jats:italic>traditional<\/jats:italic> charts with discrete control statistics.\nSeveral illustrations of the ARL-unbiased modified <jats:italic>np<\/jats:italic>-chart are provided, using the statistical software R and resorting to real and simulated data.<\/jats:p>","DOI":"10.1515\/eqc-2022-0052","type":"journal-article","created":{"date-parts":[[2023,3,30]],"date-time":"2023-03-30T10:33:00Z","timestamp":1680172380000},"page":"11-24","source":"Crossref","is-referenced-by-count":2,"title":["An ARL-Unbiased Modified <i>np<\/i>-Chart for Autoregressive Binomial Counts"],"prefix":"10.1515","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2214-2910","authenticated-orcid":false,"given":"Manuel Cabral","family":"Morais","sequence":"first","affiliation":[{"name":"Department of Mathematics & CEMAT (Center for Computational and Stochastic Mathematics), Instituto Superior T\u00e9cnico \u2014 Universidade de Lisboa , Av. Rovisco Pais, 1049-001 Lisboa , Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7151-8243","authenticated-orcid":false,"given":"Philipp","family":"Wittenberg","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics , Helmut Schmidt University , Holstenhofweg 85, 22043 Hamburg , Germany"}]},{"given":"Camila Jeppesen","family":"Cruz","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico , Universidade de Lisboa , Av. Rovisco Pais, 1049-001 Lisboa , Portugal"}]}],"member":"374","published-online":{"date-parts":[[2023,3,31]]},"reference":[{"key":"2023053118423055501_j_eqc-2022-0052_ref_001","doi-asserted-by":"crossref","unstructured":"M. A.  Al-Osh and A. A.  Alzaid,\nBinomial autoregressive moving average models,\nComm. Statist. Stochastic Models 7 (1991), no. 2, 261\u2013282.","DOI":"10.1080\/15326349108807188"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_002","doi-asserted-by":"crossref","unstructured":"M.  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Control 31 (2016), no. 1, 11\u201321.","DOI":"10.1515\/eqc-2015-0013"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_010","doi-asserted-by":"crossref","unstructured":"M. C.  Morais, S.  Knoth, C. J.  Cruz and C. H.  Wei\u00df,\nARL-unbiased CUSUM schemes to monitor binomial counts,\nFrontiers in Statistical Quality Control 13,\nFront. Stat. Qual. Control,\nSpringer, Cham (2021), 77\u201398.","DOI":"10.1007\/978-3-030-67856-2_6"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_011","doi-asserted-by":"crossref","unstructured":"M. C.  Morais, P.  Wittenberg and C. J.  Cruz,\nThe np-chart with 3-\u03c3 limits and the ARL-unbiased np-chart revisited,\nStoch. Qual. Control 37 (2022), no. 2, 107\u2013116.","DOI":"10.1515\/eqc-2022-0032"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_012","doi-asserted-by":"crossref","unstructured":"F.  Pascual,\nEWMA charts for the weibull shape parameter,\nJ. Qual. Technol. 42 (2010), no. 4, 400\u2013416.","DOI":"10.1080\/00224065.2010.11917836"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_013","doi-asserted-by":"crossref","unstructured":"S.  Paulino, M. C.  Morais and S.  Knoth,\nOn ARL-unbiased c-charts for INAR(1) Poisson counts,\nStatist. Papers 60 (2019), no. 4, 1021\u20131038.","DOI":"10.1007\/s00362-016-0861-9"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_014","unstructured":"J. J.  Pignatiello, Jr., C. A.  Acosta-Mej\u00eda and B. V.  Rao,\nThe performance of control charts for monitoring process dispersion,\n4th Industrial Engineering Research Conference Proceedings,\nInstitute of Industrial Engineers, Peachtree Corners (1995), 320\u2013328."},{"key":"2023053118423055501_j_eqc-2022-0052_ref_015","doi-asserted-by":"crossref","unstructured":"A. C.  Rakitzis, C. H.  Wei\u00df and P.  Castagliola,\nControl charts for monitoring correlated counts with a finite range,\nAppl. Stoch. Models Bus. Ind. 33 (2017), no. 6, 733\u2013749.","DOI":"10.1002\/asmb.2275"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_016","unstructured":"I.  Silva,\nAnalysis of Discrete-valued Time Series: Some Contributions to Discrete-Valued Time Series,\nLambert Academic, Saarbr\u00fccken, 2005."},{"key":"2023053118423055501_j_eqc-2022-0052_ref_017","doi-asserted-by":"crossref","unstructured":"F. W.  Steutel and K.  van Harn,\nDiscrete analogues of self-decomposability and stability,\nAnn. Probab. 7 (1979), no. 5, 893\u2013899.","DOI":"10.1214\/aop\/1176994950"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_018","unstructured":"C. H.  Wei\u00df,\nCategorical time series analysis and applications in statistical quality control,\nPhD thesis, Universit\u00e4t W\u00fcrzburg, 2009."},{"key":"2023053118423055501_j_eqc-2022-0052_ref_019","doi-asserted-by":"crossref","unstructured":"C. H.  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Papers 54 (2013), no. 3, 563\u2013590.","DOI":"10.1007\/s00362-012-0449-y"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_023","doi-asserted-by":"crossref","unstructured":"C. H.  Wei\u00df and P. K.  Pollett,\nChain binomial models and binomial autoregressive processes,\nBiometrics 68 (2012), no. 3, 815\u2013824.","DOI":"10.1111\/j.1541-0420.2011.01716.x"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_024","doi-asserted-by":"crossref","unstructured":"C. H.  Wei\u00df and M. C.  Testik,\nCUSUM monitoring of first-order integer-valued autoregressive processes of poisson counts,\nJ. Qual. Technol. 41 (2009), no. 4, 389\u2013400.","DOI":"10.1080\/00224065.2009.11917793"},{"key":"2023053118423055501_j_eqc-2022-0052_ref_025","unstructured":"ISO, ISO\/IEC 14882:2011 Information technology \u2014 Programming languages \u2014 C++, International Organization for Standardization, Geneva, 2020."}],"container-title":["Stochastics and Quality Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/eqc-2022-0052\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/eqc-2022-0052\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T18:42:41Z","timestamp":1685558561000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/eqc-2022-0052\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,31]]},"references-count":25,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,3,31]]},"published-print":{"date-parts":[[2023,6,1]]}},"alternative-id":["10.1515\/eqc-2022-0052"],"URL":"https:\/\/doi.org\/10.1515\/eqc-2022-0052","relation":{},"ISSN":["2367-2390","2367-2404"],"issn-type":[{"type":"print","value":"2367-2390"},{"type":"electronic","value":"2367-2404"}],"subject":[],"published":{"date-parts":[[2023,3,31]]}}}