{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T00:45:54Z","timestamp":1770511554451,"version":"3.49.0"},"reference-count":30,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2016,4,21]],"date-time":"2016-04-21T00:00:00Z","timestamp":1461196800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"Fundamental Research Grant Scheme (FRGS)","award":["FRGS\/1\/2015\/SG04\/UTAR\/02\/3"],"award-info":[{"award-number":["FRGS\/1\/2015\/SG04\/UTAR\/02\/3"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quality &amp; Reliability Eng"],"published-print":{"date-parts":[[2017,2]]},"abstract":"<jats:p>The variable sample size (VSS)<jats:inline-graphic xmlns:xlink=\"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/qre1994-math-0004.png\" xlink:title=\"urn:x-wiley:07488017:media:qre1994:qre1994-math-0004\"\/>chart, devoted to the detection of moderate mean shifts, has been widely investigated under the context of the average run\u2010length criterion. Because the shape of the run\u2010length distribution alters with the magnitude of the mean shifts, the average run length is a confusing measure, and the use of percentiles of the run\u2010length distribution is considered as more intuitive. This paper develops two optimal designs of the VSS<jats:inline-graphic xmlns:xlink=\"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/qre1994-math-0005.png\" xlink:title=\"urn:x-wiley:07488017:media:qre1994:qre1994-math-0005\"\/>chart, by minimizing (i) the median run length and (ii) the expected median run length for both deterministic and unknown shift sizes, respectively. The 5th and 95th percentiles are also provided in order to measure the variation in the run\u2010length distribution. Two VSS schemes are considered in this paper, that is, when the (i) small sample size (<jats:italic>n<jats:sub>S<\/jats:sub><\/jats:italic>) or (ii) large sample size (<jats:italic>n<jats:sub>L<\/jats:sub><\/jats:italic>) is predefined for the first subgroup (<jats:italic>n<\/jats:italic><jats:sub>1<\/jats:sub>). The Markov chain approach is adopted to evaluate the performance of these two VSS schemes. The comparative study reveals that improvements in the detection speed are found for these two VSS schemes without increasing the in\u2010control average sample size. For moderate to large mean shifts, the optimal VSS<jats:inline-graphic xmlns:xlink=\"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/qre1994-math-0006.png\" xlink:title=\"urn:x-wiley:07488017:media:qre1994:qre1994-math-0006\"\/>chart with<jats:italic>n<\/jats:italic><jats:sub>1<\/jats:sub>\u2009=\u2009<jats:italic>n<jats:sub>L<\/jats:sub><\/jats:italic>significantly outperforms the optimal EWMA<jats:inline-graphic xmlns:xlink=\"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/qre1994-math-0007.png\" xlink:title=\"urn:x-wiley:07488017:media:qre1994:qre1994-math-0007\"\/>chart, while the former is comparable to the latter when<jats:italic>n<\/jats:italic><jats:sub>1<\/jats:sub>\u2009=\u2009<jats:italic>n<jats:sub>S<\/jats:sub><\/jats:italic>. Copyright \u00a9 2016 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/qre.1994","type":"journal-article","created":{"date-parts":[[2016,4,22]],"date-time":"2016-04-22T13:14:54Z","timestamp":1461330894000},"page":"121-134","source":"Crossref","is-referenced-by-count":41,"title":["Optimal Designs of the Variable Sample Size Chart Based on Median Run Length and Expected Median Run Length"],"prefix":"10.1002","volume":"33","author":[{"given":"W. L.","family":"Teoh","sequence":"first","affiliation":[{"name":"Department of Physical and Mathematical Sciences, Faculty of Science Universiti Tunku Abdul Rahman 31900 Kampar Perak Malaysia"}]},{"given":"J. K.","family":"Chong","sequence":"additional","affiliation":[{"name":"Department of Physical and Mathematical Sciences, Faculty of Science Universiti Tunku Abdul Rahman 31900 Kampar Perak Malaysia"}]},{"given":"M. B. C.","family":"Khoo","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences Universiti Sains Malaysia 11800 Penang Malaysia"}]},{"given":"P.","family":"Castagliola","sequence":"additional","affiliation":[{"name":"Department of Quality and Logistics, LUNAM Universit\u00e9 Universit\u00e9 de Nantes &amp; IRCCyN UMR CNRS 6597 Carquefou France"}]},{"given":"W. C.","family":"Yeong","sequence":"additional","affiliation":[{"name":"Department of Physical and Mathematical Sciences, Faculty of Science Universiti Tunku Abdul Rahman 31900 Kampar Perak Malaysia"}]}],"member":"311","published-online":{"date-parts":[[2016,4,21]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.1850"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/00224065.1998.11979850"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207549308956906"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1080\/00224065.1994.11979523"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610919408813182"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474946.2011.563703"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2010.07.045"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.1261"},{"key":"e_1_2_9_10_1","first-page":"1353","article-title":"The variable sample size t control chart for monitoring short production runs","volume":"66","author":"Castagliola P","year":"2013","journal-title":"International Journal of Advanced Manufacturing Technology"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.1807"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-015-6985-6"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/00224065.2007.11917673"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/0740817X.2011.609526"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474940802445790"},{"key":"e_1_2_9_16_1","volume-title":"Statistical Quality Control: A Modern Introduction","author":"Montgomery DC","year":"2013"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949659308811479"},{"key":"e_1_2_9_18_1","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1111\/j.2517-6161.1995.tb02052.x","article-title":"Sequential change point detection in quality control and dynamical systems","volume":"57","author":"Lai TL","year":"1995","journal-title":"Journal of the Royal Statistical Society: Series B: Methodological"},{"key":"e_1_2_9_19_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2012.682811"},{"key":"e_1_2_9_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/00224065.1990.11979261"},{"key":"e_1_2_9_21_1","doi-asserted-by":"publisher","DOI":"10.1081\/QEN-200056484"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1080\/08982110701276653"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610910500308719"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.1198\/004017008000000280"},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474940701247099"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1081\/STA-120018196"},{"key":"e_1_2_9_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2013.11.001"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.1080\/00224065.2011.11917861"},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1504\/IJQET.2010.034610"},{"key":"e_1_2_9_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijpe.2012.05.031"},{"key":"e_1_2_9_31_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207540210128260"}],"container-title":["Quality and Reliability Engineering International"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fqre.1994","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fqre.1994","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/qre.1994","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,15]],"date-time":"2024-06-15T22:39:58Z","timestamp":1718491198000},"score":1,"resource":{"primary":{"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/onlinelibrary.wiley.com\/doi\/10.1002\/qre.1994"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,21]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,2]]}},"alternative-id":["10.1002\/qre.1994"],"URL":"https:\/\/summer-heart-0930.chufeiyun1688.workers.dev:443\/https\/doi.org\/10.1002\/qre.1994","archive":["Portico"],"relation":{},"ISSN":["0748-8017","1099-1638"],"issn-type":[{"value":"0748-8017","type":"print"},{"value":"1099-1638","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,21]]}}}