{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T00:14:26Z","timestamp":1770509666443,"version":"3.49.0"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,5,19]],"date-time":"2017-05-19T00:00:00Z","timestamp":1495152000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Syst Sci Complex"],"published-print":{"date-parts":[[2018,6]]},"DOI":"10.1007\/s11424-017-6144-2","type":"journal-article","created":{"date-parts":[[2017,5,23]],"date-time":"2017-05-23T05:44:20Z","timestamp":1495518260000},"page":"773-786","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["On Construction of Optimal Two-Level Designs with Multi Block Variables"],"prefix":"10.1007","volume":"31","author":[{"given":"Yuna","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shengli","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Minqian","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,5,19]]},"reference":[{"key":"6144_CR1","first-page":"308","volume":"36","author":"S Bisgaard","year":"1994","unstructured":"Bisgaard S, A note on the definition for blocked 2n\u2212p designs, Technometrics, 1994, 36: 308\u2013311.","journal-title":"Technometrics"},{"key":"6144_CR2","volume-title":"Experiments: Planning, Analysis and Optimization","author":"C F J Wu","year":"2009","unstructured":"Wu C F J and Hamada M S, Experiments: Planning, Analysis and Optimization, 2nd Edition, Wiley, New Jersey, 2009.","edition":"2"},{"key":"6144_CR3","first-page":"601","volume":"22","author":"A Fries","year":"1980","unstructured":"Fries A and Hunter W G, Minimum aberration 2k\u2212p designs, Technometrics, 1980, 22: 601\u2013608.","journal-title":"Technometrics"},{"key":"6144_CR4","doi-asserted-by":"publisher","first-page":"3213","DOI":"10.1016\/j.jspi.2010.04.009","volume":"140","author":"H Q Xu","year":"2010","unstructured":"Xu H Q and Mee R W, Minimum aberration blocking schemes for 128-run designs, J. Statist. Plann. Inference, 2010, 140: 3213\u20133229.","journal-title":"J. Statist. Plann. Inference"},{"key":"6144_CR5","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1093\/biomet\/ass061","volume":"100","author":"S L Zhao","year":"2013","unstructured":"Zhao S L, Li P F, and Karunamuni R, Blocked two-level regular factorial designs with weak minimum aberration, Biometrika, 2013, 100: 249\u2013253.","journal-title":"Biometrika"},{"key":"6144_CR6","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1080\/00401706.1992.10484905","volume":"34","author":"C F J Wu","year":"1992","unstructured":"Wu C F J and Chen Y, A graph-aided method for planning two-level experiments when certain interactions are important, Technometrics, 1992, 34: 162\u2013175.","journal-title":"Technometrics"},{"key":"6144_CR7","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1016\/j.jco.2013.04.002","volume":"29","author":"S L Zhao","year":"2013","unstructured":"Zhao S L, Li P F, and Liu M Q, On blocked resolution IV designs containing clear two-factor interactions, J. Complexity, 2013, 29: 389\u2013395.","journal-title":"J. Complexity"},{"key":"6144_CR8","volume-title":"Estimation capacity and related topics in experimental designs","author":"D X Sun","year":"1993","unstructured":"Sun D X, Estimation capacity and related topics in experimental designs, Ph.D. dissertation, University of Waterloo, Waterloo, 1993."},{"key":"6144_CR9","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1214\/aos\/1009210551","volume":"29","author":"C S Cheng","year":"2001","unstructured":"Cheng C S and Mukerjee R, Blocked regular fractional factorial designs with maximum estimation capacity, Ann. Statist., 2001, 29: 530\u2013548.","journal-title":"Ann. Statist."},{"key":"6144_CR10","first-page":"1689","volume":"18","author":"R C Zhang","year":"2008","unstructured":"Zhang R C, Li P, Zhao S L, et al., A general minimum lower-order confounding criterion for two-level regular designs, Statist. Sinica, 2008, 18: 1689\u20131705.","journal-title":"Statist. Sinica"},{"key":"6144_CR11","first-page":"363","volume":"19","author":"R C Zhang","year":"2009","unstructured":"Zhang R C and Mukerjee R, Characterization of general minimum lower order confounding via complementary sets, Statist. Sinica, 2009, 19: 363\u2013375.","journal-title":"Statist. Sinica"},{"key":"6144_CR12","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.5705\/ss.2008.314","volume":"21","author":"J Chen","year":"2011","unstructured":"Chen J and Liu M Q, Some theory for constructing general minimum lower order confounding designs, Statist. Sinica, 2011, 21: 1541\u20131555.","journal-title":"Statist. Sinica"},{"key":"6144_CR13","first-page":"1571","volume":"21","author":"P F Li","year":"2011","unstructured":"Li P F, Zhao S L, and Zhang R C, A theory on constructing 2n\u2212m designs with general minimum lower-order confounding, Statist. Sinica, 2011, 21: 1571\u20131589.","journal-title":"Statist. Sinica"},{"key":"6144_CR14","doi-asserted-by":"publisher","first-page":"1719","DOI":"10.1016\/j.jspi.2009.12.024","volume":"140","author":"R C Zhang","year":"2010","unstructured":"Zhang R C and Cheng Y, General minimum lower order confounding designs: An overview and a construction theory, J. Statist. Plann. Inference, 2010, 140: 1719\u20131730.","journal-title":"J. Statist. Plann. Inference"},{"key":"6144_CR15","doi-asserted-by":"publisher","first-page":"2384","DOI":"10.1016\/j.jspi.2010.02.006","volume":"140","author":"Y Cheng","year":"2010","unstructured":"Cheng Y and Zhang R C, On construction of general minimum lower order confounding 2n\u2212m designs with \n                              $$\\frac{N}{4} + 1 \\leqslant n \\leqslant \\frac{{9N}}{{32}}$$\n                              \n                                 \n                                 \n                                    \n                                       \n                                          N\n                                          4\n                                       \n                                       +\n                                       1\n                                       \u2264\n                                       n\n                                       \u2264\n                                       \n                                          \n                                             9\n                                             N\n                                          \n                                          \n                                             32\n                                          \n                                       \n                                    \n                                 \n                              \n                              \n                           \n, J. Statist. Plann. Inference, 2010, 140: 2384\u20132394.","journal-title":"J. Statist. Plann. Inference"},{"key":"6144_CR16","first-page":"1787","volume":"19","author":"R C Zhang","year":"2009","unstructured":"Zhang R C and Mukerjee R, General minimum lower order confounding in block designs using complementary sets, Statist. Sinica, 2009, 19: 1787\u20131802.","journal-title":"Statist. Sinica"},{"key":"6144_CR17","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.jspi.2015.12.007","volume":"172","author":"S L Zhao","year":"2016","unstructured":"Zhao S L, Lin D K J, and Li P F, A note on the construction of blocked two-level designs with general minimum lower order confounding, J. Statist. Plann. Inference, 2016, 172: 16\u201322.","journal-title":"J. Statist. Plann. Inference"},{"key":"6144_CR18","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1080\/15598608.2014.840517","volume":"8","author":"J L Wei","year":"2014","unstructured":"Wei J L, Li P, and Zhang R C, Blocked two-level regular designs with general minimum lower order confounding, J. Statist. Theory Pract., 2014, 8: 46\u201365.","journal-title":"J. Statist. Theory Pract."},{"key":"6144_CR19","doi-asserted-by":"publisher","first-page":"1082","DOI":"10.1016\/j.jspi.2012.12.011","volume":"143","author":"S L Zhao","year":"2013","unstructured":"Zhao S L, Li P F, Zhang R C, et al., Construction of blocked two-level regular designs with general minimum lower order confounding, J. Statist. Plann. Inference, 2013, 143: 1082\u20131090.","journal-title":"J. Statist. Plann. Inference"},{"key":"6144_CR20","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/s11464-015-0484-9","volume":"11","author":"Y N Zhao","year":"2016","unstructured":"Zhao Y N, Zhao S L, and Liu M Q, A theory on constructing blocked two-level designs with general minimum lower order confounding, Front. Math. China, 2016, 11: 207\u2013235.","journal-title":"Front. Math. China"},{"key":"6144_CR21","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1080\/15598608.2011.10412058","volume":"5","author":"R C Zhang","year":"2011","unstructured":"Zhang R C, Li P, and Wei J L, Optimal two-level regular designs with multi block variables, J. Statist. Theory Pract., 2011, 5: 161\u2013178.","journal-title":"J. Statist. Theory Pract."},{"key":"6144_CR22","first-page":"311","volume":"3","author":"G E P Box","year":"1961","unstructured":"Box G E P and Hunter J S, The 2k\u2212p fractional factorial designs I and II, Technometrics, 1961, 3: 311\u2013351; 449\u2013458.","journal-title":"Technometrics"},{"key":"6144_CR23","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1002\/cjs.11190","volume":"41","author":"Q Zhou","year":"2013","unstructured":"Zhou Q, Balakrishnan N, and Zhang R C, The factor aliased effect number pattern and its application in experimental planning, Canad. J. Statist., 2013, 41: 540\u2013555.","journal-title":"Canad. J. Statist."}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-017-6144-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-017-6144-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-017-6144-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,7,4]],"date-time":"2018-07-04T08:26:21Z","timestamp":1530692781000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-017-6144-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,19]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,6]]}},"alternative-id":["6144"],"URL":"https:\/\/doi.org\/10.1007\/s11424-017-6144-2","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,19]]}}}