{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,10]],"date-time":"2026-05-10T08:29:20Z","timestamp":1778401760038,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2012,3,14]],"date-time":"2012-03-14T00:00:00Z","timestamp":1331683200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This article proposes a quantitative risk assessment for security systems which have multiple protected assets and a risk-based benefit-cost analysis for decision makers. The proposed methodology consists of five phases: identification of assets, security unit and intrusion path, security unit effectiveness estimation, intrusion path effectiveness estimation, security system risk assessment and benefit-cost estimation. Key innovations in this methodology include its use of effectiveness entropy to measure the degree of uncertainty of a security system to complete a protection task, and the fact it measures risk like information theory measures the amount of information. A notional example is provided to demonstrate an application of the proposed methodology.<\/jats:p>","DOI":"10.3390\/e14030571","type":"journal-article","created":{"date-parts":[[2012,3,14]],"date-time":"2012-03-14T14:17:19Z","timestamp":1331734639000},"page":"571-580","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Benefit-Cost Analysis of Security Systems for Multiple Protected Assets Based on Information Entropy"],"prefix":"10.3390","volume":"14","author":[{"given":"Jingjing","family":"Dai","sequence":"first","affiliation":[{"name":"National Engineering Research Center for Multimedia Software, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruimin","family":"Hu","sequence":"additional","affiliation":[{"name":"National Engineering Research Center for Multimedia Software, Wuhan University, Wuhan 430072, China"},{"name":"School of Computer, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Chen","sequence":"additional","affiliation":[{"name":"National Engineering Research Center for Multimedia Software, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qing","family":"Cai","sequence":"additional","affiliation":[{"name":"National Engineering Research Center for Multimedia Software, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,3,14]]},"reference":[{"key":"ref_1","unstructured":"Graves, G.H. (2006). Analytical foundations of physical security system assessment. [Ph.D. Thesis, Texas A&M University]."},{"key":"ref_2","unstructured":"US Department of Homeland Security National infrastructure protection plan, Available online: http:\/\/www.dhs.gov\/xlibrary\/assets\/NIPP_Plan.pdf."},{"key":"ref_3","first-page":"16","article-title":"Research and practice of effectiveness evaluation of security system (in Chinese)","volume":"11","author":"Chen","year":"2007","journal-title":"China Security & Protection"},{"key":"ref_4","first-page":"20","article-title":"Quantitative assessment of physical protection system for nuclear power plant (in Chinese)","volume":"30","author":"Sun","year":"2009","journal-title":"Nuclear Power Engineering"},{"key":"ref_5","first-page":"10","article-title":"The risk assessment model for enterprise security (in Chinese)","volume":"10","author":"Wu","year":"2010","journal-title":"Safety & Security Technology"},{"key":"ref_6","first-page":"29","article-title":"Inquiry on the design of museum building security prevention system (in Chinese)","volume":"37","author":"Li","year":"2011","journal-title":"Shanxi Architecture"},{"key":"ref_7","unstructured":"Bennett, H.A. (1977). The EASI approach to physical security evaluation, Sandia Labs.. SAND76-0500."},{"key":"ref_8","unstructured":"Chapman, L.D., and Harlan, C.P. (1985). EASI estimate of adversary sequence interruption on an IBM PC, Sandia Labs.. SAND-85-1105."},{"key":"ref_9","unstructured":"Matter, J.C. (1988). SAVI: APC-based vulnerability assessment program, Sandia Labs.. SAND 88-1279."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Garcia, M.L. (2007). Design and Evaluation of Physical Protection Systems, Butterworth-Heinemann.","DOI":"10.1016\/B978-0-08-055428-0.50005-1"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1109\/62.756078","article-title":"Physical protection systems\u2014Cost and performance analysis: A case study","volume":"14","author":"Hicks","year":"1999","journal-title":"IEEE Aero. Electron. Syst. Mag."},{"key":"ref_12","unstructured":"Fischer, R.J., and Green, G. (2004). Introduction to Security, Elsevier. [7th ed.]."},{"key":"ref_13","unstructured":"Shen, N. (2003). Design and development of physical protection system. [Master Thesis, China Institute of Atomic Energy]."},{"key":"ref_14","unstructured":"Cummings, M.C., Mcgarvey, D.C., and Vinch, P.M. (2006). Homeland security risk assessment. Volume II. Methods, techniques, and tools, Homeland Security Institute. RP05-024-01a."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1111\/j.1539-6924.2007.00910.x","article-title":"Modeling values for anti-terrorism analysis","volume":"27","author":"Keeney","year":"2007","journal-title":"Risk Anal."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Nikoofal, M., and Zhuang, J. (2011). Robust allocation of a defensive budget considering an attacker\u2019s private information. Risk Anal.","DOI":"10.1111\/j.1539-6924.2011.01702.x"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1111\/j.1539-6924.2010.01531.x","article-title":"Modeling arbitrary layers of continuous level defenses in facing with a strategic attacker","volume":"31","author":"Golalikhani","year":"2011","journal-title":"Risk Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1287\/opre.1070.0434","article-title":"Balancing terrorism and natural disasters\u2014Defensive strategy with endogenous attack effort","volume":"55","author":"Zhuang","year":"2007","journal-title":"Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.ejor.2009.07.028","article-title":"Modeling secrecy and deception in a multiple-period attacker-defender signaling game","volume":"203","author":"Zhuang","year":"2010","journal-title":"Eur. J. Oper. Res."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hausken, K., and Zhuang, J. (2011). The timing and deterrence of terrorist attacks due to exogenous dynamics. Eur. J. Oper. Res.","DOI":"10.1057\/jors.2011.79"},{"key":"ref_21","unstructured":"Hao, M., Jin, S., and Zhuang, J. (June, January 30). Robustness of optimal defensive resource allocations in the face of less than fully rational attackers. Proceedings of the 2009 Industrial Engineering Research Conference, Miami, FL, USA."},{"key":"ref_22","unstructured":"Fisscher, R.J., and Green, G. (2004). Introduction to Security, Elsevier. [7th ed.]."},{"key":"ref_23","unstructured":"Clausius, R. (1986). The Mechanical Theory of Heat\u2014With Its Applications to the Steam Engine and to Physical Properties of Bodies, John van Voorst."},{"key":"ref_24","unstructured":"Sandler, S.I. (1999). Chemical and Engineering Thermodynamics, Wiley. [3rd ed.]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1080\/07474930801959685","article-title":"Information theoretic and entropy methods: An overview","volume":"27","author":"Golan","year":"2008","journal-title":"Economet. Rev."},{"key":"ref_27","unstructured":"Davies, S.J., and Minion, R.R. (2008). Security Supervision: Theory and Practice of Asset Protection, Butterworth-Heinemann. [3rd ed.]."},{"key":"ref_28","unstructured":"Rico, G., and Beasley, J.S. Physical protection systems: Concepts, analysis, and practice in the ET classroom. Available online: http:\/\/spacegrant.nmsu.edu\/NMSU\/2006\/rico.pdf."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/3\/571\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:49:23Z","timestamp":1760219363000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/3\/571"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,14]]},"references-count":28,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2012,3]]}},"alternative-id":["e14030571"],"URL":"https:\/\/doi.org\/10.3390\/e14030571","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,14]]}}}