Title
Mixture Model of the Power Law

Authors
H. Hirose

Source
IEEE Transactions on Reliability, Vol.46, No.1, pp.146-153 (1997.3)

Abstract
This paper deals with a new degradation model, a power-law mixture-model which extends the power law in accelerated life testing, Some types of insulation deteriorate at a rate determined by the stress. If the stresses are classified into distinct groups, a total degradation model could be a mixture of several degradation models, If the breakdown voltage (V-B) has a certain failure probability distribution and the degradation follows a power law, then a mixture model of the power law can be constructed. The cluster analysis is done by maximum likelihood estimation. For instance, by using the intermittently-inspected V-B test-data of electrical insulation removed from active power-lines, the remaining life of the insulation can be assessed based on this mixture model. Application of the model to the V-B data of cross-linked polyethylene-insulated cables is demonstrated: the breakdown data are classified into groups using the Akaike Information Criterion and the generalized likelihood ratio test method. The remaining life of the insulation can be estimated with approximate standard deviation.

Key Words
mixture, power law, Weibull power law, lifetime, threshold, maximum likelihood estimation, Akaike information criterion, generalized likelihood-ratio test, intermittent inspection, WEIBULL-DISTRIBUTIONS, MAXIMUM-LIKELIHOOD, PARAMETERS

Citation

 

Times Cited in Web of Science: 7

Times Cited in Scopus: 4

Times Cited in Google Scholar: 13

Inspec: 1

Cited in Books: Vilijandas Bagdonavicius, Mikhail Nikulin, Accelerated Life Models: Modeling and Statistical Analysis, Chapman & Hall/CRC (2001)

Cited in Proceedings: W. Y. Yun, J. W. Kim, "Estimating the Parameters of the Mixture of Proportinal Hazards Models with Three Types of Data", 2002年信頼性・品質3学会合同シンポジウム, 7-4, 107-112, (2002.11.15) 中央電気倶楽部

WoS: 2012 ASIA-PACIFIC POWER AND ENERGY ENGINEERING CONFERENCE (APPEEC) シリーズタイトル: Asia-Pacific Power and Energy Engineering Conference 発行: 2012; IIE TRANSACTIONS 巻: 43 号: 11 ページ: 783-796 DOI: 10.1080/0740817X.2011.590436 発行: 2011; 2009 IEEE INSTRUMENTATION & MEASUREMENT TECHNOLOGY CONFERENCE, VOLS 1-3 巻: 号: ページ: 1144 発行: 2009; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 14 (5): 1255-1263 OCT 2007; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 13 (1): 146-159 FEB 2006; JOURNAL OF APPLIED STATISTICS 33 (1): 17-34 JAN 2006; IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES E86A (5): 1256-1265 MAY 2003