Abstract
In this paper we propose an efficient algorithm based on Yang’s (Fuzzy Sets Syst 57:365–337, 1993) concept, namely the fuzzy classification maximum likelihood (FCML) algorithm, to estimate the mixed-Weibull parameters. Compared with EM and Jiang and Murthy (IEEE Trans Reliab 44:477–488, 1995) methods, the proposed FCML algorithm presents better accuracy. Thus, we recommend FCML as another acceptable method for estimating the mixed-Weibull parameters.
Similar content being viewed by others
References
Al-Saleh JA and Agarwal SK (2006). Extended Weibull type distribution and finite mixture of distributions. Stat Methodol 3: 224–233
Attardi L, Guida M and Pulcini G (2005). A mixed-Weibull regression model for the analysis of automotive warranty data. Reliab Eng Syst Safety 87: 265–273
Bezdek JC (1981). Pattern recognition with fuzzy objective function algorithm. Plenum Press, New York
Carta JA and Ramírez P (2007). Use of finite mixture distribution models in the analysis of wind energy in the Canarian Archipelago. Energy Conversion Manage 48: 281–291
Dempster AP, Laird NM and Rubin DB (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). J R Stat Soc B 39: 1–38
Elandt RC and Johnson NL (1980). Survival model and data analysis. Wiley, New York
Gong Z (2006). Estimation of mixed Weibull distribution parameters using the SCEM-UA algorithm: application and comparison with MLE in automotive reliability analysis. Reliab Eng Syst Safety 91: 915–922
Govaert G and Nadif M (2006). Fuzzy clustering to estimate the parameters of block mixture models. Soft Comput 10: 415–422
Jiang S and Kececioglu D (1992a). Graphical representation of two mixed-Weibull distributions. IEEE Trans Reliab 41: 241–247
Jiang S and Kececioglu D (1992b). Maximum likelihhod estiamtes, from censored data, for mixed-Weibull distributions. IEEE Trans Reliab 41: 248–255
Jiang R and Murthy DNP (1995). Modeling failure-data by mixture of 2 Weibull distributions: a graphical approach. IEEE Trans Reliab 44: 477–488
Kottas A (2006). Nonparametric Bayesian survival analysis using mixtures of Weibull distributions. J Stat Plan Inference 136: 578–596
Lawless JF (1982). Statistical models and methods for lifetime data. Wiley, New York
McLachlan GJ and Basford KE (1988). Mixture models: inference and application to clustering. Marcdl Dekker, New York
McLachlan GJ and Peel D (2001). Finite mixture models. Wiley, New York
Sinha SK (1986). Reliability and life testing. Wiley Eastern Limited, New Delhi
Wondmagegnehu ET, Navarro J and Hernandez PJ (2005). Bathtub shaped failure rates from mixtures: a practical point of view. IEEE Trans Reliab 54: 270–275
Yang MS (1993). On a class of fuzzy classification maximum likelihood procedures. Fuzzy Sets Syst 57: 365–337
Yang MS and Su CF (1994). On parameter estimation for normal mixtures based on fuzzy clustering algorithms. Fuzzy Sets Syst 68: 13–28
Yang MS and Yu NY (2005). Estimation of parameters in latent class model using fuzzy clustering algorithms. Eur J Oper Res 160: 515–531
Zadeh LA (1965). Fuzzy sets. Inform Control 8: 338–353
Zhang L and Liu C (2006). Fitting irregular diameter distributions of forest stands by Weibull, modified Weibull and mixture Weibull models. J For Res 11: 369–372
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hung, WL., Chang, YC. & Chuang, SC. Fuzzy classification maximum likelihood algorithms for mixed-Weibull distributions. Soft Comput 12, 1013–1018 (2008). https://doi.org/10.1007/s00500-007-0266-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-007-0266-8