Open Access Open Access  Restricted Access Subscription or Fee Access

Weibull Mixture Model for Reliability Analysis

H. Benaicha(1*), A. Chaker(2)

(1) Laboratory SCAMRE -ENSET, Oran, Algeria
(2) Laboratory SCAMRE -ENSET, Oran, Algeria
(*) Corresponding author


DOI: https://doi.org/10.15866/iree.v9i5.4021

Abstract


In reliability analysis, electrical systems can have more than one failure mode .For example, systems may have been used in different operating environments or there could be differences in design and /or material. In these cases, failure time data of systems would not fall on a straight line on a Weibull probability paper. Consequently, the finite mixed Weibull can be used to analyze this data .In this paper, we propose a maximum likelihood algorithm for mixture of two Weibull distributions. The mixture distribution and the traditional Weibull distribution are applied to historical failure time data of power transformers of National Society for Electricity and Gas (SONELGAZ) in Western Algeria. A comparison of the reliability analysis through respective probability distributions is presented in this study. Finally, Akaike information criterion (AIC) is used to select a best distribution for modeling this data.
Copyright © 2014 Praise Worthy Prize - All rights reserved.

Keywords


Weibull Model; Mixture Weibull Distribution; Parameters Estimation; Maximum Likelihood Algorithm; Reliability Analysis; AIC

Full Text:

PDF


References


K.S. Sultan, M.A. Ismail, A.S. Al-Moisheer, Mixture of two inverse Weibull distributions, Properties and estimation, Computational Statistics & Data Analysis, vol. 51 n. 11, July 2007, pp. 5377–5387.
http://dx.doi.org/10.1016/j.csda.2006.09.016

J.F. Lawless, Statistical Models and Methods for Lifetime Data, (John Wiley & Sons, Inc.,2002).
http://dx.doi.org/10.1002/9781118033005

S.K. Sinha, Reliability and Life Testing (Wiley Eastern Limited, New Delhi,1986)
http://dx.doi.org/10.1002/qre.4680030314

R. Jiang, DNP. Murthy, Modeling failure data by mixtures of 2-Weibull distributions: a graphical approach, IEEE Transactions on Reliability, vol. 44 n.3, September 1995, pp. 477–87.
http://dx.doi.org/10.1109/24.406588

R. Jiang, DNP. Murthy, P. Ji, Models involving two inverse Weibull distributions, Reliability Engineering & System Safety, vol. 73 n. 1, July 2001, pp. 73–81.
http://dx.doi.org/10.1016/s0951-8320(01)00030-8

D.B. Kececioglu, W. Wendai, Parameter estimation for mixed- Weibull distribution. In: Proc. of the Annual Symposium on Reliability and Maintainability, 1998, pp. 247–252 .
http://dx.doi.org/10.1109/rams.1998.653782

EK. Al-Hussaini , GR. Al-Dayian, SA. Adham, On finite mixture of two component Gompertz lifetime model, Journal of Statistical Computation and Simulation, vol. 67 n.1, January 2000,pp.61–20.
http://dx.doi.org/10.1080/00949650008812033

F. Louzada-Neto, J. Mazucheli, JA. Achcar, Mixture hazard models for lifetime data, Biomet J, vol. 44, January 2002,pp. 3–14.
http://dx.doi.org/10.1002/1521-4036(200201)44:1%3C3::aid-bimj3%3E3.0.co;2-d

PH. Kvam, A parametric mixture-model for common-cause failure data, IEEE Transactions on Reliability, vol. 47 n. 1,March 1998, pp. 30–34.
http://dx.doi.org/10.1109/24.690894

S.K. Sinha, Bayesian estimation of the parameters and reliability function of a mixture of Weibull life distributions, Journal of Statistical Planning and Inference, vol. 16 n. 3,1987,pp. 377–387.
http://dx.doi.org/10.1016/0378-3758(87)90090-5

K.-W.Chen, A.S. Papadopoulos, P. Tamer, On Bayes estimation for mixtures of two Weibull distributions under type I censoring, Microelectronics and Reliability, vol. 29 n.4 , November1989, pp. 609– 617.
http://dx.doi.org/10.1016/0026-2714(89)90351-x

C.M. Tan, N. Raghavan, An approach to statistical analysis of gate oxide breakdown mechanisms, Microelectronics Reliability, vol. 47 n. 9 , July 2007, pp. 1336–1342.
http://dx.doi.org/10.1016/j.microrel.2007.07.011

k. Athanasios, Nonparametric Bayesian survival analysis using mixtures of Weibull distributions, Journal of Statistical Planning and Inference, vol.136 n. 3,March 2006, pp. 578–596.
http://dx.doi.org/10.1016/j.jspi.2004.08.009

JA. Al-Saleh, SK. Agarwal ,Extended Weibull type distribution and finite mixture of distributions, Statistical Methodology, vol. 3 n. 3, July 2006, pp. 224–233.
http://dx.doi.org/10.1016/j.stamet.2005.09.010

DNP. Murthy, M. Xie, R. Jiang , Weibull Models, (John Wiley and Sons, Hoboken, New Jersey, 2004).

A. Mahir Razali and A. Salih, Combining Two Weibull Distributions Using a Mixing Parameter, European Journal of Scientific Research, vol. 31 n. 2, 2009, pp.296–305.

R. Jiang, M.J. Zuo, H.X. Li, Weibull and inverse Weibull mixture models allowing negative weights, Reliability Engineering & System Safety, vol. 66 n. 3 , December1999, pp. 227 – 234.
http://dx.doi.org/10.1016/s0951-8320(99)00037-x

D. Cousineau, Fitting the three-parameter weibull distribution: review and evaluation of existing and new methods, Dielectrics and Electrical Insulation, IEEE Transactions on, vol. 16 n. 1, August 2009, pp. 281 – 288.
http://dx.doi.org/10.1109/tdei.2009.4784578

P. Norman, A. Archer, computational technique for maximum likelihood estimation with weibull models , IEEE Transactions on Reliability, vol. 29 n. 1, April1980 , pp. 57-62.
http://dx.doi.org/10.1109/tr.1980.5220713

S.Y. Jiang, D. Kececioglu, Maximum Likelihood Estimation from Censored-Data Mixed Weibull Distribution, IEEE Transactions on Reliability, vol. 41 n. 2, Jun 1992, pp. 248 – 255.
http://dx.doi.org/10.1109/24.257791

M.R. Herving & al, Newton-Raphson algorithm for load-flow calculation in transmission and distribution networks, Generation, Transmission and Distribution, IEE Proceedings,
http://dx.doi.org/10.1049/ip-c.1987.0053

vol. 134 n. 5, Semptember1987, pp.325-330.

S. Rosilene & al, Comparison between ordinary least squares regression and weighted least squares regression in the calibration of metals present in human milk determined by ICP-OES, Talanta, vol. 80 n. 3 , January 2010 , pp. 1102–1109.
http://dx.doi.org/10.1016/j.talanta.2009.08.043

Sonelgaz reference, Laboratory SCAMRE- ENSET, Oran, Algeria.

H. Akaike, A new look at the statistical model identification. IEEE Transactions. Automatic. Control, vol. 19 n. 6 , December 1974 , pp. 716–723.
http://dx.doi.org/10.1109/tac.1974.1100705

T. Bucar & al, Reliability approximation using finite Weibull mixture distributions, Reliability Engineering and System Safety, vol. 84 n. 3, November 2004, pp. 241 – 251.
http://dx.doi.org/10.1016/j.ress.2003.11.008

Mosayebian, M.E., Monsef, H., Reliability evaluation in power system integrated with wind power, (2010) International Review on Modelling and Simulations (IREMOS), 3 (3), pp. 368-372.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2022 Praise Worthy Prize