A Reliability Data Analysis Method Using Mixture Weibull Distribution Model

Abstract:

The weibull distribution plays a crucial role in reliability theory and life-testing experiments. Weibull mixtures are widely used to model lifetime and failure time data, since they exhibit a wide range of shapes for the failure rate function. In this paper, the failure data of crank rod system was analyzed by using mixture weibull distribution model. The distribution parameters of the mixture weibull distribution model were estimated by using maximum likelihood estimation and drawing method. The comparison of fitting degree of failure location between standard weibull distribution model and mixture weibull model was given. Results show that the fitting degree of the failure data in the mixture weibull distribution model is higher than that of the simple weibull distribution model, and it can more accurately described the failure distribution curve of the system in life cycle.

• Periodical: Applied Mechanics and Materials (Volumes 148-149)
• Pages: 1449-1453
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.148-149.1449
• Online since: December 2011
• Authors: Ying Kui Gu, De Liang Ge, Yao Gang Xiong
• Keywords: Maximum Likelihood-Estimation (MLE), Mixture Weibull Distribution, Reliability Data Analysis, Weibull Probability Plot

References

[1] D. Murthy, M. Bulmer, J. Eccleston. Weibull model selection for reliability modelling. Reliability Engineering and System Safety Vol. 86 (2004), pp.257-267.

DOI: 10.1016/j.ress.2004.01.014

[2] Jiang Renyan. Weibull Model Family－Characteristics, Parameter Estimation and Application (Beijing: Science Press, 1998).

[3] D. Murthy, J. A. Eccleston. Weibull model selection for reliability modelling. Reliability Engineering and System Safety Vol. 86(20043), pp.257-67.

DOI: 10.1016/j.ress.2004.01.014

[4] M. Xie, T. N. Goh, Y. Tang. On changing points of mean residual life and failure rate function for some generalized weibull distributions. Reliability Engineering and System Safety Vol. 84(2004), p . 293-299.

DOI: 10.1016/j.ress.2003.12.005

[5] S. Nadarajah. On the moments of the modified weibull distribution. Reliability Engineering and System Safety Vol. 90(2005), pp.114-117.

DOI: 10.1016/j.ress.2004.09.002

[6] H. K. T. Ng. Parameter estimation for a modified weibull distribution, for progressively type-II censored samples. IEEE Trans Reliability Vol. 54(2005), pp.374-80.

DOI: 10.1109/tr.2005.853036

[7] M. Franco, J. M. Vivo, N. Balakrishnan. Reliability properties of generalized mixtures of weibull distributions with a common shape parameter. Journal of Statistical Planning and Inference Vol. 141 (2011) 2600-2613.

DOI: 10.1016/j.jspi.2011.02.012

[8] R. Ross. Graphical methods for plotting and evaluating weibull distributed data. IEEE Trans Dielectr Electr Insul Vol. 1(1994), pp.247-53.

[9] L.F. Zhang, M. Xie, L. C. Tang. A study of two estimation approaches for parameters of weibull distribution based on WPP. Reliability Engineering and System Safety Vol. 92 (2007), pp.360-368.

DOI: 10.1016/j.ress.2006.04.008

[10] R. Y. Jiang, D. Murthy. Reliability modeling involving two weibull distributions. Reliability Engineering and System Safety Vol. 47(1995), pp.187-198.

DOI: 10.1016/0951-8320(94)00045-p

[11] D. Ling, H. Z. Huang, Y. Liu. A method for parameter estimation of mixed Weibull distribution. Annual Reliability and Maintainability Symposium (2009), pp.129-133.

DOI: 10.1109/rams.2009.4914663