Application of Mixture Models for Analyzing Reliability Data: A Case Study

Sabba Ruhi

Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh.

DOI: 10.4236/oalib.1101815                

Abstract

Whenever purchasing durable goods, customers expect it to perform properly at least for a reasonable period of time. Over the last 30 years there has been a heightened interest in improving quality, productivity and reliability of manufactured products. As discussed by Murthy, Xie and Jiang, [1] analyzed “Aircraft windshield failure data” and fitted 2-fold Weibull mixture model for this data set. They estimated the model parameters from WPP plot. In this study, a set of competitive 2-fold mixture models (including Weibull, Exponential, Normal, Lognormal, Smallest extreme value distribution) are applied to find out the suitable statistical models. The data consist of both failure and censored lifetimes of the windshield. In the existing literature, there are many uses of mixture models for the complete data, but very limited literature available about it uses for the censored data case. Maximum likelihood estimation method is used to estimate the model parameters and the Akaike Information Criterion (AIC), Anderson-Darling (AD) and Adjusted Anderson Darling (AD*) test statistics are applied to select the suitable models among a set of competitive models. Various characteristics of the mixture models, such as the cumulative distribution function, reliability function, mean time to failure, B10 life, etc. are estimated to assess the reliability of the component.

Keywords

Case Study, Data Analysis, EM Algorithm, Mixture Model, Reliability

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Murthy, D.N.P., Xie, M. and Jiang, R. (2004) Weibull Models. John Wiley & Sons, New York.
[2]	Karim, M.R. and Suzuki, K. (2005) Analysis of Warranty Claim Data: A Literature Review. International Journal of Quality & Reliability Management, 22, 667-686. http://dx.doi.org/10.1108/02656710510610820
[3]	Karim, M.R., Yamamoto, W. and Suzuki, K. (2001) Statistical Analysis of Marginal Count Failure Data. Lifetime Data Analysis, 7, 173-186. http://dx.doi.org/10.1023/A:1011300907152
[4]	Meeker, W.Q. and Escobar, L.A. (1998) Statistical Methods for Reliability Data. Wiley, New York.
[5]	Murthy, D.N.P. and Djamaludin, I. (2002) New Product Warranty: A Literature Review. International Journal of Production Economics, 79, 231-260. http://dx.doi.org/10.1016/S0925-5273(02)00153-6
[6]	Suzuki, K. (1985a) Non-Parametric Estimation of Lifetime Distribution from a Record of Failures and Follow-Ups. Journal of the American Statistical Association, 80, \68-72.
[7]	Suzuki, K., Karim, M.R. and Wang, L. (2001) Statistical Analysis of Reliability Warranty Data. In: Balakrishnan, N. and Rao, C.R., Eds., Handbook of Statistics: Advances in Reliability, Vol. 20, Elsevier Science, 585-609. http://dx.doi.org/10.1016/s0169-7161(01)20023-6
[8]	Blischke, W.R. and Murthy, D.N.P. (2000) Reliability. Wiley, New York, 18-19. http://dx.doi.org/10.1002/9781118150481
[9]	Kalbfleisch, J.D. and Prentice, R.L. (1980) The Statistical Analysis of Failure Time Data. John Wiley & Sons Inc., New York.
[10]	Lawless, J.F. (2003) Statistical Methods for Lifetime Data. Wiley, New York.
[11]	Lawless, J.F. (1998) Statistical Analysis of Product Warranty Data. International Statistical Review, 66, 41-60. http://dx.doi.org/10.1111/j.1751-5823.1998.tb00405.x