Probability Plotting with Independent Competing Risks
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In this chapter, we discuss probability plotting for competing risk data in the presence of Type I or right censoring. The construction of probability plots is based on the linearization of the cumulative distribution function of the first-order statistic. We consider the case when risks are independent. We describe procedures for constructing pointwise confidence intervals based on large-sample properties of maximum likelihood estimators. The proposed method is compared with traditional probability plotting that assumes that causes of failure can be eliminated.
- Boag, J.W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of Royal Statistical Society, Series B, 11, 15–53.
- Cox, D.R. (1959). The analysis of exponentially distributed lifetimes with two types of failures. Journal of the Royal Statistical Society, Series B, 21, 411–421.
- Craiu, R.V. and Lee, T.C.M. (2005). Model selection for the competing-risks model with and without masking. Technometrics, 47, 457–467. CrossRef
- Crowder, M.J., Kimber, A.C., Smith, R.L., and Sweeting, T.J. (1991). Statistical Analysis of Reliability Data. Chapman and Hall, New York.
- David, H.A. and Moeschberger, M.L. (1978). The Theory of Competing Risks. Macmillan Publishing Co., Inc., New York.
- Herman, R.J. and Pattel, R.K.N. (1971). Maximum likelihood estimation for multi-risk model. Technometrics, 13, 385–396. CrossRef
- Ishioka, T. and Nonaka, Y. (1991). Maximum likelihood estimation of Weibull parameters for two independent competing risks. IEEE Transactions on Reliability, 40, 71–74. CrossRef
- Jiang, R. and Murthy, D.N.P. (2003). Study of n-fold Weibull competing risk model. Mathematical and Computer Modelling, 38, 1259–1273. CrossRef
- Kaplan, E.L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457–481. CrossRef
- Kim, C.M. and Bai, D.S. (2002). Analyses of accelerated life test data under two failure modes. International Journal of Reliability, Quality and Safety Engineering, 9, 111–126. CrossRef
- Meeker, W.Q. and Escobar, L.A. (1998). Statistical Methods for Reliability Data. John Wiley & Sons, New York.
- Meeker, W.Q. and Escobar, L.A. (2008). Splida Splus life data analysis. http://www.public.iastate.edu/~splida
- Michael, J.R. (1983). The stabilized probability plot. Biometrika, 70, 11–17. CrossRef
- Moeschberger, M.L. and David, H.A. (1971). Life tests under competing causes of failure and the theory of competing risks. Biometrics, 27, 909–933. CrossRef
- Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans, and Data Analyses. John Wiley & Sons, New York.
- O’Connor, P.D.T. (1995). Practical Reliability Engineering. John Wiley &; Sons, New York.
- Pascual, F.G. (2007). Accelerated life test planning with independent Weibull competing risks with known shape parameter. IEEE Transactions on Reliability, 56, 85–93. CrossRef
- Pascual, F.G. (2008). Errata to accelerated life test planning with independent Weibull competing risks with known shape parameter. IEEE Transactions on Reliability, 57, 531–532. CrossRef
- Pascual, F.G. (2008). Accelerated life test planning with independent Weibull competing risks. IEEE Transactions on Reliability, 57, 435–444. CrossRef
- Pascual, F.G. (2009). Accelerated life test planning with independent lognormal competing risks. Under review.
- Probability Plotting with Independent Competing Risks
- Book Title
- Advances in Degradation Modeling
- Book Subtitle
- Applications to Reliability, Survival Analysis, and Finance
- pp 397-414
- Print ISBN
- Online ISBN
- Series Title
- Statistics for Industry and Technology
- Birkhäuser Boston
- Copyright Holder
- Birkhäuser Boston
- Additional Links
- Competing riskscompeting risks
- maximum likelihood estimationmaximum likelihood estimation
- probability plottingprobability plotting
- right censoringright censoring
- Industry Sectors
- eBook Packages
- Editor Affiliations
- ID1. Université Victor Segalen Bordeaux 2, I’lnstitut de Mathématiques de Bordeaux
- ID2. Département Génie Informatique, Labo. Mathématiques Appliquées Compiègne, Université de Technologie de Compiègne
- ID3. McMaster University, Department of Mathematics and Statistics
- ID4. Fak. Mathematik, Inst. Mathematische Stochastik, Otto-von-Guericke-Universität
- ID5. Laboratoire de Statistique Medicale, Université René Descartes, Paris 5
- Author Affiliations
- 1. Department of Statistics, Washington State University, Pullman, WA, USA
- 2. Axio Research Acquisition Co. LLC, Seattle, WA, USA
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