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Title: | Modified weibull distributions in reliability engineering | Authors: | JIANG HONG | Keywords: | Modified Weibull, Reliability, Lifetime Data, Maximum Likelihood Estimation, Markov chain Monte Carlo, Burn-in | Issue Date: | 4-Aug-2009 | Citation: | JIANG HONG (2009-08-04). Modified weibull distributions in reliability engineering. ScholarBank@NUS Repository. | Abstract: | This thesis concerns the modeling of the Weibull family to lifetime data, studies the statistical properties of the distributions, and considers the parameter estimation based on a complete or censored sample. Related issues such as model selection, evaluating mean residual life and burn-in time are addressed as well. In our research, the modified Weibull distribution and odd Weibull distribution are studied. As an important step in Weibull analysis, model characterization provides insight into the properties and applicability to model data of the distributions. For the distributions considered, we describe the important statistics and distribution functions, both in analytical and numerical ways. Parameter estimation is crucial for the model to be built and is often a difficult problem, especially for distributions with more than 2 parameters. In this thesis, maximum likelihood estimation is studied in detail. Several techniques regarding this estimation method are proposed to simplify computation, which help look into the existence and uniqueness properties of the estimators. Another estimation method called Markov chain Monte Carlo is used to estimate the parameters of the modified Weibull distribution and is found to outperform MLE in several aspects when the prior is independent generalized uniform and the size of sample data is small. A graphic parameter estimation method is proposed for the odd Weibull distribution. The method is especially useful when the shape parameters are negative. |
URI: | http://scholarbank.nus.edu.sg/handle/10635/17099 |
Appears in Collections: | Ph.D Theses (Open) |
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