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Title: Modified weibull distributions in reliability engineering
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.
Appears in Collections:Ph.D Theses (Open)

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