Chin-Diew Lai

Bio: Chin-Diew Lai is an academic researcher from Massey University. The author has contributed to research in topics: Weibull distribution & Reliability (statistics). The author has an hindex of 28, co-authored 96 publications receiving 4138 citations. Previous affiliations of Chin-Diew Lai include University of Auckland.

Continuous Bivariate Distributions

Abstract: Univariate distributions. - Bivariate copulas. - Distributions expressed as copulas. - Concepts of stochastic dependence. - Measures of dependence. - Constructions of bivariate distributions.- Bivariate distributions constructed by conditional approach. - Variables in common method. - Bivariate gamma and related distributions. - Simple forms of the bivariate density function. - Bivariate exponentional and related distributions. - Bivariate normal distribution. - Bivariate extreme value distributions. - Elliptically symmetric bivariate distributions and other symmetric distributions. - Simulation of bivariate observations.

A modified Weibull distribution

Abstract: A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Stochastic Ageing and Dependence for Reliability

Abstract: This book provides a panoramic view of theory and applications of Ageing and Dependence in the use of mathematical methods in reliability and survival analysis. Ageing and dependence are important characteristics in reliability and survival analysis. They affect decisions with regard to maintenance, repair/replacement, price setting, warranties, medical studies, and other areas. Most of the works containing the topics covered here are theoretical in nature. However, this book offers applications, exercises, and examples. It serves as a reference for professors and researchers involved in reliability and survival analysis.

Reliability Engineering and System Safety

Abstract: This paper presents a polynomial dimensional decomposition (PDD) method for global sensitivity analysis of stochastic systems subject to independent random input following arbitrary probability distributions. The method involves Fourier-polynomial expansions of lower-variate component functions of a stochastic response by measure-consistent orthonormal polynomial bases, analytical formulae for calculating the global sensitivity indices in terms of the expansion coefficients, and dimension-reduction integration for estimating the expansion coefficients. Due to identical dimensional structures of PDD and analysis-of-variance decomposition, the proposed method facilitates simple and direct calculation of the global sensitivity indices. Numerical results of the global sensitivity indices computed for smooth systems reveal significantly higher convergence rates of the PDD approximation than those from existing methods, including polynomial chaos expansion, random balance design, state-dependent parameter, improved Sobol’s method, and sampling-based methods. However, for non-smooth functions, the convergence properties of the PDD solution deteriorate to a great extent, warranting further improvements. The computational complexity of the PDD method is polynomial, as opposed to exponential, thereby alleviating the curse of dimensionality to some extent. Mathematical modeling of complex systems often requires sensitivity analysis to determine how an output variable of interest is influenced by individual or subsets of input variables. A traditional local sensitivity analysis entails gradients or derivatives, often invoked in design optimization, describing changes in the model response due to the local variation of input. Depending on the model output, obtaining gradients or derivatives, if they exist, can be simple or difficult. In contrast, a global sensitivity analysis (GSA), increasingly becoming mainstream, characterizes how the global variation of input, due to its uncertainty, impacts the overall uncertain behavior of the model. In other words, GSA constitutes the study of how the output uncertainty from a mathematical model is divvied up, qualitatively or quantitatively, to distinct sources of input variation in the model [1].

Handbook of software reliability engineering

Abstract: Technical foundations introduction software reliability and system reliability the operational profile software reliability modelling survey model evaluation and recalibration techniques practices and experiences best current practice of SRE software reliability measurement experience measurement-based analysis of software reliability software fault and failure classification techniques trend analysis in validation and maintenance software reliability and field data analysis software reliability process assessment emerging techniques software reliability prediction metrics software reliability and testing fault-tolerant SRE software reliability using fault trees software reliability process simulation neural networks and software reliability. Appendices: software reliability tools software failure data set repository.