Akaike Information Criterion-Based Reliability Analysis for Discrete Bimodal Information

The distribution of a response usually depends on the distribution of the variables. When a variable shows a distribution with two different modes, the response also shows a distribution with two different modes. In this case, recently developed methods for reliability analysis assume that the distribution functions are continuous with a mode. In actual problems, however, because information is often provided in a discrete form with two or more modes, it is important to estimate the distributions for such information. In this study, we employ the finite mixture model to estimate the response distribution with two different modes, and we select the best candidate distribution through AIC. Mathematical examples are illustrated to verify the proposed method.

[1]  Dong-Ho Lee,et al.  Reliability based optimal design of a helicopter considering annual variation of atmospheric temperature , 2011 .

[2]  James E. Hines,et al.  Estimating Annual Survival and Movement Rates of Adults within a Metapopulation of Roseate Terns , 1995 .

[3]  Min Cheol Lee,et al.  Fuzzy-sliding mode control of a polishing robot based on genetic algorithm , 2001 .

[4]  Clifford M. Hurvich,et al.  Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion , 1998 .

[5]  Byung Man Kwak,et al.  Efficient statistical tolerance analysis for general distributions using three-point information , 2002 .

[6]  Byung Man Kwak,et al.  Response surface augmented moment method for efficient reliability analysis , 2006 .

[7]  W. Pan.  Akaike's Information Criterion in Generalized Estimating Equations , 2001, Biometrics.

[8]  Tae Hee Lee,et al.  Reliability-Based Design Optimization Using Akaike Information Criterion for Discrete Information , 2012 .

[9]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[10]  Jong-Su Choi,et al.  Probability distribution for the shear strength of seafloor sediment in the KR5 area for the development of manganese nodule miner , 2011 .

[11]  S. Rahman,et al.  A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics , 2004 .

[12]  Gongkang Fu,et al.  Multimodal simulation method for system reliability analysis , 1993 .

[13]  Gang Li,et al.  A combined reliability analysis approach with dimension reduction method and maximum entropy method , 2011 .

[14]  C A Cornell,et al.  A PROBABILITY BASED STRUCTURAL CODE , 1969 .

[15]  K. Breitung.  Asymptotic approximations for multinormal integrals , 1984 .

[16]  Leonardo Barbosa Godefroid,et al.  Statistical modeling of fatigue crack growth rate in Inconel alloy 600 , 2007 .