Grey theory initiated by Deng (1982) is a mathematical branch dealing with systemdynamics having sparse data availability. Grey reliability analysis is thus advantageous because of the small sample size requirements, for example, the first-order one-variable grey differential equation only needs as little as four data points. However, the grey estimation of state dynamic law uses least-square approach, i.e., parameter estimation under L_(2) norm. Problems associated with L_(2) norm grey estimation are the model accuracy specifications. The L_(2) norm grey modeling campus often borrows the model fitting criteria from statistical linear model analysis, for example, using mean-sum-of squared errors as model fitting criterion and even using probability bound for it. These exercises are putting themselves in controversy. In numerical analysis and approximation theory, relative error is a standard approximation criterion although the L_(2) norm grey modeling campus also uses relative error as model accuracy measure. In this paper, we propose a L_(1) norm based grey modeling and search the grey parameters in terms of simplex technique in linear programming. We will discuss briefly the grey reliability analysis under L_(1) norm based grey state dynamics.
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