Among many dimensional and dimensionless amplitude parameters, kurtosis (4th normalized moment of probability density function) is recognized to be a sensitive good parameter for machine diagnosis. In this paper, one sided affiliated impact vibration is approximated by half triangle and a simplified calculation method is introduced. Various models are examined for this model and it is shown that simplified calculation method of 6-th normalized moment is much more sensitive than those of kurtosis. For the further detection, the concept of an absolute deterioration factor of n -th order moment in a broad sense is introduced and the analysis is executed. From the result of comparison, an absolute deterioration factor of 6-th order moment in a broad sense is better than other factors in the n viewpoint of sensitivity and practical use. Thus, n-th order moment in a broad sense was examined and evaluated, and we have obtained practical good results.