Reliability calculation of a system is frequently required in industrial, military, and everyday life situations. For such a calculation, it is necessary to specify the configuration of components and subsystems, the failure mode of each component, and the states in which the system is classified as failed. In this paper, we are primary interested in the time to the first failure of a system. And we discuss failure probability of coherent system under various condition, especially focus on probability calculation of subsystem failure before system failure used by Bayes formula. Problem statement and general applications illustrated by several examples.

The calculation of earthwork plays a major role in plan or design of many civil engineering projects, and thus it has become very important to advanced the accuracy of earthwork calculation. Current method used for estimating the volume of pit excavation assumes that the ground profile between the grid points is linear(trapezoidal rule), or nonlinear(simpson's formulas). In this paper the spot height method, least square method, and chamber formulas, Chen and Lin method are compared with the volumes of the pits in these examples. As a result of this study, algorithm of chen and Lin me쇙 by spline method should provide a better accuracy than the spot height method, least square method, chamber formulas. The Chen and Lin formulas can be used for estimating the excavation volume of a pit divide into a grid with unequal intervals. From the characteristics of the cubic spline polynomial, the modeling curve of the Chen and Lin method is smooth and matches the ground profile well. Generally speaking, the nonlinear profile formulas provide better accuracy than the linear profile formulas. The mathematical model mentioned make an offer maximum accuracy in estimating the volume of a pit excavation.