A method for computing the joint failure probability of a parallel system consisting of two linear limit state equations is given to indirectly obtain the value of the integral of the standard bivariate normal distribution by using the conclusion that the joint failure probability of the parallel system is equal to the value of the double integral. In the two-dimensional standard normal coordinate system, some circles whose centres are all at the coordinate origin are used to divide the two-dimensional standard sample space into a number of pairwise disjoint sub-sample spaces and obtain a number of pairwise disjoint sub-failure domains. According to the probability theory, the probability of any sub-failure domain can be expressed by using a sub-sample space probability and a conditional probability. Based on the total probability formula, the joint failure probability can be obtained by the sum of the probabilities of the sub-failure domains because the sub-sample spaces or the sub-failure domains are pairwise disjoint. By introducing a random variable obeying the Rayleigh distribution, it is possible to compute probabilities of the sub-sample spaces accurately. The formulae of computing the conditional probability are derived. The main parameters related to the computation of the joint failure probability, such as the minimum and maximum radii, and the number of the dividing circles, are discussed to make the computation process easy and the computed result meet a required precision. Examples show that it is possible and significant for the method in the paper to complete the computation of the standard bivariate normal distribution integral with high accuracy.

给出了一种计算由两个线性极限状态方程组成的并联系统的联合失效概率的方法，利用并联系统的联合失效概率相等的结论，间接获得标准二元正态分布的积分值。为二重积分的值。在二维标准法线坐标系中，利用一些圆心都在坐标原点的圆，将二维标准样本空间划分为若干成对不相交的子样本空间，得到若干成对不相交的子样本空间。故障域。根据概率论，任何子失效域的概率都可以用子样本空间概率和条件概率来表示。根据全概率公式，由于子样本空间或子失效域是成对不相交的，因此联合失效概率可以通过子失效域的概率之和获得。通过引入服从瑞利分布的随机变量，可以准确计算子样本空间的概率。推导出条件概率的计算公式。讨论了与关节失效概率计算相关的主要参数，如最小和最大半径、分割圆的个数，使计算过程简单，计算结果满足要求的精度。实例表明，本文提出的方法能够高精度地完成标准二元正态分布积分的计算是可能的，也是有意义的。