In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal random variables. We approximate a discrete time problem with a continuous time problem allowing us to apply established theory for stationary Gaussian processes. By then subsequently correcting approximations for discrete time, we show that the developed approximations are very accurate even for a small window length. Also, they have high accuracy when the original r.v. are not exactly normal and when the weights in the moving window are not all equal. We then provide accurate and simple approximations for ARL, the average run length until crossing the boundary.

在本文中，我们研究iid正态随机变量的移动和的边界穿越概率的近似值。我们用连续时间问题来近似离散时间问题，从而使我们能够将建立的理论应用于平稳的高斯过程。然后，通过随后校正离散时间的近似值，我们表明即使对于较小的窗口长度，所开发的近似值也非常准确。此外，当原始rv并非完全正常且移动窗口中的权重也不相等时，它们具有很高的精度。然后，我们提供ARL的准确而简单的近似值，即到达边界之前的平均行程长度。