Abstract: The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly find the starting time or the change point of a process disturbance. To do this, after a control chart triggers an out-of-control signal, an order of points in time (known as a plan) should be identified such that if the process examined sequentially at them, the true change point is detected as soon as possible. A typical method is to start the examination of the process from the signal time of the control chart and proceed to neighbouring points. In this paper, we establish a Bayesian method to solve this problem, i.e. to find a plan for examining the process sequentially such that it minimizes the Bayes risk among all other possible plans. At last, our proposed Bayes method is applied to a normal process, and compared to a typical method which is usually used to find the true change point through a series of simulations.