The problems of sequential change-point have several important applications, including quality control, failure detection in industrial, ﬁnance and signal detection. We discuss a Bayesian approach in the context of statistical process control: at an unknown time τ, the process behavior changes and the distribution of the data changes from p0 to p1. Two cases are considered: (i) p0 and p1 are fully known, (ii) p0 and p1 belong to the same family of distributions and some θ1 , θ2 parameters are unknown. We present a maximum a posteriori estimate of the Change-point which, for the case (i) can be computed in a sequential manner. In addition, we propose to use the Shiryaev’s loss function. Under this assumption, we deﬁne a Bayesian stopping rule. For the Poisson distribution and in two cases (i) and (ii), we obtain results for the conjugate prior.