The problems of sequential change-point have several important applications in quality control, signal processing, and failure detection in industry and finance. We discuss a Bayesian approach in the context of statistical process control: at an unknown time $tau$, 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 with some unknown parameters θ_{1}≠θ_{2}. 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 the use of the Shiryaev's loss function. Under this assumption, we define a Bayesian stopping rule. For the Poisson distribution and in the two cases (i) and (ii), we obtain results for the conjugate prior.

Type of Study: Original Paper |
Subject:
62Jxx: Linear inference, regression

Received: 2016/09/15 | Accepted: 2016/09/15 | Published: 2016/09/15

Received: 2016/09/15 | Accepted: 2016/09/15 | Published: 2016/09/15