ENBIS-18 in Nancy

2 – 25 September 2018; Ecoles des Mines, Nancy (France) Abstract submission: 20 December 2017 – 4 June 2018

A Bayesian Self-Starting Shiryaev Statistic for Phase I Data

4 September 2018, 10:10 – 10:30

Abstract

Submitted by
Panagiotis Tsiamyrtzis
Authors
Panagiotis Tsiamyrtzis (Athens University of Economics and Business), Konstantinos Bourazas (Athens University of Economics and Business)
Abstract
In Statistical Process Control & Monitoring (SPC&M), our interest is in detecting when a process deteriorates from its “in control” state, typically established during a phase I exercise. Thus the phase I data play a very crucial role, as it is assumed to be a random sample from the in control distribution and are used to calibrate a control chart that will evaluate the process in phase II.

In this work, we focus our attention on detecting persistent shifts in the parameters of interest under at most one change (AMOC) scenarios during phase I, where low volume data are available. We propose a Bayesian scheme, which is based on the cumulative posterior probability that a step change has already occurred. The proposed methodology is a generalization of Shiryaev’s methodology, as it allows both the parameters and shift magnitude to be unknown. Furthermore, the Shiryaev’s assumption that the prior probability on the location of the change point is constant will be relaxed. Posterior inference for the unknown parameters and the location of a (potential) change point will be provided.

A real data set will illustrate the Bayesian self-starting Shiryaev’s scheme, while a simulation study will evaluate its performance against standard competitors in the case of Normal data.

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