ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Bayesian Self-Starting CUSUM

13 September 2017, 09:40 – 10:00


Submitted by
Panagiotis Tsiamyrtzis
Konstantinos Bourazas (Athens University of Economics and Business), Panagiotis Tsiamyrtzis (Athens University of Economics and Business)
In Statistical Process Control & Monitoring (SPC&M), the phase I data play a crucial role in the attempt to obtain reliable estimates of the unknown model parameters. A major concern, while in phase I, is to be able to identify (in an online fashion if possible) any persistent shift of even small size of the unknown model parameters. To confront this issue, certain self-staring frequentist methods have been proposed (like self starting CUSUM/ EWMA), which on one hand, calibrate the control chart and on the other, perform the on-line inference.

In this study, we propose a Bayesian oriented type of self-starting CUSUM, which is based on the posterior predictive distribution. The idea is to utilize available prior information, speeding up the parameter learning (calibration) compared to the traditional self-starting frequentist based methods. Prior elicitation is formalized by the use of power priors, where available historic data and/or expert’s opinion can be incorporated. The proposed methodology is general enough to cover various sampling distributions, as long as they are members of the regular exponential family (continuous or discrete). A simulation study will compare the frequentist against the Bayesian self-starting CUSUMs and a real data example will illustrate the proposed methodology.
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