1 Citation (Scopus)

Abstract

When a multivariate control chart raises an out-of-control signal, several diagnostic questions arise. When did the change occur? Which components or quality characteristics changed? For those components for which the mean shifted, what are the new values for the mean? While methods exist for addressing these questions individually, we present a Bayesian approach that addresses all three questions in a single model. We employ Markov chain Monte Carlo (MCMC) methods in a Bayesian analysis that can be used in a unified approach to the diagnostics questions for multivariate charts. We demonstrate how a reversible jump Markov chain Monte Carlo (RJMCMC) approach can be used to infer (1) the change point, (2) the change model (i.e., which components changed), and (3) post-change estimates of the mean.

Original languageEnglish (US)
Pages (from-to)303-325
Number of pages23
JournalJournal of Quality Technology
Volume48
Issue number4
StatePublished - Oct 1 2016

Fingerprint

Markov processes
Monte Carlo methods
Control charts
Multivariate control charts
Diagnostics
Bayesian approach
Markov chain Monte Carlo methods
Jump
Markov chain Monte Carlo
Bayesian analysis
Quality characteristics
Charts
Change point

Keywords

  • Markov Chain Monte Carlo
  • Multivariate control chart
  • Posterior distribution
  • Transdimensional

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

Cite this

A Bayesian approach to diagnostics for multivariate control charts. / Steward, Robert M.; Rigdon, Steven E.; Pan, Rong.

In: Journal of Quality Technology, Vol. 48, No. 4, 01.10.2016, p. 303-325.

Research output: Contribution to journalArticle

Steward, Robert M. ; Rigdon, Steven E. ; Pan, Rong. / A Bayesian approach to diagnostics for multivariate control charts. In: Journal of Quality Technology. 2016 ; Vol. 48, No. 4. pp. 303-325.
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