Journal
TECHNOMETRICS
Volume 54, Issue 3, Pages 294-307Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/00401706.2012.694789
Keywords
Fault isolation; Gibbs sampling; Hierarchical Bayes; Interpretation of out-of-control signal; Multivariate statistical process control; Variable selection
Categories
Funding
- NSF [DMS0705261, DMS1007574, CMMI-0927574]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1007574] Funding Source: National Science Foundation
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [0927574] Funding Source: National Science Foundation
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Multivariate quality characteristics are often monitored using a single statistic or a few statistics. However, it is difficult to determine the causes of an out-of-control signal based on a few summary statistics. Therefore, if a control chart for the mean detects a change in the mean, the quality engineer needs to determine which means shifted and the directions of the shifts to facilitate identification of root causes. We propose a Bayesian approach that gives a direct answer to this question. For each mean, an indicator variable that indicates whether the mean shifted upward, shifted downward, or remained unchanged is introduced. Prior distributions for the means and indicators capture prior knowledge about mean shifts and allow for asymmetry in upward and downward shifts. The mode of the posterior distribution of the vector of indicators or the mode of the marginal posterior distribution of each indicator gives the most likely scenario for each mean. Evaluation of the posterior probabilities of all possible values of the indicators is avoided by employing Gibbs sampling. This renders the computational cost more affordable for high-dimensional problems. This article has supplementary materials online.
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