### Abstract

For signalling alarms sooner when the dispersion of a multivariate process is "increased", a multivariate control chart for Phase II process monitoring is proposed as a supplementary tool to the usual monitoring schemes designed for detecting general changes in the covariance matrix. The proposed chart is constructed based on the one-sided likelihood ratio test (LRT) for testing the hypothesis that the covariance matrix of the quality characteristic vector of the current process, Sigma, is "larger" than that of the in-control process, Sigma(0), in the sense that Sigma - Sigma(0) is positive semidefinite and Sigma not equal Sigma(0). Assuming Sigma(0) is known, the LRT statistic is derived and then used to construct the control chart. A simulation study shows that the proposed control chart indeed outperforms three existing two-sided-test-based control charts under comparison in terms of the average run length. The applicability and effectiveness of the proposed control chart are demonstrated through a semiconductor example and two simulations.

Original language | English |
---|---|

Pages (from-to) | 1683-1707 |

Number of pages | 25 |

Journal | Statistica Sinica |

State | Published - Oct 2010 |

### Keywords

- Average run length; likelihood ratio test; multivariate process dispersion; one-sided test; two-sided test
- ONE-SIDED TEST; PROCESS VARIABILITY; COMPONENTS; EQUALITY; CRITERIA

## Fingerprint Dive into the research topics of 'A MULTIVARIATE CONTROL CHART FOR DETECTING INCREASES IN PROCESS DISPERSION'. Together they form a unique fingerprint.

## Cite this

Yen, C. L., & Horng, J-J. (2010). A MULTIVARIATE CONTROL CHART FOR DETECTING INCREASES IN PROCESS DISPERSION.

*Statistica Sinica*, 1683-1707.