### Abstract

An important question within industrial statistics is how to find operating conditions that achieve some goal for the mean of a characteristic of interest while simultaneously minimizing the characteristic's process variance. Often, people refer to this kind of situation as the robust parameter design problem. The robust parameter design literature is rich with ways to create separate models for the mean and variance from this type of experiment. Many times time and/or cost constraints force certain factors of interest to be much more difficult to change than others. An appropriate approach to such an experiment restricts the randomization, which leads to a split-plot structure. The paper modifies the central composite design to allow the estimation of separate models for the characteristic's mean and variances under a split-plot structure. The paper goes on to discuss an appropriate analysis of the experimental results. It illustrates the methodology with an industrial experiment involving a chemical vapour deposition process for the manufacture of silicon wafers. The methodology was used to achieve a silicon layer thickness value of 485 A while minimizing the process variation.

Original language | English (US) |
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Pages (from-to) | 615-630 |

Number of pages | 16 |

Journal | Journal of the Royal Statistical Society. Series C: Applied Statistics |

Volume | 55 |

Issue number | 5 |

DOIs | |

State | Published - Oct 25 2006 |

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### Keywords

- Central composite designs
- Mean-variance modelling
- Response surface methodology
- Robust parameter design
- Split-plot experiments

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Journal of the Royal Statistical Society. Series C: Applied Statistics*,

*55*(5), 615-630. https://doi.org/10.1111/j.1467-9876.2006.00556.x