### Abstract

At Los Alamos National Laboratory, engineers conduct experiments to evaluate how well detonators and high explosives work. The experimental unit, often called an "onionskin," is a hemisphere consisting of a detonator and a booster pellet surrounded by high explosive material. When the detonator explodes, a streak camera mounted above the pole of the hemisphere records when the shock wave arrives at the surface. The output from the camera is a two-dimensional image that is transformed into a curve that shows the arrival time as a function of polar angle. The statistical challenge is to characterize the population of arrival time curves and to compare the baseline population of onionskins to a new population. The engineering goal is to manufacture a new population of onionskins that generate arrival time curves with the same shape as the baseline. We present two statistical approaches that test for differences in mean curves and provide simultaneous confidence bands for the difference: (i) a B-Spline basis approach and (ii) a Bayesian hierarchical Gaussian process approach. In problems that involve complex modeling with modest sample sizes, it is important to apply multiple approaches with complementary strengths such as these to determine whether all approaches provide similar results. Solid performances of the two approaches are demonstrated on several simulations that were constructed to mimic the actual onionskin analysis. Finally, an analysis of onionskin data is presented. This article also has supplementary materials available online.

Original language | English (US) |
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Pages (from-to) | 436-449 |

Number of pages | 14 |

Journal | Technometrics |

Volume | 55 |

Issue number | 4 |

DOIs | |

State | Published - Nov 1 2013 |

Externally published | Yes |

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### Keywords

- B-splines
- Functional data analysis
- Gaussian process
- Hierarchical modeling
- Nonparametric regression
- Onionskin

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics

### Cite this

*Technometrics*,

*55*(4), 436-449. https://doi.org/10.1080/00401706.2013.805662