### Statistical Methods in Metrology

Session Chair: Daniel Jeske, University of California - Riverside**The Prediction Properties of Classical and Inverse Regression for the Simple Linear Calibration Problem**

Sara R. Wilson

NASA

Abstract: The calibration of measurement systems is a fundamental problem within industrial statistics; however, the statistical literature in this area seems somewhat underdeveloped. The origins of this problem go back to basic chemical analysis based on NIST standards. In today’s world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST.

In the classical calibration approach, the initial experiment to calibrate the instrument treats the standards as the regressor and the observed measurements as the response. The resulting regression model must then be inverted in order to use the instrument to make actual measurements in practice. This classical calibration approach is compared to inverse regression, which treats the standards as the response and the observed values as the regressor in the calibration experiment. Although it is both simple and easy to implement, inverse regression violates some of the basic regression assumptions.

**Confidence Intervals for Clock Offset in Networks with Bivariate Exponential Delays**

Jeff Pettyjohn, Daniel R. Jeske, Jun Li, and Barry C. Arnold

University of California - Riverside

Abstract: In the literature, much attention has been paid to statistical modeling-based estimation of the offset between two clocks. Recently, this has been extended to the construction of confidence intervals for offset. However, in this work it has been assumed that the network delays that occur during the synchronization process are independent. We feel that this is not a reasonable assumption and argue that the network delays should thought of as correlated. Commonly, the network delays are modeled as independent exponential random variables. Thus we instead assume the network delays follow a bivariate exponential distribution and under this assumption, confidence intervals for offset, which we then compare with the existing independent case intervals in situations of independent and bivariate exponential distributed network delays.

**A Simple, Robust, and Candid Approach for Expressing the Uncertainty of Repeated Measurements**

Volker Abel

Munich University of Applied Sciences

Current world-wide practice expresses the uncertainty of repeated measurements through the sample´s arithmetic mean and standard deviation, assuming an (approximate) normal distribution or even an exact prior (like the rectangular or triangular) distribution. By contrast, we suggest the use of the median and the distribution-free confidence interval for the median for that purpose.

**Laplace Random Effects Models for Interlaboratory Studies**

Andrew L. Rukhin and Antonio Possolo

NIST

A model is introduced for measurements obtained in collaborative interlaboratory studies, comprising measurement errors and random laboratory effects that have Laplace distributions, possibly with heterogeneous, laboratory-specific variances. Estimators are suggested for the common median (mean) and for its standard deviation. We provide predictors of the laboratory effects, and of their pairwise differences, along with the uncertainties of these predictors. Explicit formulas are given for these estimators, and their sampling performance is assessed in a Monte Carlo simulation study.