<abstract xmlns="http://www.w3.org/1999/xhtml">The statistical calibration problem treated here consists of constructing the interval estimates for future unobserved values of a univariate explanatory variable corresponding to an unlimited number of future observations of a univariate response variable. An interval estimate is to be computed for a value <italic>x</italic> of an explanatory variable after observing a response <italic>Yx</italic> by using the same calibration data from a single calibration experiment, and it is called the multiple use confidence interval. It is assumed that the normally distributed response variable <italic>Yx</italic> is related to the explanatory variable <italic>x</italic> through a linear regression model, a polynomial regression is probably the most frequently used model in industrial applications. Construction of multiple use confidence intervals (MUCI’s) by inverting the tolerance band for a linear regression has been considered by many authors, but the resultant MUCI’s are conservative. A new method for determining MUCI’s is suggested straightforward from their marginal property assuming a distribution of the explanatory variable. Using simulations, we show that the suggested MUCI’s satisfy the coverage probability requirements of MUCI’s quite well and they are narrower than previously published. The practical implementation of the proposed MUCI’s is illustrated in detail on an example.</abstract>

The statistical calibration problem treated here consists of constructing the interval estimates for future unobserved values of a univariate explanatory variable corresponding to an unlimited number of future observations of a univariate response variable. An interval estimate is to be computed for a value x of an explanatory variable after observing a response Yx by using the same calibration data from a single calibration experiment, and it is called the multiple use confidence interval. It is assumed that the normally distributed response variable Yx is related to the explanatory variable x through a linear regression model, a polynomial regression is probably the most frequently used model in industrial applications. Construction of multiple use confidence intervals (MUCI’s) by inverting the tolerance band for a linear regression has been considered by many authors, but the resultant MUCI’s are conservative. A new method for determining MUCI’s is suggested straightforward from their marginal property assuming a distribution of the explanatory variable. Using simulations, we show that the suggested MUCI’s satisfy the coverage probability requirements of MUCI’s quite well and they are narrower than previously published. The practical implementation of the proposed MUCI’s is illustrated in detail on an example.

Multiple Use Confidence Intervals for a Univariate Statistical Calibration

Measurement Science Review

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Multiple Use Confidence Intervals for a Univariate Statistical Calibration"}

The statistical calibration problem treated here consists of constructing the interval estimates for future unobserved values of a univariate explanatory...

Multiple Use Confidence Intervals for a Univariate Statistical Calibration

Published Online: Nov 21, 2019

Page range: 264 - 270

Received: Jul 08, 2019

Accepted: Nov 13, 2019

DOI: https://doi.org/10.2478/msr-2019-0034

Keywords
Statistical calibration, linear regression model, tolerance interval, multiple use confidence interval

© 2019 Martina Chvosteková, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Multiple Use Confidence Intervals for a Univariate Statistical Calibration

Published Online: Nov 21, 2019

Page range: 264 - 270

Received: Jul 08, 2019

Accepted: Nov 13, 2019

DOI: https://doi.org/10.2478/msr-2019-0034

KeywordsStatistical calibration, linear regression model, tolerance interval, multiple use confidence interval

© 2019 Martina Chvosteková, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Statistical calibration, linear regression model, tolerance interval, multiple use confidence interval