ISSN: 1945-7553
Page Count: 5

Calibrating Instrument Readings Using a Bivariate Confidence Interval

McDonald, BJ
The University of Toledo, Toledo,OH

Trautner, JJ
University of Utah, Salt Lake City,UT

(Received 24 May 1995; accepted 17 July 1996)

Abstract

A method of calibration that establishes a new bound of confidence for instrument measurements is derived and applied. This bound is named the McDonald-Trautner Interval (MTI). The derivation of the MTI incorporates the bivariate probability distributions of each data point conventionally used to form a regression line. A statistically significant number of parameter measurements on a sample must be made by both the instrument being calibrated and the calibrating medium. When calibration is based solely on regression analysis, the calibrating medium is assumed to be 100% reliable. The MTI includes the variability of the medium. The method is demonstrated on the calibration of a heavy metal detector. The calibrating medium is a chemical process. Compared to the conditional standard deviation bounds of linear regression, it is found that the MTI is a simple means to obtain a more statistically rigorous calibration procedure and is a better indication of the expected value of a variable.

Keywords:
regression analysis, calibration, probability, statistics, confidence interval, bivariate confidence intervals, reliability

Paper ID: JTE11322J
DOI: 10.1520/JTE11322J
ASTM International is a member of CrossRef.