THE COSINE ERROR: AN EXAMPLE OF A MODEL WITH NON-REPETITIVE SYSTEMATIC EFFECTS

Ignacio Lira, Dieter Grientschnig
Abstract:
An inconsistency with respect to variable transformations in our previous treatment of the cosine error example with repositioning (Metrologia, vol. 47, pp. R1–R14) is pointed out and three remedial procedures are proposed. The problem refers to the measurement of the vertical height of a column of liquid in a manometer. A systematic effect arises because of the possible deviation of the measurement axis from the vertical, which may be different each time the measurement is performed. The proposed procedures are: a) merging of independent probability density functions for the measurand and the non-repetitive systematic effect transformed to a common parameterization; b) straightforward application of Bayesian statistics using a conditional reference prior with partial information; and c) an ad hoc procedure based on interpreting the measured quantities and the different influences of the systematic effect as points in Cartesian coordinates. Of these, procedure b) is the most sound theoretically.
Keywords:
cosine error, probability density function, Bayesian statistics, reference prior, Borel’s paradox
Download:
IMEKO-WC-2015-TC21-404.pdf
DOI:
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Event details
Event name:
XXI IMEKO World Congress
Title:

Measurement in Research and Industry

Place:
Prague, CZECH REPUBLIC
Time:
30 August 2015 - 04 September 2015
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