NDLI: Deriving PDFs for Interrelated Quantities: What to Do If There Is “More Than Enough” Information?

Content Provider	IEEE Xplore Digital Library
Author	Lira, I. Grientschnig, D.
Copyright Year	1963
Abstract	The GUM and its supplements one and two have come to be regarded as de facto standards for evaluating measurement uncertainty. The latter documents have stressed the benefits of deriving probability density functions (PDFs) for the output quantities instead of just evaluating the standard and expanded uncertainties associated with their best estimates. Those supplements, however, present a brute force numerical method for obtaining the output PDFs. In this paper, we rely instead on the use of the change-of-variables theorem as a way of obtaining analytical expressions for PDFs in the form of integrals that, at least in principle, can be numerically evaluated. But more importantly, the GUM supplements do not include situations in which the available information is more than enough, in the sense that by separately considering its various components one may arrive at concurrent PDFs for the quantity or quantities of interest. In some situations these PDFs will be largely similar, so that implementing some form of merging method would perhaps be reasonable. But it may also happen that significant discrepancies between those PDFs are apparent, in which case a modification of the measurement model might make all information appear to be consistent. Herein we review two procedures for merging concurrent and not too dissimilar PDFs. We also discuss some elements to be considered if extending the measurement model appears to be a better alternative.
Sponsorship	IEEE Instrumentation and Measurement Society Bureau international des poids et mesures IEEE International Bureau of Weights and Measures (BIPM) URSI NBS Agency Ind. Sci. & Technol., Min. Int. Trade & Ind. Sci. Council Japan International Union of Pure and Applied Physics (IUPAP) NIST NRCC National Conference of Standards Laboratories (NCSL) Allen Osborne Associates Andeen-Hagerling, Inc. Ballantine Lab. Inc. Clarke-Hess Communications Research Corp. Fluke Corporation Guildline Instruments Hewlett-Packard Co. Julie Res. Lab. Inc. Keithley Instruments, Inc. Measurements International Ltd. Canada QuadTech Inc. Quantum Design Inc. Rotek Instrum. Corp. Tegam Inc. Tektronix Inc
Starting Page	1937
Ending Page	1946
Page Count	10
File Size	583059
File Format	PDF
ISSN	00189456
Volume Number	63
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Mathematical model Standards Uncertainty Equations Joints Merging Probability density function uncertainty. Bayes procedures parameter estimation probability statistics uncertainty
Content Type	Text
Resource Type	Article
Subject	Instrumentation Electrical and Electronic Engineering

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