Contributions to the Theory of Single-Sample Uncertainty Analysis

Abstract

Uncertainty Analysis is the prediction of the uncertainty interval which should be associated with an experimental result, based on observations of the scatter in the raw data used in calculating the result. In this paper, the process is discussed as it applies to single-sample experiments of the sort frequently conducted in research and development work. Single-sample uncertainty analysis has been in the engineering literature since Kline and McClintock's paper in 1953 [1] and has been widely, if sparsely, practiced since then. A few texts and references on engineering experimentation present the basic equations and discuss its importance in planning and evaluating experiments (see Schenck, for example [2]). Uncertainty analysis is frequently linked to the statistical treatment of the data, as in Holman [3], where it may be lost in the fog for many student engineers. More frequently, only the statistical aspects of data interpretation are taught, and uncertainty analysis is ignored. For whatever reasons, uncertainty analysis is not used as much as it should be in the planning, development, interpretation, and reporting of scientific experiments in heat transfer and fluid mechanics. There is a growing awareness of this deficiency among standards groups and funding agencies, and a growing determination to insist on a thorough description of experimental uncertainty in all technical work. Both the International Standards Organization [4] and the American Society of Mechanical Engineers [5] are developing standards for the description of uncertainties in fluid-flow measurements. The U. S. Air Force [6] and JANNAF [7] each have handbooks describing the appropriate procedures for their classes of problems. The International Committee on Weights and Measures (CIPM) is currently evaluating this issue [8]. The prior references, with the exception of Schenck and, to a lesser extent, Holman, treat uncertainty analysis mainly as a process for describing the uncertainty in an experiment, and end their discussion once that evaluation has been made. The present paper has a somewhat different goal: to show how uncertainty analysis can be used as an active tool in developing a good experiment, as well as reporting it. The concepts presented here were developed in connection with heat transfer and fluid mechanics research experiments of moderately large size (i.e., larger than a breadbox and smaller than a barn) and which may frequently require three

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Affiliated Institutions

• Stanford University US

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