116
CHAPTER 4
MEASUREMENTS
E. L. Hixson and E. A. Ripperger
University of Texas
Austin, Texas
1 STANDARDS AND ACCURACY
116
1.1 Standards
116
1.2 Accuracy and Precision
117
1.3 Sensitivity and Resolution
118
1.4 Linearity
118
2 IMPEDANCE CONCEPTS
119
3 ERROR ANALYSIS
123
3.1
Internal Estimates
124
3.2 Use of Normal Distribution
to Calculate Probable Error
in X
125
3.3 External Estimates
126
REFERENCES
129
1 STANDARDS AND ACCURACY
1.1 Standards
Measurement is the process by which a quantitative comparison is made between a standard
and a measurand. The measurand is the particular quantity of interest—the thing that is to
be quantified. The standard of comparison is of the same character as the measurand, and
so far as mechanical engineering is concerned the standards are defined by law and main-
tained by the National Institute of Standards and Technology (NIST, formerly known as the
National Bureau of Standards). The four independent standards which have been defined are
length, time, mass, and temperature.1 All other standards are derived from these four. Before
1960 the standard for length was the international prototype meter, kept at Sevres, France.
In 1960 the meter was redefined as 1,650,763.73 wavelengths of krypton light. Then in 1983,
at the Seventeenth General Conference on Weights and Measures, a new standard was
adopted: A meter is the distance traveled in a vacuum by light in 1/299,792,458 seconds.2
However, there is a copy of the international prototype meter, known as the national pro-
totype meter, kept by NIST. Below that level there are several bars known as national ref-
erence standards and below that there are the working standards. Interlaboratory standards
in factories and laboratories are sent to NIST for comparison with the working standards.
These interlaboratory standards are the ones usually available to engineers.
Standards for the other three basic quantities have also been adopted by NIST, and
accurate measuring devices for those quantities should be calibrated against those standard