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span more than one order of magnitude. With data that follow a trend of the form y ¼ ax
n , a linear
curve will be obtained in log-log format.
Significant Digits
Significant digits refer to the number of digits found before and after the decimal point in a reported
number. While leading zeros are not significant, all trailing zeros are significant. For example, 42.0
has three significant digits, including one decimal digit. The number of significant digits needed
depends on the problem and the close discretion of the engineer. But in the course of working a
problem, there should be consistency in the number of significant digits used and reported. The
number of digits reported reflects a measure of the uncertainty in the value assigned by the engineer.
So to determine the number of significant digits required, just ask yourself: ‘‘What value makes
sense to this problem?’’ For example, to maintain a relative uncertainty of within 1%, we need to
report values to three significant figures. But because rounding errors tend to accumulate during
calculations, we would perform all intermediate calculations to at least four significant figures, and
then round the final result down to three significant figures.
1.7 SUMMARY
During a measurement the input signal is not known but is inferred from the value of the output
signal from the measurement system. We discussed the process of calibration as the means to
relate a measured input value to the measurement system output value and the role of standards
in that process. An important step in the design of a measurement system is the inclusion of a
means for a reproducible calibration that closely simulates the type of signal to be input during
actual measurements. A test is the process of ‘‘asking a question.’’ The idea of a test plan was
developed to answer that question. However, a measured output signal can be affected by many
variables that will introduce variation and trends and confuse that answer. Careful test planning is
required to reduce such effects. A number of test plan strategies were developed, including
randomization. The popular term ‘‘accuracy’’ was explained in terms of the more useful concepts
of random error, systematic error, random uncertainty, and systematic uncertainty and their
effects on a measured value. We also explored the idea of test standards and engineering codes,
legal documents that influence practically every manufactured product around us.
REFERENCES
1. Peace, G. S., Taguchi Methods, Addison-Wesley, Reading, MA, 1993.
2. Bridgeman, P. W., Dimensional Analysis, 2nd ed., Yale University Press, New Haven, CT, 1931.
3. Duncan, W. J., Physical Similarity and Dimensional Analysis, Arnold, London, 1953.
4. Massey, B. S., Units, Dimensions and Physical Similarity, Van Nostrand-Reinhold, New York,
1971.
5. Lipsen, C.,and N. J. Sheth, Statistical Design and Analysis of Engineering Experimentation,
McGraw-Hill, New York, 1973.
6. Peterson, R. G., Design and Analysis of Experiments, Marcel-Dekker, New York, 1985.
7. Mead, R., The Design of Experiments: Statistical Principles for Practical Application,
Cambridge Press, New York, 1988.
References 31
15:40:36 Page 31
span more than one order of magnitude. With data that follow a trend of the form y ¼ ax
n , a linear
curve will be obtained in log-log format.
Significant Digits
Significant digits refer to the number of digits found before and after the decimal point in a reported
number. While leading zeros are not significant, all trailing zeros are significant. For example, 42.0
has three significant digits, including one decimal digit. The number of significant digits needed
depends on the problem and the close discretion of the engineer. But in the course of working a
problem, there should be consistency in the number of significant digits used and reported. The
number of digits reported reflects a measure of the uncertainty in the value assigned by the engineer.
So to determine the number of significant digits required, just ask yourself: ‘‘What value makes
sense to this problem?’’ For example, to maintain a relative uncertainty of within 1%, we need to
report values to three significant figures. But because rounding errors tend to accumulate during
calculations, we would perform all intermediate calculations to at least four significant figures, and
then round the final result down to three significant figures.
1.7 SUMMARY
During a measurement the input signal is not known but is inferred from the value of the output
signal from the measurement system. We discussed the process of calibration as the means to
relate a measured input value to the measurement system output value and the role of standards
in that process. An important step in the design of a measurement system is the inclusion of a
means for a reproducible calibration that closely simulates the type of signal to be input during
actual measurements. A test is the process of ‘‘asking a question.’’ The idea of a test plan was
developed to answer that question. However, a measured output signal can be affected by many
variables that will introduce variation and trends and confuse that answer. Careful test planning is
required to reduce such effects. A number of test plan strategies were developed, including
randomization. The popular term ‘‘accuracy’’ was explained in terms of the more useful concepts
of random error, systematic error, random uncertainty, and systematic uncertainty and their
effects on a measured value. We also explored the idea of test standards and engineering codes,
legal documents that influence practically every manufactured product around us.
REFERENCES
1. Peace, G. S., Taguchi Methods, Addison-Wesley, Reading, MA, 1993.
2. Bridgeman, P. W., Dimensional Analysis, 2nd ed., Yale University Press, New Haven, CT, 1931.
3. Duncan, W. J., Physical Similarity and Dimensional Analysis, Arnold, London, 1953.
4. Massey, B. S., Units, Dimensions and Physical Similarity, Van Nostrand-Reinhold, New York,
1971.
5. Lipsen, C.,and N. J. Sheth, Statistical Design and Analysis of Engineering Experimentation,
McGraw-Hill, New York, 1973.
6. Peterson, R. G., Design and Analysis of Experiments, Marcel-Dekker, New York, 1985.
7. Mead, R., The Design of Experiments: Statistical Principles for Practical Application,
Cambridge Press, New York, 1988.
References 31