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8. Montgomery, D., Design and Analysis of Experiments, 7th ed., Wiley, New York, 2009.
9. Taylor, B., Guide for the Use of the International System of Units, NIST Special Publication,
330, 2001.
10. NBS Technical News Bulletin 52(1), January 1968.
11. International Temperature Scale–1990, Metrologia 27(3), 1990.
12. Taylor, B., NIST Guide to SI Units, NIST Special Publication 811, 1995.
13. ASME Power Test Codes, American Society of Mechanical Engineers, New York.
14. ASHRAE Handbook of Fundamentals, American Society of Heating, Refrigeration and Air
Conditioning Engineers, New York, 2009.
15. ANSI Standard, American National Standards Institute, New York, 2009.
16. Annual Book of ASTM Standards, American Society for Testing and Materials, Philadelphia,
PA, 2010.
NOMENCLATURE
e absolute error
p pressure (ml
À1
t
À2 )
r i input span
r o output span
s x standard deviation of x
u c overall instrument uncertainty
u h hysteresis uncertainty; uncertainty assigned to
hysteresis error
u K sensitivity uncertainty; uncertainty assigned to
sensitivity error
u L linearity uncertainty; uncertainty assigned to
linearity error
u R repeatability uncertainty; uncertainty assigned
to repeatability error
u z zero uncertainty; uncertainty assigned to zero error
x independent variable; input value; measured
variable
y dependent variable; output value
y L linear polynomial
A relative error; relative accuracy
K static sensitivity
T temperature (
)
8 volume (l
3
)
PROBLEMS
1.1 Discuss your understanding of the hierarchy of standards beginning with the primary standard. In
general, what is meant by the term ‘‘standard’’? Can you cite examples of standards in everyday use?
1.2 What is the purpose of a calibration? Suppose an instrument is labeled as ‘‘calibrated.’’ What should
this mean to you as an engineer?
1.3 Suppose you found a dial thermometer in a stockroom. Discuss several methods by which you might
estimate random and systematic error in the thermometer? How would you estimate its uncertainty?
1.4 Consider the example described in Figure 1.6. Discuss the effect of the extraneous variable,
barometric pressure, in terms of noise and interference relative to any one test and relative to several
tests. Discuss how the interference effect can be broken up into noise.
1.5 How would the resolution of the display scale of an instrument affect its uncertainty? Suppose the
scale was somehow offset by one least count of resolution. How would this affect its uncertainty?
Explain in terms of random and systematic error.
1.6 How would the hysteresis of an instrument affect its uncertainty? Explain in terms of random and
systematic error.
32 Chapter 1 Basic Concepts of Measurement Methods
15:40:38 Page 32
8. Montgomery, D., Design and Analysis of Experiments, 7th ed., Wiley, New York, 2009.
9. Taylor, B., Guide for the Use of the International System of Units, NIST Special Publication,
330, 2001.
10. NBS Technical News Bulletin 52(1), January 1968.
11. International Temperature Scale–1990, Metrologia 27(3), 1990.
12. Taylor, B., NIST Guide to SI Units, NIST Special Publication 811, 1995.
13. ASME Power Test Codes, American Society of Mechanical Engineers, New York.
14. ASHRAE Handbook of Fundamentals, American Society of Heating, Refrigeration and Air
Conditioning Engineers, New York, 2009.
15. ANSI Standard, American National Standards Institute, New York, 2009.
16. Annual Book of ASTM Standards, American Society for Testing and Materials, Philadelphia,
PA, 2010.
NOMENCLATURE
e absolute error
p pressure (ml
À1
t
À2 )
r i input span
r o output span
s x standard deviation of x
u c overall instrument uncertainty
u h hysteresis uncertainty; uncertainty assigned to
hysteresis error
u K sensitivity uncertainty; uncertainty assigned to
sensitivity error
u L linearity uncertainty; uncertainty assigned to
linearity error
u R repeatability uncertainty; uncertainty assigned
to repeatability error
u z zero uncertainty; uncertainty assigned to zero error
x independent variable; input value; measured
variable
y dependent variable; output value
y L linear polynomial
A relative error; relative accuracy
K static sensitivity
T temperature (
)
8 volume (l
3
)
PROBLEMS
1.1 Discuss your understanding of the hierarchy of standards beginning with the primary standard. In
general, what is meant by the term ‘‘standard’’? Can you cite examples of standards in everyday use?
1.2 What is the purpose of a calibration? Suppose an instrument is labeled as ‘‘calibrated.’’ What should
this mean to you as an engineer?
1.3 Suppose you found a dial thermometer in a stockroom. Discuss several methods by which you might
estimate random and systematic error in the thermometer? How would you estimate its uncertainty?
1.4 Consider the example described in Figure 1.6. Discuss the effect of the extraneous variable,
barometric pressure, in terms of noise and interference relative to any one test and relative to several
tests. Discuss how the interference effect can be broken up into noise.
1.5 How would the resolution of the display scale of an instrument affect its uncertainty? Suppose the
scale was somehow offset by one least count of resolution. How would this affect its uncertainty?
Explain in terms of random and systematic error.
1.6 How would the hysteresis of an instrument affect its uncertainty? Explain in terms of random and
systematic error.
32 Chapter 1 Basic Concepts of Measurement Methods