E1C05 09/14/2010
14:36:25 Page 161
Chapter 5
Uncertainty Analysis
5.1 INTRODUCTION
Whenever we plan a test or later report a test result, we need to know something about the quality of
the results. Uncertainty analysis provides a methodical approach to estimating the quality of the
results from an anticipated test or from a completed test. This chapter focuses on how to estimate the
‘‘Æ what?’’ in a planned test or in a stated test result.
Suppose the competent dart thrower of Chapter 1 tossed several practice rounds of darts at a bull’seye. This would give us a good idea of the thrower’s tendencies. Then, let the thrower toss another
round. Without looking, can you guess where the darts will hit? Test measurements that include
systematic and random error components are much like this. We can calibrate a measurement system
to get a good idea of its behavior and accuracy. However, from the calibration we can only estimate
how well any measured value might estimate the actual ‘‘true’’ value in a subsequent measurement.
Errors are a property of the measurement. Measurement is the process of assigning a value to
a physical variable based on a sampling from the population of that variable. Error causes a difference
between the value assigned by measurement and the true value of the population of the variable.
Measurement errors are introduced from various elements, for example, the individual instrument
calibrations, the data set finite statistics, and the approach used. But because we do not know the true
value and we only know the measured values, we do not know the exact values of errors. Instead, we
draw from what we do know about the measurement to estimate a range of probable error. This
estimate is an assigned value called the uncertainty. The uncertainty describes an interval about the
measured value within which we suspect that the true value must fall with a stated probability.
Uncertainty analysis is the process of identifying, quantifying, and combining the errors.
Uncertainty is a property of the result. The outcome of a measurement is a result, and the
uncertainty quantifies the quality of that result. Uncertainty analysis provides a powerful design tool
for evaluating different measurement systems and methods, designing a test plan, and reporting
uncertainty. This chapter presents a systematic approach for identifying, quantifying, and combining the estimates of the errors in a measurement. While the chapter stresses the methodology of
analyses, we emphasize the concomitant need for an equal application of critical thinking and
professional judgment in applying the analyses. The quality of an uncertainty analysis depends on
the engineer’s knowledge of the test, the measured variables, the equipment, and the measurement
procedures (1).
Errors are effects, and uncertainties are numbers. While errors are the effects that cause a
measured value to differ from the true value, the uncertainty is an assigned numerical value that
quantifies the probable range of these errors.
161
14:36:25 Page 161
Chapter 5
Uncertainty Analysis
5.1 INTRODUCTION
Whenever we plan a test or later report a test result, we need to know something about the quality of
the results. Uncertainty analysis provides a methodical approach to estimating the quality of the
results from an anticipated test or from a completed test. This chapter focuses on how to estimate the
‘‘Æ what?’’ in a planned test or in a stated test result.
Suppose the competent dart thrower of Chapter 1 tossed several practice rounds of darts at a bull’seye. This would give us a good idea of the thrower’s tendencies. Then, let the thrower toss another
round. Without looking, can you guess where the darts will hit? Test measurements that include
systematic and random error components are much like this. We can calibrate a measurement system
to get a good idea of its behavior and accuracy. However, from the calibration we can only estimate
how well any measured value might estimate the actual ‘‘true’’ value in a subsequent measurement.
Errors are a property of the measurement. Measurement is the process of assigning a value to
a physical variable based on a sampling from the population of that variable. Error causes a difference
between the value assigned by measurement and the true value of the population of the variable.
Measurement errors are introduced from various elements, for example, the individual instrument
calibrations, the data set finite statistics, and the approach used. But because we do not know the true
value and we only know the measured values, we do not know the exact values of errors. Instead, we
draw from what we do know about the measurement to estimate a range of probable error. This
estimate is an assigned value called the uncertainty. The uncertainty describes an interval about the
measured value within which we suspect that the true value must fall with a stated probability.
Uncertainty analysis is the process of identifying, quantifying, and combining the errors.
Uncertainty is a property of the result. The outcome of a measurement is a result, and the
uncertainty quantifies the quality of that result. Uncertainty analysis provides a powerful design tool
for evaluating different measurement systems and methods, designing a test plan, and reporting
uncertainty. This chapter presents a systematic approach for identifying, quantifying, and combining the estimates of the errors in a measurement. While the chapter stresses the methodology of
analyses, we emphasize the concomitant need for an equal application of critical thinking and
professional judgment in applying the analyses. The quality of an uncertainty analysis depends on
the engineer’s knowledge of the test, the measured variables, the equipment, and the measurement
procedures (1).
Errors are effects, and uncertainties are numbers. While errors are the effects that cause a
measured value to differ from the true value, the uncertainty is an assigned numerical value that
quantifies the probable range of these errors.
161