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plan and will minimize or eliminate interference trends. Several methods are discussed in the
paragraphs that follow.
Random Tests
Recall our car fuel-usage example in which the question is: ‘‘What fuel usage should I expect from
this car?’’ Let y be the fuel use, which depends on x a , fuel volume consumption, and x b , distance
traveled. We determine y by varying these two variables (that is, we drive the car). But the test result
can be affected by discrete extraneous variables such as the route, driver, weather, and road
conditions. For example, driving only on interstate highways would impose a false (untypical) trend
on our intended average fuel estimate, so we could drive on different types of roads to break up this
trend. This approach introduces a random test strategy.
In general, consider the situation in which the dependent variable, y, is a function of several
independent variables, x a , x b , . . . . However, the measurement of y can also be influenced by
several extraneous variables, z j , where j ¼ 1, 2, . . . , such that y ¼ f x a ; x b ; . . . ; z j
À
Á
. To find the
dependence of y on the independent variables, they are varied in a controlled manner. Although the
influence of the z j variables on these tests cannot be eliminated, the possibility of their introducing a
false trend on y can be minimized by a proper test strategy. Randomization is one such strategy.
Randomization
We define a random test by a measurement matrix that sets a random order to the change in the value
of the independent variable applied. The effect of the random order on the results of the test is termed
randomization. Trends normally introduced by the coupling of a relatively slow and uncontrolled
variation in the extraneous variables with a sequential application in values of the independent
variable applied will be broken up. This type of plan is effective for the local control of extraneous
variables that change in a continuous manner. Consider Examples 1.1 and 1.2.
Discrete extraneous variables are treated a little differently. The use of different instruments,
different test operators, and different test operating conditions are examples of discrete extraneous
variables that can affect the outcome of a measurement. Randomizing a test matrix to minimize discrete
influences can be done efficiently through the use of experimental design using random blocks. A block
consists of a data set of the measured variable in which the controlled variable is varied but the
extraneous variable is fixed. The extraneous variable is varied between blocks. This enables some
amount of local control over the discrete extraneous variable. In the fuel-usage example, we might
consider several blocks, each comprised of a different driver (extraneous variable) driving similar
routes, and averaging the results. In the example of Figure 1.6, if we cannot control the barometric
pressure in the test, then the imposed strategy of using several tests (blocks) under different values of
barometric pressure breaks up the interference effect found in a single test. Many strategies for
randomized blocks exist, as do advanced statistical methods for data analysis (5–8). In any event, a
random test is useful to assess the influence of an uncontrolled variable. Consider Examples 1.3 and 1.4.
Example 1.1
In the pressure calibration system shown in Figure 1.8, a sensor–transducer is exposed to a known
pressure, p. The transducer, powered by an external supply, converts the sensed signal into a
voltage that is measured by a voltmeter. The measurement approach is to control the applied
10 Chapter 1 Basic Concepts of Measurement Methods
15:40:34 Page 10
plan and will minimize or eliminate interference trends. Several methods are discussed in the
paragraphs that follow.
Random Tests
Recall our car fuel-usage example in which the question is: ‘‘What fuel usage should I expect from
this car?’’ Let y be the fuel use, which depends on x a , fuel volume consumption, and x b , distance
traveled. We determine y by varying these two variables (that is, we drive the car). But the test result
can be affected by discrete extraneous variables such as the route, driver, weather, and road
conditions. For example, driving only on interstate highways would impose a false (untypical) trend
on our intended average fuel estimate, so we could drive on different types of roads to break up this
trend. This approach introduces a random test strategy.
In general, consider the situation in which the dependent variable, y, is a function of several
independent variables, x a , x b , . . . . However, the measurement of y can also be influenced by
several extraneous variables, z j , where j ¼ 1, 2, . . . , such that y ¼ f x a ; x b ; . . . ; z j
À
Á
. To find the
dependence of y on the independent variables, they are varied in a controlled manner. Although the
influence of the z j variables on these tests cannot be eliminated, the possibility of their introducing a
false trend on y can be minimized by a proper test strategy. Randomization is one such strategy.
Randomization
We define a random test by a measurement matrix that sets a random order to the change in the value
of the independent variable applied. The effect of the random order on the results of the test is termed
randomization. Trends normally introduced by the coupling of a relatively slow and uncontrolled
variation in the extraneous variables with a sequential application in values of the independent
variable applied will be broken up. This type of plan is effective for the local control of extraneous
variables that change in a continuous manner. Consider Examples 1.1 and 1.2.
Discrete extraneous variables are treated a little differently. The use of different instruments,
different test operators, and different test operating conditions are examples of discrete extraneous
variables that can affect the outcome of a measurement. Randomizing a test matrix to minimize discrete
influences can be done efficiently through the use of experimental design using random blocks. A block
consists of a data set of the measured variable in which the controlled variable is varied but the
extraneous variable is fixed. The extraneous variable is varied between blocks. This enables some
amount of local control over the discrete extraneous variable. In the fuel-usage example, we might
consider several blocks, each comprised of a different driver (extraneous variable) driving similar
routes, and averaging the results. In the example of Figure 1.6, if we cannot control the barometric
pressure in the test, then the imposed strategy of using several tests (blocks) under different values of
barometric pressure breaks up the interference effect found in a single test. Many strategies for
randomized blocks exist, as do advanced statistical methods for data analysis (5–8). In any event, a
random test is useful to assess the influence of an uncontrolled variable. Consider Examples 1.3 and 1.4.
Example 1.1
In the pressure calibration system shown in Figure 1.8, a sensor–transducer is exposed to a known
pressure, p. The transducer, powered by an external supply, converts the sensed signal into a
voltage that is measured by a voltmeter. The measurement approach is to control the applied
10 Chapter 1 Basic Concepts of Measurement Methods