Lecture5 Mech SU

8/12/2019 Lecture5 Mech SU

http://slidepdf.com/reader/full/lecture5-mech-su 1/15



Measurement Error

•Single measurement = bias +precision error

•Total error = average bias

error + statistical estimate of

precision error

•

Precision error is described bynormal distribution of

measured values about the

sample mean

•Bias error shifts the sample

mean away from the true mean



Measurement Error (cont.)

Thus, errors are divided into two categories,bias and precision errors. The true value of

a quantity is related to the mean of several

measurements by:

Uncertainty analysis is the method used toquantify the U

x term.



Design-Stage Uncertainty Analysis

An intial analysis performed before the

measurement, it is

• Useful for selection of instruments,techniques and obtaining estimates

• Selection of equipment and procedures base

on performance and cost• To minimize uncertainty which contain in

sensors and instruments



Design-Stage Uncertainty

Analysis (cont.)Zero-order uncertainty, u0

variation expected due to the

instrument resolution

95% probability describe that

1 in 20 measurementwould exceed the interval

defined by u0

Instrument error , uc

Bias error caused by theinstrument (each part

caused by something

contributing factor)



Design-Stage Uncertainty

Analysis (cont.)Combining Elemental Errors: RSS Method



Error Sources

• Calibration

Bias and precision errors in the standard used in

calibration, and the manner in which the standard is

applied to the measuring system



Error Sources (cont.)

• Data Acquisition



Error Sources (cont.)

• Data Reduction



Error PropagationMost measurements are subject to more than one type of error.

We need to estimate the cumulative effect of these errors. It isunlikely that all of the errors will be in one direction - more

likely there will be some cancellation. The root-sum-squares

(RSS) approximation previously mentioned is a good estimate:

Since the overall result may be more sensitive to some errors

than to others, we need to consider the functional

relationships between the output and the various inputs.



Error Propagation (cont.)

The uncertainty in the dependent variable will be related to

the uncertainty in the independent variable by the slope ofthe curve.



Error Propagation (cont.)If we have more than one independent variable

The true mean R' can be obtained from the sample

mean wi th a precision ± uR

In order to account for the different sensitivities of the

measurement to different inputs, we define a sensitivity

index:



Advanced-Stage and Single

Measurement Uncertainty AnalysisIn this analysis procedural and test control errors

that effect the measurement are considered

The first-order level considers the effectOf time, while the second-level considers

Assessing the limits of the ability to

Duplicate the exact operating conditionsAnd the consequences on the test outcome

The Nth-order considers instrument

Calibration characterstics



Multiple-Measurement Uncertainty

Analysis

The procedures for multiple-measurementuncertainty analysis consist of the following

steps:

•

Identify the elemental errors in the measurement(calibration, data acquisition, and data

reduction).

• Estimate the magnitude of systematic and

random error in each of the elemental errors.

•Calculate the uncertainty estimate for the result.



Multiple-Measurement

Uncertainty Analysis (Cont.)

Documents

Lecture5 Mech SU