Topic 2 error & uncertainty- part 3

TOPIC 2 :

STATISTICS IN DIMENSIONAL

MEASUREMENT- part 3

Topic Contents :

1. Terminology in Engineering Statistic for measurement and

Instrumentation.

1.1 Types of studies

1.2 Types of Data

1.3 Samples study

1.4 Sampling

1.5 Recording

1.6 Mean, Median Mode

1.7 Dispersion

Topic Contents :

2. Control Chart 2.1 X bar R Chart

3. Measurement System Analysis 3.1 Definition And Terminology 3.2 Methodologies for assessing measurement system Stability Linearity 3.3 Gage repeatability & reproducibility (GRR)

4. Errors and Uncertainty 4.1 Types od Errors 4.2 Sources of Measurement Errors 4.3 Types of Uncertainty 4.4 Calculating of Uncertainty

Part 3

4. Errors and Uncertainty

• Error in science does not mean the terms

of mistake . • Error in a scientific measurement means

the different between the individual result and true value.

• Errors cannot be eliminated although the measurement is being done very carefully .

• The total value of error is made up of a number of error source.

4.1 What is Error …?


• Repeated measurement will contribute the

discrepancy or random errors. The

discrepancy can only be obtained when

there are differences between the

readings and the true value. The smaller

the random errors, the greater the

precision.

• If the individual readings are the same,

there still an error called uniform error or

systematic error.

THE ROLE OF ERROR

4.1 What is Error …? THE ROLE OF ERROR

Random Error Systematic Error

a) A component of the error of measurement which, in the course of a number of measurements of the same measurand, varies in an unpredictable way.

b) The mean of a large number of measurement influenced by random errors matches the true value. c) It can be evaluate by study the

repeated measurement values.

a) The exist of the error is known by inference.

b) A component of the error of measurement which, in the course of a number of measurements of the same measurand, remains constant or varies in a predictable way

c) The mean of a large number of measurements influenced by systematic errors deviates from the true value.

c) It can be evaluate by comparing the

measurement results with a higher standard, which is measurement.


THE ROLE OF ERROR

4.2 Sources of Measurement Errors

Dynamic error

• Characterised by frequency and phase response of the

system for periodic variations in the measured input.

Loading error

• It is the difference between the value measured before

and after the measurement system is measured.

Static error

• It is cause by physical nature of various components of

the measuring system.


Characteristic error

• It is the deviation of measurement under constant

environmental conditions from the theoretical predicted

performance.

Elastic deformation

• It is divided into two ;

a)Error cause from reflection when end gage is used for

setting or measure.

b)Error cause from deflection due to self weight of the object.

Parallax

• Any instrument that using pointer and scale may have

parallax error because the gap between pointer and scale is

different at any reading angle.


Contact pressure

• While measuring, the pressure at contact causes some

penetration causing error in measurement.

Backlash

• Due to backlash in gears and screw threads, some

motion is lost to overcome backlash

Hysteretic

• It is a source of errors in electrical instruments.

Ascending values are observed when decrease current

or voltage.

Avoidable error

• The errors occurred due to non-alignment of workpiece

centre, improper of measuring instruments, etc.


Human Error

• Difficult to detect. It can be include a tendency to read

high or low using a wrong instrument. Human training is

the best way to prevent these error.

Errors in Technique and Experimental Error

• If wrong techniques is used. Example: Calibration

technique for vernier is used for micrometer. Education

helps to prevent these errors.


Computational Error

• Can be random or continuous, but, once an error has

started, it usually establishes itself in the computation.

This error is affected by environmental, fatigue and

instrumentation.

Chaotic Error

• Extreme disturbances that ruin or hide the measurement

results. This error include vibration, shock, extreme

noise and etc.

4.3 Types of Uncertainty

• No measurement is ever guaranteed to be perfect.

• Uncertainty of measurement is the doubt that exists

about the result of any measurement. By quantifying the

possible spread of measurements, we can say how

confident we are about the result.

• A measurement result is only complete when

accompanied by a statement of its uncertainty. A

statement of uncertainty is required in order to decide if

the result is adequate for its intended purpose and

consistent with other similar results.


Many things can undermine a measurement:

• The measuring instrument

Errors due to bias, wear, drift, noise, reliability…

• The measurand

Stability

• The measurement process

Difficulty of measurement …

• Imported uncertainties

Uncertainty associated with your instrument affects the uncertainty of the measurements you make.

Where do the uncertainty originate?


Where do the uncertainty originate?

• Operator skill

Skill and judgment of the operator … how would you quantify this?

• Sampling issues

When and where you take measurements

• The environment

Temperature, air pressure, humidity etc can affect the measurement.



Calculating and expressing uncertainty is important to

anybody wishing to make good ‘quality’ measurements.

Other cases:

• calibration - the uncertainty of measurement must be

quoted.

• test - uncertainty of measurement is needed to determine

pass or fail.

• tolerance - you need to know the uncertainty before a

decision on whether the tolerance is met can be made.

Why does Uncertainty matter?

4.4 Calculating Uncertainty

To calculate the uncertainty of a measurement,

firstly you must identify the sources of uncertainty

in the measurement, then estimate the size of the

uncertainty from each source.

The individual uncertainties are combined to give

an overall figure for the measurement uncertainty.

There are two types of evaluation of measurement

uncertainty:

1) TYPE A

2) TYPE B

Type A evaluation

method of evaluation of uncertainty by the

statistical analysis of series of

observations.

Type B evaluation

method of evaluation of uncertainty by

means other than the statistical

analysis of series of observations.


1. Decide what you need from your measurements. Requirements.

2. Carry out the measurements.

3. Estimate the uncertainty of each input quantity that leads to the final result. Express all uncertainties in similar terms.

4. Calculate the result of your measurement (including known corrections for things such as calibration, temperature etc.

5. Determine the combined uncertainty from all the individual aspects.

6. Express the uncertainty in terms of the coverage factor, together with a size of the uncertainty interval, and state the level of confidence.

7. Write down the measurement result and the uncertainty, and state how you arrived at these values.

Steps to Evaluating Uncertainty


• Obtain a series of repeated measurements and

determine the variance of the measurement

result, from which the estimated standard

uncertainty, UA, can be calculated:

• where s is the estimated standard deviation of

the sample of n measurements taken (referred

to as the standard deviation of the mean).


Type A Evaluation


Type B Evaluation • These are uncertainty estimates found from any

other source, such as calibration reports,

manufacturer’s specifications, calculations,

published information etc.

• The calculation of the Type B uncertainty, UB,

depends on the information made available.

• It is important to realize that Type B uncertainty

can be as important (and reliable) as a Type A

evaluation.


Type B Evaluation


Type B Evaluation


Example : Calculation of Uncertainty…



STEP 1 :



STEP 2 :



STEP 3 :



STEP 4 :

Topic 2 error & uncertainty- part 3

Business

error of measurement

uncertainty of measurement

parallax error

experimental error

uniform error

static error

avoidable error

measurement results