Errors in Measurement

Muhajir Ab. RahimSchool of Mechatronic Engineering

Universiti Malaysia Perlis

Introduction

• Any measurement made with a measuring device is approximate. 

• If you measure the same object two different times, the two measurements may not be the same.  The difference between two measurements is called a variation in the measurements.

What is Error?

• Another word for this variation - or uncertainty in measurement - is "error." 

• This "error" is not the same as a "mistake."  It does not mean that you got the wrong answer. 

• The error in measurement is a mathematical way to show the uncertainty in the measurement.

Type of Measurement Errors

• Measurement errors generally fall into two categories:

1) Random Errors

2) Systematic Errors

Random Errors• Random error is the portion of

error that varies randomly on repeated measurements of the same variable.

• Random error refers to the precision of the measurement.

• Causes of random errors are electrical noise and environmental effects.

• Random errors are ones that are easier to deal with because they cause the measurements to fluctuate around the true value.

• If we are trying to measure some parameter X, greater random errors cause a greater dispersion of values, but the mean of X still represents the true value for that instrument.

Systematic Errors

• Systematic error is the portion of error that remains constant in repeated measurements of the same variable.

• systematic error refers to the accuracy of the measurement

• Non calibrated instruments will cause this systematic error.

• A systematic error can be more tricky to track down and is often unknown.

• This error is often called a bias in the measurement.

Exercise

What type of error is occurred?1. If you report the barefoot height of a person based on

measurement taken, while the person was wearing heeled shoes.

2. Electronic noise in the circuit of an electrical instrument.

3. The error which is repetitive in nature is:

4. Zero error in micrometer is:

Systematic Error

Random Error

Systematic Error

Systematic Error

How to represent Error?

• Error in measurement can be represented into:

1) Tolerance Interval

2) Percentage of Error

Tolerance Interval

• Tolerance is the greatest range of variation that can be allowed.

• To determine the tolerance interval in a measurement, add and subtract one-half of the precision of the measuring instrument to the measurement.  

• For example, if a measurement made with a metric ruler is 5.6 cm and the ruler has a precision of  0.1 cm, then the tolerance interval in this measurement is 5.6 + 0.05 cm, or from 5.55 cm to 5.65 cm. 

Percentage of Error

• Error in measurement may also be expressed by a percentage of error

• For example, a measurement of 12 feet may be said to be off by 2%.  This means that the actual measurement could be between12 - (2% of 12) and 12 + (2% of 12)12 - (.02)12 and 12 + (.02)1211.76 ft. and 12.24 feet

How to determine percentage error?

• To determine the percent error between our measurement of a value and the actual value, use the formula: Percentage Error = [Measured – Actual] x 100

Actual

Rounded

• Error in measurement may also be indicated by the terms "rounded" or "to the nearest". 

• When dealing with rounded measurements, remember the basic rules for rounding:  when rounding to a place value, look at the value to the right of that position.  If this value is 5 or bigger, round up.

• For example, the length of a side of a square to the nearest inch is 10 inches.  This means that the actual length of the side could be between9.5 inches and 10.4 inches (since all of these values round to 10).

What is Precision?

• The precision of a measuring instrument is determined by the smallest unit to which it can measure. 

• The precision is said to be the same as the smallest fractional or decimal division on the scale of the  measuring instrument.

What is Accuracy?

• Accuracy is a measure of how close the result of the measurement comes to the "true" value. 

• The accuracy of the instruments can be specified in either the following forms;

1. Percentage of true value = measured value – true value x 100

true values

2. Percentage of full-scale deflection

= measured value – true value x 100

maximum scale value

Exercise

• A pressure gauge ranges from 0 to 50 psi, the worst case spread in readings is +4.35 psi. What is the %FSD accuracy?

%FSD = +(4.35 psi/ 50 psi) x 100 = +8.7

Ways to Improve Accuracy in Measurement

1. Make the measurement with an instrument that has the highest level of precision.  The smaller the unit, or fraction of a unit, on the measuring device, the more precisely the device can measure. 

2. Know your tools!  Apply correct techniques when using the measuring instrument and reading the value measured.  Avoid the error called "parallax" -- always take readings by looking straight down (or ahead) at the measuring device.  Looking at the measuring device from a left or right angle will give an incorrect value.

3. Repeat the same measure several times to get a good average value.

4. Measure under controlled conditions.  If the object you are measuring could change size depending upon climatic conditions (swell or shrink), be sure to measure it under the same conditions each time.  This may apply to your measuring instruments as well.