Module 1 Errors in measurement, Statistical analysis of experimental data, error

estimation, regression analysis, Use of Excel, Design of experiments Quadrant 2 List of animations/Videos: Errors in measurement:

1. Accuracy and precision are shown in this video http://www.youtube.com/watch?v=pWEflsClyTk

2. This video describes the concept of measurement error, and the difference between random and systematic measurement error. http://www.youtube.com/watch?v=8vKo_TBBX8E

3. This video describes how to read a scale and report a measurement. It also describes the types of errors (random and systematic) inherent in that measurement and how to deal with them. A brief overview of accuracy and precision are also given. http://www.youtube.com/watch?v=jyxA96w-gqQ

4. This video describes how to read a scale and report a measurement. It also describes the types of errors (random and systematic) inherent in that measurement and how to deal with them. A brief overview of accuracy and precision are also given: http://www.youtube.com/watch?v=jyxA96w-gqQ

5. A description of the uncertainty of a measurement, the fractional error, and the percent error: http://www.youtube.com/watch?v=4T_vEI0ZFPE

Statistical analysis of experimental data: 6. Measurements, Uncertainties, and Error Propagation are discussed as an

introductory lab: http://www.youtube.com/watch?v=R3B4EKiwo4I 7. Uncertainty and error distribution : http://www.youtube.com/watch?v=QruAxiYSIAY

Regression analysis:

8. Multiple regression analysis is discussed in this video: http://videolectures.net/ssmt09_kittel_mra/

9. Linear regression video: http://www.statisticslectures.com/topics/linearregression/ 10. This is a 15 minute lecture on the Introduction to Regression Analysis. It is assumed

the viewer has little background in statistics http://www.youtube.com/watch?v=k_OB1tWX9PM

11. This video explains regression analysis in greater detail http://freevideolectures.com/Course/3091/Regression-Analysis#

12. Linear regression – least squares criterion : http://www.statisticslectures.com/topics/linearregression/

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13. How to calculate linear regression using least square method http://www.youtube.com/watch?v=JvS2triCgOY

14. An introduction to linear regression analysis : http://www.youtube.com/watch?v=zPG4NjIkCjc&list=TLyg23-wxvVtA

15. Introduction to simple linear regression – residuals and the error term : http://www.youtube.com/watch?v=snG7sa5CcJQ&list=TLyg23-wxvVtA

Use of Excel:

16. Regression analysis using Microsoft Excel 2007 http://www.youtube.com/watch?v=O0X8jAfApbk

17. Multiple regression : http://www.youtube.com/watch?v=2J8WBo2CKM4 Design of experiments:

18. Design of experiments : http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/design-of-experiments.html

19. Design and analysis of experiments : http://sms.cam.ac.uk/collection/125 20. How does DOE work? :

http://www.youtube.com/watch?v=lgdBHKMJQqc&list=TL--jpuN41x_I 21. A brief tutorial on DOE :

http://www.youtube.com/watch?v=mrhrfiqpQCU&list=TL--jpuN41x_I 22. Design of experiments – overview :

http://www.youtube.com/watch?v=sIRl1xWrViY&list=TL--jpuN41x_I Illustrations:

23. Accuracy and precision images are presented http://www.spcforexcel.com/monitoring-test-methods-using-spc

List of questions (FAQ): Introduction:

1. What is measurement? 2. List the different measurement categories. Give examples for each category 3. Explain intrusive and non intrusive methods of measurement. 4. Illustrate a general measurement scheme 5. Explain precision and accuracy with a neat diagram 6. Give some examples for intrusive and non-intrusive type of measurement 7. What is uncertainty? Also, explain uncertainty propagation. 8. Differentiate between accuracy and uncertainty 9. What is calibration? How is it indicated? 10. Discuss the different stages of a measurement system giving an example. 11. Define the terms : measurement, accuracy, sensitivity, error.

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12. Discuss the following properties of an instrument: range, true value, readability, indicated value, error, least count, accuracy, sensitivity, precision, hysteresis, uncertainty.

13. What is drift? 14. What is dead zone? 15. What do you understand by characteristics of a measuring instrument? 16. What are static characteristics? How do they differ from dynamic characteristics?

Errors in measurement: 17. What are systematic and random errors? 18. Discuss the various types of errors in measurement 19. What are limiting errors? Briefly explain 20. How errors are classified? Explain the errors that occur in measurements. 21. What are gross errors? How can these be eliminated? 22. How do you locate systematic errors? 23. What are assembly errors? Is it possible to discover and rectify these errors? 24. State the reasons for occurrence of observational errors.

Statistical analysis: 25. What is statistical analysis of experimental data? 26. What is error distribution? 27. Explain the principle of least squares as applied to error distribution.

Regression analysis, use of excel, design of experiments:

28. Illustrate linear and non-linear regression analysis. 29. Briefly explain use excel for regression analysis 30. Briefly explain the steps involved in designing the experiments. 31. What is full factorial design? 32. Explain half factorial design.

Quadrant 3 Wiki links/reference links/courses from other university websites Errors in measurement:

1. Error types are mentioned in this site http://en.wikipedia.org/wiki/Observational_error

2. Instrument error and its removal are discussed http://en.wikipedia.org/wiki/Instrument_error

3. Reducing measurement error in informal sector surveys is discussed

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http://mospi.nic.in/informal_paper_17.htm 4. Measurement uncertainty is discussed

http://en.wikipedia.org/wiki/Measurement_uncertainty

Regression analysis: 5. Introduction to simple and multiple regression analysis is presented

https://www.moresteam.com/toolbox/regression-analysis.cfm6. Regression analysis tutorial is presented

http://freevideolectures.com/Course/3091/Regression-Analysis#

Design of experiments: 7. Basics of design of experiments are presented with examples

http://en.wikipedia.org/wiki/Design_of_experiments8. Design of experiments – tutorial

http://www.home.agilent.com/upload/cmc_upload/All/DesignOfExperimentsTutorial.pdf?&cc=IN&lc=eng

9. Basics of design of experiments are presentedhttp://www.itl.nist.gov/div898/handbook/pri/section1/pri11.htm

10. Multiple choice quiz on DOE is presentedhttp://highered.mcgraw-hill.com/sites/0073525960/student_view0/chapter13/multiple_choice_quiz.html

11. Quiz on factorial design is presentedhttp://highered.mcgraw-hill.com/novella/QuizProcessingServlet

12. Images of design of experiments :https://www.google.co.in/search?q=design+of+experiments&tbm=isch&tbo=u&source=univ&sa=X&ei=8Hk5UpXFBYeOrQfJrIDoAw&sqi=2&ved=0CDwQsAQ&biw=1280&bih=677&dpr=1

13. Design of experiments – basics : http://asq.org/learn-about-quality/data-collection-analysis-tools/overview/design-of-experiments.html

14. Design of experiments – tutorialhttp://asq.org/learn-about-quality/data-collection-analysis-tools/overview/design-of-experiments-tutorial.html

Quadrant 4 Numerical problems: Problems on confidence interval

1. Nine copper rods were found to have the following diameters in cm: 5.36, 5.76,6.77, 5.26, 4.39, 5.45, 6.09, 5.64, 5.81. Find out any reading that can be rejected.The ratio of maximum deviation to standard deviation should not exceed 1.80

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(Chauvenet’s criterion). Eliminate questionable points and calculate a new standard deviation for the adjusted data. Solution: SN Diameter

q, cm Deviation, d=q-q� d2 |d|/s

1 5.36 d1=5.36 – 5.614= -0.254 0.0647 0.3938 2 5.76 d2= 0.145 0.0211 0.2254 3 6.77 d3=1.155 1.3354 1.7891 4 5.26 d4= -0.354 0.1255 0.5486 5 4.39 d5= -1.224 1.4991 1.8956 6 5.45 d6 = -0.164 0.0270 0.2545 7 6.09 d7= 0.475 0.2261 0.7363 8 5.64 d8=0.025 0.0006 0.0396 9 5.81 d9=0.195 0.0382 0.3028 n = 9 Σq= 50.53 Σd2 = 3.3377 Arithmetic mean = q� = Σq / n = 50.53/9 = 5.614

Standard deviation = s = � ∑d2

(n−1) = �3.3377

8 = 0.6459

Fifth reading (ie 4.39) is eliminated, as the ratio �|d|s� is more than 1.80.

Calculation of new mean after excluding 5th reading is = 46.14/8 = 5.767 New Σd2 = 1.6511

New standard deviation = s = �(1.6511/7) = 0.4855

2. Given the following set of data: 18, 16, 11, 14, 12, 15, 13, 14, 12, 15, determine mean, mean deviation, and standard deviation. Solution: Readers are advised to solve the above problem, following the steps given in problem 1

3. Using the following data get y as a linear function of x using the method of least squares. Plot the scatter diagram and best fit line. Make a comment on the plot. Also, calculate the correlation coefficient. xi yi 1.1 1.2 1.6 2.0 3.4 2.5 4.0 4.3 5.5 4.3

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Solution: Σxi = 15.6 Σyi = 14.3 Σxiyi = 53.87 Σxi

2 = 61.58 Seeking an equation of the form y= ax+b

a= 𝑛 𝛴𝑥𝑖𝑦𝑖 − 𝛴𝑥𝑖 𝛴𝑦𝑖𝑛Σ𝑥𝑖2 –(Σxi )2

= 0.717

b= (Σyi)(Σ𝑥𝑖2 ) –(Σxiyi )(Σxi)

𝑛Σ𝑥𝑖2 –(Σxi )2 = 0.623

Desired relation is y = ax + b Y=0.717x+0.623 When , X=0, y=0.623 x=1, y = 0.717 + 0.623 = 1.34 x=5, y=4.208 x=6, y=4.925 Scatter diagram and best fit line obtained using Excel:

Comment on the plot: Initially, a scatter diagram is drawn. If particular data points have an erratic behavior as observed from the scatter diagram ( for example 3rd and 4th data points in the above scatter diagram), such points may be excluded, before attempting least square analysis , so that a better correlation is obtained. Readers may note that the values obtained for a and b are same as obtained by equations. Correlation coefficient:

y = 0.7169x + 0.6232 R² = 0.8536

0

1

2

3

4

5

0 2 4 6

y

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Ym = Σyi /n = 14.3/5 = 2.86 From the correlating equation, yic = ax+b = 0.717x+0.623 i xi yi yic (Yi - yic)2 (Yi – ym)2

1 1.1 1.2 1.411 0.044 2.755 2 1.6 2.0 1.77 0.053 0.739 3 3.4 2.5 3.061 0.314 0.129 4 4.0 4.3 3.491 0.654 2.073 5 5.5 4.3 4.566 0.071 2.073 Σ(Yi - yic)2 = 1.136 Σ(Yi – ym)2 = 7.769

σy,x = �Σ(Yi − yic)2 /(n − 2)P

= �1.136/3 = 0.615

σy = �Σ(Yi − ym)2 /(n − 1) = �7.769/4 = 1.393

Correlation coefficient = r =�1 − (σy, x)2/ (σy)2 = �1 − 0.6152

1.3932 = √0.805 = 0.897

Readers may calculate revised correlation coefficient , after removing the 3rd and 4th data points.

4. By using a vernier caliper, the following ten readings of diameter of thin cylinders are obtained: 1.34, 1.38, 1.56, 1.47, 1.42, 1.44, 1.53, 1.50, 1.40 and 1.60 mm. Calculate the following: arithmetic mean, average deviation, standard deviation and variance. What is the error with 95% confidence? Solution:

xi di = xi - �̅� di2 1.34 1.34 – 1.464 = -0.124 0.0153 1.38 -0.084 0.0070 1.56 0.096 0.0092 1.47 - 0.006 0.000036 1.42 -0.044 0.0019 1.44 -0.024 0.000576 1.53 0.066 0.0043 1.50 0.036 0.00129 1.40 -0.064 0.004 1.60 0.136 0.0185 Σx i = 14.64 Σdi2 = 0.0621

Arithmetic mean = �̅� = Σx i /n = 1.464 mm

Standard deviation = σ = �0.062110−1

= 0.0832

Variance = σ2 = 0.00692

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Error with 95% confidence = 1.96 σ = 0.1630 mm

Problem on Student’s t – distribution 5. Ten voltage readings are recorded in an experiment, with mean value of 16 V and

standard deviation of ± 0.1 V determine the 5% significance levels. Solution: n=10 Degrees of freedom = n-1 = 9

At 5% significance level, the probability is 95% and t95 = 2.262 (from table D5, Mechanical measurements by Prof SP. Venkateshan , Ane books pvt ltd.) ∆= t σ / √n = 2.262 x 0.1 /√10 = 0.0713 At 95% confidence level, the voltage is 16 ± 0.0713 V

6. Ten readings are taken of the diameter, in mm, of metal rods and are given below:

3.72 3.63 3.70 3.62 3.71 3.72 3.64 3.64 3.72 3.73 Determine the mean value and tolerance limits for a 95% confidence lev el. Solution: Σx i = 36.83, �̅� = 3.683 Σ d2 = Σ(xi - �̅�)2 = 0.0176

Sample standard deviation = σ = � ∑d2

(n−1) = �0.0176

9 = 0.044

Degrees of freedom = n-1 = 9, t95 = 2.262 (from table D5, Mechanical measurements by Prof S.P. Venkateshan , Ane books Pvt Ltd.) ∆ = t σ / √n = 2.262 x 0.044 / √10 = 0.0314 Tolerance limits for 95% confidence level = �̅� ± ∆ = 3.683 ± 0.0314

Multiple choice questions (Choose the correct answer)

1. A pressure gauge 0 to 100 Pa has a guaranteed accuracy of 1% of full scale deflection. The limiting error while reading 25 Pa will be a. 1% b. 2% c. 2.5% d. 4%

2. Measurement finds application in

a. Automatic control of processes and operations b. Engineering experimental analysis c. Monitoring of processes and operations d. All of these

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3. The measurement of a quantity or a variable is an act of comparison of an unknown quantity a. Or a variable with a predefined acceptable standard which is accurately

known b. Or a variable with another quantity or variable c. With a known quantity whose accuracy may be known or may not be known d. None of these

4. Which of the following can occur, due to mistakes in reading, parallax, improper

instrument location and poor lighting a. Construction error b. Transmission error c. Observation error d. Translation error

5. Gearing, backlash, friction between moving parts, and scale accuracies are

normally called a. Instrument errors b. Interference errors c. Calibration errors d. Interaction errors

6. Errors which may be variable both in magnitude and nature (positive or negative)

are classified as ------- errors a. Hysteresis b. Random c. Systematic d. Interaction

7. The characteristic of an observer to take either systematically higher or

systematically lower than other observers is referred to as a. Insensitivity b. Lack of precision c. Lack of discrimination d. Operator bias

8. Systematic errors in a Bourdon tube pressure gauge may be due to

a. Friction in the pins and gears of the amplifying mechanism b. Incorrect zero setting of the pointer c. Variation of atmospheric pressure d. Incorrect readings of the scale due to parallax

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9. A set of observations has a wide range and hence it has

a. Low precision b. High precision c. Low accuracy d. High accuracy

10. The surface temperature measurement in an exposed condition where

atmospheric variation can interfere with temperature measurement gives rise to a. Transmission error b. Interaction error c. Operation error d. Interference error

11. What represents the departure of the observed readings from arithmetic mean

of the group of readings? a. Dispersion b. Deviation c. Variance d. Median

12. A 0-300 V voltmeter has an error of ± 2% of full scale deflection. What would be

the range of readings if true voltage is 30V? a. 24V-36V b. 29.4V-30.6V c. 20V-40V d. None of these

13. A wattmeter has a full scale range of 2500 W. It has an error of ± 1% of true

value. What would be the range of reading if true power is 1250W? a. 1225W-1275W b. 1245W-1255W c. 1200W-1300W d. 1237.5W-1262.5W

14. A pressure gauge is calibrated between 10 bar and 250 bar. The span of the

gauge is a. 10 bar b. 250 bar c. 240 bar d. 260 bar

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15. The conformity of the output to the true value is known as

a. Precision b. Accuracy c. Sensitivity d. All of the above

16. The resolution of a system refers to

a. Smallest change in the measurand that can be measured b. True value of the input signal c. Retardation of the response d. None of the above

17. The biggest change in the measured variable which produces no response is

called a. Threshold b. Dynamic error c. Dead band d. None of the above

18. Which of the following describes the linearity of the measuring device

a. Range of inaccuracy which can be tolerated b. Biggest change in the measured value which produces no response c. Relationship between the output and the input d. None of the above

19. A reliable instrument

a. Presents reproducible results within specified limits b. Has good frequency response c. Has errors of same size and sign under the same working conditions d. Gives linear characteristics within the entire range

20. The dead time of a measuring instrument refers to

a. Change of input quantity for which there is no output b. The time encountered when the instrument has to wait for some recations to

take place c. The time before the measuring device begins to respond after the quantity

has altered d. Delay in response of a device to a change in the input signal

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21. In the simple linear regression model, if there is a very strong correlation between the independent and dependent variables, then the correlation coefficient should be close to a. Either -1 or +1 b. -1 c. +1 d. Near zero

22. In simple linear regression analysis, the input variable that is used to get the predicted value is the a. Random variable b. Independent variable c. Dependent variable d. Least-square variable

23. In simple linear regression analysis with X representing the independent variable and Y representing the dependent variable, if the Y intercept is negative, then the a. correlation between X and Y is positive b. correlation between X and Y could be either negative, positive, or zero c. predicated Y value is always negative d. correlation between X and Y is negative

24. Which of the following plots can be used to evaluate whether the normality assumption in regression analysis has been seriously violated? a. normal probability plot b. all of the above choices are correct c. histogram d. stem and leaf plot

25. Which of the following values is not a valid number for the coefficient of correlation? a. 1.2300 b. 0.7900 c. -0.9233 d. 0.0001

26. The standard deviation of the line of regression is called the

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a. Regression coefficient b. Standard error of the estimate c. Error sum of squares d. Regression sum of squares

27. __________ designs are research designs with more than one independent variable. a. Factored b. Monotonic c. Factorial d. Monotorial

28. In a 3 x 3 factorial design, ----------conditions are there in the experiment. a. 2 b. 3 c. 6 d. 9

Answer Table 1. d 2. d 3. a 4. c 5. a 6. b 7. d 8. b 9. a 10. d

11. b 12. a 13. d 14. c 15. b 16. a 17. c 18. c 19. a 20. c

21. a 22. b 23. b 24. b 25. a 26. b 27. c 28. d

Fill in the blanks with appropriate word/s

29. The prime function of the first stage is to --- -------the input signal 30. The function of the intermediate stage is to ----- amplitude or power of the signal 31. The third stage provides-----------to the observer or to a controlling unit 32. Error is the difference between ---- value and--- value 33. Precision is the degree of ---- of measurement

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34. Calibration consists of determining the ---- of system 35. Calibration is the process of ascertaining the ---- error 36. Bias error is a systematic error that can be removed by ----- 37. Accuracy is defined as the extent to which the reading of an instrument

approaches------- the value 38. The laser doppler velocimeter is an example for ----method of measurement 39. Measurement using pitot tube is an example for ---- type of measurement 40. Loading errors occur because of ---------by the process as it takes some energy

from the input source 41. Mean deviation is the sum of the------------divided by the number of deviations 42. Standard deviation is the -------------of the mean of the squares of the deviations 43. Variance is the-------------of the standard deviation 44. One kilogram is defined as the mass of ------bar maintained under very specific

conditions at International Bureau of Weights and Measurements at Sevres, France

45. Backlash is maximum----------- through which any part of mechanical system may be moved in one direction without causing motion of the next part

46. A device which amplifies the input signal is --------- 47. The act or process of making adjustments or markings on scale so that the

instruments readings conform to accepted standards is called ------- 48. In modern measurement systems, undesirable static characteristics are ----------, -

--------------,------------- and ------------- 49. Measurement is the act, or the result, of a quantitative -----between a pre

defined standard and an unknown magnitude 50. The limits of the deviations from the nominal value of a particular quantity are

termed as ---- errors 51. The ----- errors are due to conditions external to the measuring instrument 52. ---------- errors occur due to carelessness of operators 53. ----------is any signal that does not convey useful information 54. --------------- time is the time used by the instrument to show 63.2% change in

reading to a step input 55. Accuracy of a measuring instrument is expressed as a -------- of the true value of

the measurand 56. Dead zone is the biggest change in -------- quantity for which a noticeable change

in the output quantity is noticed from zero reading 57. Dead zone is caused due to ------ and ----- in the measuring device 58. The biggest change of input signal for which there is no output of the measuring

device is known as ----- 59. The time needed by an instrument to begin to respond to a change in the

measurand is known as ----

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60. The inability of the system to faithfully measure the input signal in undisturbed form is known as ---- --

61. The maximum amount by which the pointer moves beyond steady state is known as -------

62. The capability of the measuring instrument to react to the weakest signal is known as -------------

63. The deviation of the measured value to the preferred value is known as --------- Answer Table

29. Detect 30. Increase 31. Measured

information 32. Measured, true 33. Reproducibility 34. Scale 35. Systematic 36. Calibration 37. True 38. Non-intrusive 39. Intrusive 40. The change of input

source

41. Absolute deviations 42. Square root 43. Square 44. A particular platinum

–iridium 45. Angle or distance 46. Amplifier 47. Calibration 48. Dead zone, drift,

static error and non linearity

49. Comparison 50. Limiting 51. Environmental

52. Observational 53. noise 54. response 55. percentage 56. input quantity 57. backlash and

hysteresis 58. dead zone 59. dead time 60. load effect 61. overshoot 62. sensitivity 63. error

True /false

64. The random errors are small, accidental and independent 65. The random errors are predictable 66. The square of the standard deviation is variance 67. Accuracy is the nearness to the most wanted value 68. Precise, but inaccurate, measurement is feasible 69. Precision is nothing but exact value to the preferred value 70. Consistency describes the accuracy of the measurement 71. Due to wear and tear of the instruments systematic errors can occur

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Answer Table 64. T 65. F 66. T 67. T 68. T 69. F 70. F 71. T

Assignment questions and answers:

1. How the measurement systems are classified on the basis of applications? Ans: The measurement systems are classified on the basis of applications into 3 categories:

a. Monitoring of processes and operations. This refers to the situations where the measuring instrument is used to monitor a physical quantity. Examples of monitoring instruments are barometers, thermometers, anemometers etc. These devices simply indicate the environmental condition, and they do not do any control functions. Another example is a pressure gauge mounted on a boiler to indicate the pressure inside the boiler.

b. Controlling of processes and operations. This refers to an automatic feedback control system. Examples of this are room air conditioning system, temperature controlling system in a melting furnace.

c. Experimental engineering analysis. This refers to a laboratory testing system which measures some physical quantity such as pressure in a cylinder or flow rate of a fluid in a pipe line

2. Mention some examples of measurement systems Ans: A few examples of measurement systems are mentioned below: 1. Digital revolution counter 2. Room air conditioning system 3. Pressure measurement in a pipe line using a Bourdon pressure gauge 4. Pressure gauge mounted on a boiler to indicate the pressure inside the boiler. 5. Temperature controlling system in a melting furnace. 6. Flow rate measurement of a fluid in a pipe line 7. Engine speed measurement system

3. Discuss the procedure of calibration with an example of Bourdon gage

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Ans: Example taken is a Bourdon pressure gauge. The detailed procedure of calibrating it is given below: 1. Remove the piston of the dead weight calibrator. 2. Fill the cylinder with hydraulic oil 3. Remove the air trapped in the oil 4. Insert the piston into the cylinder 5. Add available masses on the top of the piston and record them in a table 6. Record the pressure gage reading, along with the masses added on the piston,

total mass (piston mass and added mass) in the above table 7. Remove the masses previously added on the top of the piston and record them

in the table. The pressure gauge reading, along with the masses removed from the piston, and the total mass (piston mass and added mass) are recorded in the above table.

8. Repeat this procedure 5 times. 9. Calculate the actual pressure P due to a mass of M kg(including the piston mass),

P = M*9.81/A where A is the piston area in m2 10. Calculate the average measured pressure for increasing and decreasing pressures

and the average pressure of the two for each applied mass. 11. Calculate the standard deviation σ for each of the two procedures for each

applied mass. 12. Finally, calculate the gage % error. 13. Plot the following graphs:

a. Gage pressure versus actual pressure (both increasing and decreasing) b. Gage error versus actual pressure (both increasing and decreasing) c. Standard deviation versus actual pressure (both increasing and

decreasing) 14. Comment on errors such as incorrect marking on scale, friction between piston

and cylinder 15. Comment on the fluctuations of measurements and the repeatability of the

experiment 4. List the reasons for occurrence of random errors

Ans: The reasons for random errors are given below: a. Friction between moving parts in the instrument b. Backlash in the movement of the indicator, hysteresis in elastic members c. Mechanical vibration d. Variation of temperature e. Parallax errors between pointer and scale f. Hysteresis in elastic members

5. How the errors in measurement systems are classified?

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Ans: Error classification is given below 1. Systematic errors

a. Calibration errors b. Human errors c. Experimental errors d. Loading errors

2. Random errors a. Errors due to different experimental conditions b. Parallax errors

3. Illegitimate errors a. Blunders or mistakes b. Computational errors c. Chaotic errors

6. What is dead zone? What are the factors responsible for dead zone? Ans: Dead zone is the biggest change in the measurand for which a noticeable change in the output quantity is observed from zero reading. It occurs due to friction in the measuring instrument, which does not allow the pointer to move from zero reading till sufficient driving force is developed to overcome the frictional forces. It is also caused by backlash and hysteresis in the measuring instrument.

7. What is accuracy? Explain it with an example. Also, express it mathematically. Ans: Accuracy of a measuring instrument is expressed as a percentage of the true value of the measurand. Thus, an accuracy of +/ - 1% in a temperature measuring device would mean that inaccuracy is +/- 1oC when reading 100oC or only +/- 0.25oC when reading 25oC on an instrument having a scale range of 0-100oC. Accuracy is expressed mathematically as Accuracy (%) =(result - actual value)x100/(actual value)

8. Discuss briefly the various reasons for the occurrence of the observational errors. Ans: The various reasons for the occurrence of the observational errors are briefly discussed below: 1. Parallax: This error occurs when the pointer and the scale are not in the same plane. 2. Wrong recording of the data 3. Lack of ability to interpolate between graduations 4. Personal bias – tendency to read high or low

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9. List the common sources of errors in measuring process. Ans: 1. Poor design of measurement setup 2. Poor maintenance of the setup 3. Design limitations 4. Operator error 5. Change in process parameters 6. Inadequate data about process 7. Environmental changes

10. List the important factors to be considered for the proper selection of a correct

measurement instrument for any application Ans: 1. Accuracy and range required

2. On-line or Off-line measurement 3. Cost of measurement

4. Form of data needed (Indicating or recording) 5. Space available for assembly 6. Continuous or intermittent measurement

11. In the design of an experiment, what are the issues an experimental program should address?

Ans: Following are the issues to be addressed in an experimental program: i. Number of quantities involved in the experiment

ii. Is the trend linear or non-linear? iii. How different are the influence coefficients? iv. What does dimensional analysis indicate? v. Is it possible to identify dimensionless groups that influence the quantity or

quantities being measured.

Self answered questions and answers: 1. Explain the importance of engineering measurements

Ans: Visit website nptel.iitm.ac.in/courses/IIT-MADRAS/ Mechanical_Measurements (module 1) Fig.1

2. List the various errors in measurements Ans: Visit website nptel.iitm.ac.in/courses/IIT-MADRAS/ Mechanical_Measurements (sub-module 1.2) Fig.3

Test your skills:

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1. The arithmetic mean of given n readings is calculated using the following expression

a. �̅� = Σx /(n-1) b. 𝒙� = Σx /n c. �̅� = Σx2

/n d. �̅� = Σx /n2

2. Standard deviation and variance are related by a. V= √ σ b. V= σ2 c. V= 1/ σ d. V=1/√ σ

3. Visit an industry near to your place, and find out the various measuring instruments they are using for their processes. Also learn how they are calibrated.

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