CMC Dimension

 

DEPTH Gauge Determination of Measurement Measurement Uncertainty of Depth Gauge Up to 300 mm Range :

300

mm

Least Count:

10

microns

300

mm

300

Size of Caliper

0.316069613

Uncer. Of S.G.(micro

0

Uncertainty Of surface plate(micron) Unit of Measurement :

=

4.6 microns

Reading Point :

Uncertainty of Temperature Temperature Scanner =

0.39

o

Accuracy

0.12

Surface Plate

Slip Gauge

 C 5

microns

 

Type 'A' Evaluation

Five Readings are taken and the deviation from the nominal value is as followsn

Mean Deviation x

( xj)n

=

 j=1 2

Measured/Observed Readings

Standard Value

Avearge

(xj-x)

(xj-x)

mm

mm

mm

microns

microns

4.0000 -6.0000 4.0000 -6.0000 4.0000 -6.0000 4.0000 4.0000 -6.0000 4.0000 0.0000

16.000 36.000 16.000 36.000 16.000 36.000 16.000 16.000 36.000 16.000

5.1640

microns

1.6330 1.6330

microns microns

300 300 300 300 300 300 300 300 300 300

300.01 300.00 300.01 300.00 300.01 300.00 300.01 300.01 300.00 300.01

300.0060

   (Xj - X)

Standard Deviation =

2

  n-1 2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertaint y in Type 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. slip gauge

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab = 2

U1 

=

0.32 2

 =

0.158

microns

0.115

microns

300.000

mm

 2. Standard Uncertainty Due to the wringing of Standard Equipment used i.e. slip gauge/Slips

 

The value of Uncertainty is taken from its calibration certificate Assuming Rectangular distribution

U2

=

0.2

 =

1.732

3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard   Assuming rectangular distribution. U3

=

L X a  X dt 3

here        

Length L 20 % of a1 a2 a  a1  Th. Coefficient of Expansion of DStandard a2  Th. Coefficient of Expansion of UUC Limit or 10% of Temp. 20 °C dt = Control Limit 0.960 3

4.Standard Uncertainty Due to the Resolution of Depth Gauge

=

3.24 X 10-6 / Deg C = =

4.7 X 10-6 / Deg C 11.5 X 10-6 / Deg C 1.0

Deg C

0.554

microns

 

 

Considering half of the leas leastt count & assuming assuming rectangular distribution

U4

10

=

2x

2.887

=

1.732

microns

5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC Assuming rectangular distribution.

5 Where

3

L

 

   

L  X a  X dt

=

a

=

Length

=

 

 (a1+a2)/2

=

d

300.00

=

mm

8.1X 10

-6

-6

O

-6

O

11.5X 10 /  C

a1

=

Th. Coefficient of Expansion

=

a2

=

Th. Coefficient of Expansion 20% of Temp. Limit ± 1ºC

=

11.5 X 10 /  C 0.2

=

0.2806

U5

0.486

=

3

Deg C

microns

6.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner

 

The value of Uncertainty is taken from its calibration certificate i.e. =0.35

U6  Where

L

2

=

 

a

 

d

U6

L  X a  X dt

=

Length

= =

300

=

Th. Coefficient of Expansion of slip gauge =

0.39

Uncertainty of temperature scanner 1.346

=

=

2

mm -6 o

11.5 X 10 /  C o

 C

0.6728

microns

 7.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Surface Plate

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab = 2

U7

4.60 2

=

 =

2.300

microns

=

0.069

micron

=

2.887

micron

2.887

micron

1.950

micron

8. Standard Uncertainty Due to the Accuracy of Master Equipment Considering half of the accuracy & assuming rectangular distribution

U8 

0.12

=

 

3

8. Standard Uncertainty Due to the Accuracy of Master Equipment Considering half of the accuracy & assuming rectangular distribution

U8 

5.00

=

 

3

8. Standard Uncertainty Due to the Accuracy of Master Equipment caliper Considering half of the accuracy & assuming rectangular distribution

U8 

5.00

=

 

=

3

8. Standard Uncertainty Due to the Uncertainityof Master Equipment caliper Considering half of the accuracy & assuming rectangular distribution

U8 

3.90

=

=

2

Combined Uncertainty:

Uc

=

 Uc

=

 

2

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3)

6.135

microns

Degree of Freedom, (Veff ) 4

Veff  

=

uc(y)

4

n(ui(y) )  j=1

  Vi

 

=

1793.317216

 



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement Measurement : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.

  U e  = k e x Uc Therefore uncertainty uncertainty in above measurem measurement ent is = ±

 

=

2

x

6.135

microns

12.3

microns

   

Feeler Gauge Determination of Measuremen Determination Measurementt Uncertainty of Feeler Gauge 1.00 mm Feeler Gauge Range : Reading Point = Uncer. in D. M. M. ( mm):

mm

1. 00 =

microns

2.10

Unit of Measurement :

=

microns o

0.39

Uncertainty of Temperature Scanner =

 C

Type 'A' Evaluation

 

Five Readings are taken and the deviation from the nominal value is as follows :-

 

Mean Deviation x

n

( xj)n

=

 j=1

Standard Value mm

Measured/Observed Readings Measured/Observed mm (xj)

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

1.002 1.003 1.002 1.002 1.003 1.001 1.002 1.002 1.003 1.002  

Standard Deviation , S(X)

Average

(xj-x) microns

(x)

(x)

   (Xj - X)  

2

microns

-0.2000 0.8000 -0.2000 -0.2000 0.8000 -1.2000 -0.2000 -0.2000 0.8000 -0.2000

1.0022

=

(xj-x)

0.0400 0.6400 0.0400 0.0400 0.6400 1.4400 0.0400 0.0400 0.6400 0.0400

2

n-1

=

0.632

microns

0.200 0.200

microns microns

 =

1.050

microns

 =

0. 0003

microns

1.000

mm

2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

 

=

Standard Uncertainty in Ty Type pe 'A' Evaluation, Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the Digital Micro Meter  

The value of Uncertainty is taken from its calibration certificate

Coverage Factor of Calibrating Lab = 2

Assuming Normal distribution

2.10 2

  U1 =

2. Standard Uncertainty Due to Half of least count of Digital Micro Mete Meterr  

Assuming Rectangular distribution

U2

0.001

=

2x

3

3. Standard Uncertainty Due to thermal Coefficient between Master Instrument & UUC

Assuming rectangular distribution.

 

  L  X a  X dt 3

U 3  = Where

=

Length

20 % (a1+ a2)

 

a

 

a1

=

Th. Coefficient of Expansion

=

11.5 X 10-6 / O C

   

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

d

=

L

=

Control Limit or 10% of of Temp. 20 °C

-6

1

O

Deg C

  

0.0046 3

  U3 =

0.0027

=

microns

 4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC

Assuming rectangular distribution.

U4 Where

L

 

   

L  X a  X dt

=

a

3

=

Length

 

 (a1+a2)/2

=

d

1.00

=

mm

11.5 X 10

-6

-6

O

-6

O

a1

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

a2

=

Th. Coefficient of Expansion 20% of Temp. Limit ± 1ºC

=

11.5 X 10 /  C 0.2

=

U4

0.002

=

0.0013

=

3

Deg C

microns

 5. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner

  The value of Uncertainty is taken from its calibration certificate i.e. =  

o

0.39

 C

Assuming Normal distribution.

  Where

 

a

 

d

= =

L  X a  X dt

U6  = L

2

=

Length

Th. Coefficient of Expansion

11.5 X 10

=

Uncertainty of temperature Scanner

mm -6

/

o

 C o

0.39

=

0.00449

U 6  =

1.000

=

2

 C

=

0.002243

microns

 =

0. 0012

microns

2. Standard Uncertainty Due to Accuracy of Digital Micro Meter   Assuming Rectangular distribution

U2

0.002

=

3

Combined Uncertainty:

 

Uc

=

 

Uc

=

 

2

2

2

(UA) +(U1) +(U2) +(U3)

2……………………………………………

microns

1.069

Degree of Freedom, (Veff ) 4

 

uc(y)

Veff   =

    (ui(y)4)  j=1

  Vi

  7342.543831 Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k  =2.  

 

=

U

=

Therefore uncertainty uncertainty in above measuremen measuremen

k x Uc

 

±

=

2

2.14



=

x

microns

1.069

microns

2.138

microns

 

EXTERNAL MICROMETER  Determination of Measurement Uncertainty of Micrometer Range upto 0 to 100 mm Micrometer Range :

100

mm

Least Count:

0. 17

microns

No. Of Slip Used

Slip Gauges used for calibration Uncer.of std.

1

Reading Points

=

Unit of Measurement :

=

microns

100

mm

1

microns o

Uncertainty of Temperature Temperature Scanner =

0.39

Wringing of Slip Gauges

0. 2

microns

Accuracy of Slip Gauges

0. 12

microns

 C

 

Type 'A' Evaluation

Five Readings are taken and the Deviation from the nominal value is as follows-

  Mean Deviation x

n

( xj)n

=

 j=1

Measured/Observed Measured/Obser ved Readings

Standard Value

99.997 99.997 99.997 99.997 99.997 99.997 99.997 99.997

100 100 100 100 100 100 100 100

99.997 99.997

100 100

Avearge

(xj-x)

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.0000 0.0000

0.000 0.000

0.0000

microns

0.0000 0.0000

microns microns

 =

0. 085

microns

=

0. 289

microns

=

100.000

mm

99.9970

   (Xj - X)

Standard Deviation =

2

(xj-x)

2

n-1

= 2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainty in Type 'A' Evaluation, UA

=

Type 'B' Evalution  1. Standard Uncertainty Due to the uncertainty of Standard Equipment Equipment used i.e. Slip Gague

   

The value of Uncertainty Uncerta inty is taken from its calibration certifica certificate te Assuming Normal distribution U1 

=

0.17 2

 = 2

2. Standard Uncertainty Due to the Resolution of External Micrometer Micrometer Considering half of the least count & assuming rectangular distribution

U2

=

1 2x

3

3. Standard Uncertainty Due toThermalCoefficient of UUC & Standard   Assuming rectangular distribution.

U3

=

L X a  X dt 3

Where    

L = Length a1 a2 20 % of a  = a1  = Th. Coefficient of Expansion of DStandard a2  = Th. Coefficient of Expansion of UUC of Temp. 20 °C dt = Control Limit or 10% of

3.24 X 10-6 / Deg C 4.7 X 10-6 / Deg C

=

11.5 X 10-6 / Deg C

= 1.0

Deg C

 

0. 064 8

0. 037

microns

0. 000

microns

3 4. Standard Uncertainty Due to the Wringing of Slip Gauge Considering half of the least count & assuming rectangular distribution

U4

0

=

=

3

 5. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC assumed as 0.5 deg C   Assuming rectangular distribution.

U5  Where

L

 

a

L  X a  X dt

=

3

=

Length  (a1+a2)/2

=

  d

100.00

=

8.1 X 10

a1

=

Th. Coefficient of Expansion

=

a2

=

Th. Coefficient of Expansion

=

-6

U5 

0.162

=

 

=

3

-6 O

4.7 X 10 /  C

20% of Temp. Limit ± 1ºC

=

mm

-6

O

11.5 X 10 /  C

0.2

Deg C

0.0935

microns

6. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner

 

The value of Uncertainty Uncerta inty is taken from its calibration certifica certificate te i.e. = U6 Where

 

Length

=

Th. Coefficient of Expansion of Slip Gague =

d

U6

 C

2

=

a

o

L  X a  X dt

= L

0.39

=

=

Uncertainty of temperature scaner

2

mm -6 o

8.1 X 10 /  C

=

0.316

=

100. 0

0.39

o

 C

=

0.1580

Deg C

=

0.069

micron

7. Standard Uncertainty Due to the Accuracy of Master Equipment Considering half of the accuracy & assuming rectangular distribution

U7 

0.12

=

3

Combined Uncertainty:

 

Uc

=

 

Uc

=

2

 

2

2

(UA) +(U1) +(U2) +(U3) 0.361

2……………………………………………

microns

Degree of Freedom, (V eff ) 4

uc(y)

Veff  

=

4 n(ui(y) )  j=1

  Vi

 

=

3.0423E+44

 



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.   U e  = k e x Uc   = 2 x 0.361 Therefore uncertainty in above measurement is

=+

microns

0.722

microns

0. 7

microns

 

INTERNAL MICROMETER  Determination Determinatio n of Measuremen Measurementt Uncertainty of Micrometer Range upto 100 mm INTERNAL MM Range

100

mm

Least Count:

1

micron

 Accessories & Slip Gauge Set is Used For Calibration Uncer. Of Slip Gauge

0.12

Accuracy of Slip Gauge

0.10

micron

Uncer. Of Slip Gauge Accessories

2.40

micron

Unit of Measurement :

=

micron

microns

Uncertinty of Temperature Scanner =

0.39

Accuracy of Master Equipment (Slip Gauge)

0.1

No. of Slip

Reading Point :

Mean Deviation x

mm

50

o

 C

Surfaced plate

0

Type 'A' Evaluation Five Readings are taken and the deviation from the nominal value is as follows-

 

1

 

n

( xj)n

=

 j=1

Measured/Observed Re Readings

Standard V Va alue

49.998 49.999 49.998 49.999 49.999 49.999 49.998

50.000 50.000 50.000 50.000 50.000 50.000 50.000

49.998 49.998 49.999

50.000 50.000 50.000

Avearge

49.9985

   (Xj - X)

Standard Deviation =

2

(xj-x)

(xj-x)

microns

microns

-0.5000 0.5000 -0.5000 0.5000 0.5000 0.5000 -0.5000

0.250 0.250 0.250 0.250 0.250 0.250 0.250

-0.5000 -0.5000 0.5000

0.250 0.250 0.250

0.5270

microns

0.1667 0.1667

microns microns

0.060

microns

2

n-1

= Standard Deviation of the Mean, S ( X)

[S(X)] n

=

2

= Standard Uncertainty in Type 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty uncertainty of Standard Equipment used i.e. Slip Gauge

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution U1 

 = 2

0.12

=

 =

2

 2. Standard Uncertainty Due toThermal Coefficient of UUC & Standard   Assuming rectangular distributi on.

U2

=

L  X a  X dt 3

L

=

Length

=

 

a

=

  20% of ( a1 +a2)

 =

 

a1

=

Th. Coefficient of Expansion

=

4.7 X 10 / Deg C

 

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 / Deg C

 

d

=

Control Limit or 10% of Temp. 20 °C

U 2 

=

0.324 3

-6

3.24 X 10 / Deg C -6

-6

1

0.187

=

3. Standard Uncertainty Due to the uncertainty uncertainty of Standard Equipment used i.e. Slip Gauge Accessories

 

mm

100

Where

The value of Uncertainty is taken from its calibration certificate Assum suming Normal dist strribution Coverage Factor of Calibrating Lab =

2.40

=

=2

Deg C

microns

 

3 

.

2

4. Standard Uncertainty Due to the Resolution of lnternal Micrometer Considering half of the least count & assuming rectangular distribution

U4 

1

=

2x

=

3

0.289

microns

 5. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC Assuming rectangular distribution.

U 5 

L  X a  X dt

=

Where

L

3 =

mm

=

Length

= a1

=

 (a1+a2)/2 Th. Coefficient of Expansion

=

4.7 X 10 / Deg C

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 / Deg C

100

-6

   

a

   

d

8.1 X 10 -6

-6

20% of Temp. Limit ± 1ºC

=

U 5 

0.2

0.162

=

0.094

=

3

Deg C

microns

6. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner

   

The value of Uncertainty is taken from its calibration certificate i.e. =

0.39

o

 C

Assuming rectangular distribution.

U6  Where

L

 

a

 

d

U6 

L  X a  X dt

=

2 =

Length

= =

=

100 4.7 X 10-6 / Deg C

Th. Coefficient of Expansion of Slip Gague = Uncertainty of temperature Scanner

0.39

=

0.183

=

=

1.732

mm o

 C

0.1058

microns

0.029

micron

0.000

micron

0.029

micron

7. Standard Uncertainty Due to the Accuracy of Master Equipment (Slip Gauge) Considering half of the accuracy & assuming rectangular distribution

U 7 

0.1

=

 2

=

3

8. Standard Uncertainty Due to the Accuracy of Master Equipment (Surface Plate)  

Assuming rectangular distribution ((20% 20% of Full Accuracy)

U 8 

0

=

 

=

3

9. Standard Uncertainty Due to the Accuracy of Master Equipment (Slip GaugeAccessories) Considering half of the accuracy & assuming rectangular distribution

U 9 

0.1

=

 2

=

3

Combined Uncertainty:

 

Uc

=

 

Uc

=

2

 

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3) 1.266

microns

Degree of Freedom, (Veff ) 4

Veff  

uc(y)

=

4

n(ui(y) )  j=1

  Vi

 

=

29956.10739

 



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement : From the student's distribution table, for the Confidence Level approxim approximately ately 95%, the Coverage Factor, k =2.   Ue  = k e x Uc   = 2 x microns 1.266 Therefore uncertainty in above measurement is

=+

2.532

microns

2.53

microns

 

Micrometer Setting Standard Determination of Measurement Uncertainty of Micrometer Setting Standard  Range :

75

mm

Reading points 25

Range Uncertainty in S.G. (mm):

=

Unit of Measurement :

=

mm

75

100

50

0.14

0.17

0.12

Average

(xj-x)

(xj-x)

microns

microns

0.10

Uncer. in Comp Stand(micron)

75

2.85

microns

0.39

Deg C

microns

Uncertinty of Temperature Scanner = Uncer. Of Dial Indicator =

0.3

micron

Accuracy of Slip Gauge Set

0.12

micron

Type 'A' Evaluation Five Readings are taken and the deviation from the nominal value is as follows  Mean Deviation x

=

n

(å xj)¸n  j=1

Measured/Observed Readings

 Value

mm

mm

(xj)

 

2

(x)

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

75.0006

75

0.0000

0.000

Standard Deviation , S(X)

75.0006

2

  å (Xj - X)

=

 

n-1

=

0.0000

microns

0.000

microns

0.000

microns

2

[S(X)] Standard Deviation of the Mean, S ( X)

=

n =

Standard Uncertainty in T Type ype 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Comp Stand  

Assuming Normal distribution

Coverage Factor of Calibrating Lab

U1 

2.85

=

2

=2  =

1.425

microns

 =

0.289

microns

 2. Standard Uncertainty Due to 50% of Resolution of Standard Dial Gauge  Assuming Rectangular distribution U2 

=

0.2 2

3

3. Standard Uncertainty Due to Thermal Coefficien of Master Instrument & UUC .  

Assuming rectangular distribution.

for Master

U3

L  X a  X dt

=

3

Where

L

=

 

a

=

 

a1

=

Length   20% of ( a1 +a2) Th. Coefficient of Expansion

a2

=

Th. Coefficient of Expansion

 

d

=

Control Limit or 10% of Temp. 20 °C

U3 

=

3 4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC.  

Assuming rectangular distribution.

mm -6

-6

O

O

11.5 X 10 /  C

=

0.2430

75.00 0.0000032 4.7 X 10 /  C

=

 

=  =

=

1

Deg C

0.140

microns

  

U4 Where

L

 

L  X a  X dt

=

a

3 =

Length  (a1+a2)/2

=

75.00

=  

mm -6

O

-6

O

8.1 X 10 /  C

 

a1

=

Th. Coefficient of Expansion

=

4.7 X 10 /  C

   

a2

=

Th. Coefficient of Expansion 20% of Temp. Limit ± 1ºC

=

11.5 X 10 /  C

d

= U4

-6

0.122

=

=

3

O

0.2

Deg C

0.0702

microns

5. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner    

0.39

The value of Uncertaint Uncertainty y is taken from its calibration certific certificate ate i.e. = Assuming Normal distribution. U6  Where

   

a d

= =

L  X a  X dt

= L

2 =

Length

75.00

=

Th. Coefficient of Expansion

8.1 X 10 / Deg C

=

0.32

Deg C

0.0972

microns

0.068

microns

 =

0.150

microns

=

0.069

micron

=

3.464

micron

=

0.231

micron

= 0.194

=

mm -6

Uncertainty of temperature Scanner U6 

Deg C

=

2

6 . Standard Uncertainty Due to the uncertainty of Standard Slip Gauge set  

Assuming Normal distribution

Coverage Factor of Calibrating Lab

U7 

0.140

=

=2  =

2

 7. Standard Uncertainty Due to the uncertainty of Standard Dial Indicator  

Assuming Normal distribution

Coverage Factor of Calibrating Lab

U8 

0.30

=

2

=2

8. Standard Uncertainty Due to the Accuracy of Master Equipment Considering half of the accuracy & assuming rectangular distribution

U8 

0.12

=

 

3

9. Standard Uncertainty Due to the Accuracy of comparator Considering half of the accuracy & assuming rectangular distribution

U8 

6

=

 

3

10. Standard Uncertainty Due to the Accuracy of dial Indicator Considering half of the accuracy & assuming rectangular distribution

U8 

0.4

=

 

3

Combined Uncertainty: Uc   Uc

2

 

=

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3) 3.773

=

microns

Degree of Freedom, (Veff ) 4

Veff  

uc(y)

=

4

n(ui(y) )  j=1

  Vi

 

=

3.62159E+48

 



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.  

U = k x Uc

Therefore uncertainty in above measurement is

  = ±

2

x

3.773

microns

7.546 7.546

microns microns

 

Plain Plug Gauge Determination of Measurement Uncertainty Uncertainty of Plain Plug Gauge 100

PP Gauge Range :

mm

Reading points 25

Range Uncertainty in S.G. (mm):

=

50

0.14

0.17

0.12

Average

(xj-x)

(xj-x)

microns

microns

2.85

microns

Uncertinty of Temperature Scanner =

0.39

Deg C

Uncer. Of Dial Indicator =

0.3

micron

Accuracy of Slip Gauge Set

0.12

micron

Unit of Measurement :

=

mm

100

0.09

Uncer. in Comp Stand(micron)

100

75

microns

Type 'A' Evaluation Five Readings are taken and the deviation from the nominal value is as follows  Mean Deviation x

=

n

(å xj)¸n  j=1

Standard Value

Measured/Observed Readings mm

mm

(xj)

 

2

(x)

99.9864

0.000

0.0200

0.000

99.9866

0.000

0.2200

0.048

99.9864

0.000

0.0200

0.000

99.9866

0.000

0.2200

0.048

99.9866

0.000

0.2200

0.048

99.9864

0.000

0.0200

0.000

99.9862

0.000

-0.1800

0.032

99.9860

0.000

-0.3800

0.144

99.9864

0.000

0.0200

0.000

99.9862

0.000

-0.1800

0.032

Standard Deviation , S(X)

99.9864

2

  å (Xj - X)

=

 

n-1

=

0.1989

microns

0.063

microns

0.063

microns

2

[S(X)] Standard Deviation of the Mean, S ( X)

=

n =

Standard Uncertainty in T Type ype 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Comp Stand  

Assuming Normal distribution

Coverage Factor of Calibrating Lab

U1 

2.85

=

2

=2  =

1.425

microns

 =

0.289

microns

 2. Standard Uncertainty Due to 50% of Resolution of Standard Dial Gauge  Assuming Rectangular distribution U2 

=

0.2 2

3

3. Standard Uncertainty Due to Thermal Coefficien of Master Instrument & UUC .  

Assuming rectangular distribution.

for Master

U3

L  X a  X dt

=

3 100.00 0.0000032

mm

=

a

=

 

a1

=

Th. Coefficient of Expansion

=

4.7 X 10 /  C

 

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

 

d

=

Control Limit or 10% of Temp. 20 °C

=

0.3240

3 4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC.  

=

L

U3 

Length   20% of ( a1 +a2)

 =

Where

 

Assuming rectangular distribution.

-6

-6

=

O

O

1

Deg C

0.187

microns

  

U4 Where

L

 

L  X a  X dt

=

a

3 =

Length

=

100.00

=

 (a1+a2)/2

 

mm -6

O

-6

O

8.1 X 10 /  C

 

a1

=

Th. Coefficient of Expansion

=

4.7 X 10 /  C

   

a2

=

Th. Coefficient of Expansion 20% of Temp. Limit ± 1ºC

=

11.5 X 10 /  C

d

= U4

-6

0.162

=

=

3

O

0.2

Deg C

0.0935

microns

5. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner    

0.39

The value of Uncertaint Uncertainty y is taken from its calibration certific certificate ate i.e. = Assuming Normal distribution. U6  Where

   

a d

= =

L  X a  X dt

= L

2 =

Length

100.00

=

Th. Coefficient of Expansion

8.1 X 10 / Deg C

= = 0.259

=

mm -6

Uncertainty of temperature Scanner U6 

Deg C

=

2

0.32

Deg C

0.1296

microns

0.068

microns

0.150

microns

0.069

micron

0.231

micron

3.464

micron

6 . Standard Uncertainty Due to the uncertainty of Standard Slip Gauge set  

Assuming Normal distribution

Coverage Factor of Calibrating Lab

U7 

0.136

=

=2  =

2

 7. Standard Uncertainty Due to the uncertainty of Standard Dial Indicator  

Assuming Normal distribution

Coverage Factor of Calibrating Lab

U8 

0.30

=

=2  =

2

8. Standard Uncertainty Due to the Accuracy of Master Equipment slip gauge Considering half of the accuracy & assuming rectangular distribution

U8 

0.12

=

=

3

8. Standard Uncertainty Due to the Accuracy of Master Equipment dial indicator Considering half of the accuracy & assuming rectangular distribution

U8 

0.4

=

=

3

8. Standard Uncertainty Due to the Accuracy of Master Equipment comparator stand Considering half of the accuracy & assuming rectangular distribution 6

U8 

=

=

3

Combined Uncertainty: Uc   Uc

2

 

=

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3) 3.777

=

microns

Degree of Freedom, (Veff ) 4

Veff  

uc(y)

=

4

n(ui(y) )  j=1

  Vi

 

117040446

=

 



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.  

U = k x Uc

Therefore uncertainty in above measurement is

  = ±

2

x

3.777

microns

7.554 7.554

microns microns

 

0.851

Snap Gauge Determination Determinati on of Measuremen Measurementt Uncertainity of Snap Gauge 1 00

Snap Gauge Range : Uncertainity in S.G. (mm):

mm

Reading Point :

=

Uncertainty due to Wringing of S.G. Unit of Measurement :

=

100

mm

20

75

100

0. 09

0. 14

0. 17

Average

(xj-x)

(xj-x)

microns

microns

microns

Uncertinty of Temperature Scaner =

0.39

Deg C

Accuracy of master equipment

0. 12

Micron

Type 'A' Evalution Five Readings are taken and the deviation from the nominal value is as follows  Mean Devitation x

n

(å xj)¸n

=

 j=1

Standard Value

Measured/Observed Measured/Obser ved Readings mm

mm (x)

(xj)

 

2

119.150

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

119.150

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

119.150

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

119.150

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

119.150

0 .0 0 0

119.150

0 .0 0 0

119.150 119.150

0 .0 0 0 0

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

119.150

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

119.150

0 .0 0 0

0 .0 0 0 0

0 .0 0 0

0. 000

microns

0. 000

microns

0. 000

microns

0. 085

microns

Standard Devitation , S(X)

119.1500

2

  å (Xj - X)

=

n-1

= 2

[S(X)]

Stabdard Devitation of the Mean, S ( X)

n

= =

Standard Uncertainity in Type 'A' E Evalutation, valutation, UA

=

Type 'B' Evalution  1. Standard Uncertainity Due to the uncertainty of Standard Equipment Equipment used i.e. Slip Gague  

The value of uncertainity is taken from its calibration certificate (Up to 20 mm) Assuming Normal distribution

Coverage Factor of Calibrating Lab

U1 

0.17 2

=

=2

 =

2. Standard Uncertainity Due to Thermal Coefficient between UUC & Standard.   Assuming rectangular distribution.

U2 Where

L a

 

dt

U2

3 =

 

Length

=

=

L  X a  X dt

 

=

=

Th. Th. Coef Coeffi fici cien entt of Expa Expans nsio ion n of Slip Slip Gague ague = =

Temperature Variation or Temp. Difference =

0.470 3

100. 0

mm -6

4.7X 10 / Deg C 1

Deg C

=

0. 271

microns

=

-0.115

microns

3. Standard Uncertainity Due to the Wringing of Slip Gagues  

Assuming Rectangular distribution

U3

=

-0.20 3

 4. Standard Uncertainity Due to the Temp. Variation in Master Instrument & UUC assumed as 0.5 deg C   Assuming rectangular distribution. U4

=

L  X a  X dt 3

  

Where

L

=

 

a

 

dt

U4

Length

=

100. 0

=

Temperature Variation or Temp. Difference =

0.470

=

=

3

O

6.8 X 10 /  C

Th. Th. Coef Coeffi fici cien entt of Expa Expans nsio ion n of Slip Slip Gague ague = =

mm -6

1

Deg C

0. 271

microns

 5. Standard Uncertainity Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner Temp.Scanner    

The value of uncertainity is taken from its calibration certificate i.e. = Assuming Normal distribution.

U5  Where

a

 

dt

U5 

2 =

 

Deg C

L  X a  X dt

= L

0. 39

Length

=

=

100. 0

4.7X 10 / Deg C

Th. Th. Coef Coeffi fici cien entt of Expa Expans nsio ion n of Slip Slip Gague ague = =

Uncertainty of temperature scaner

0.183

=

= =

2

mm -6

0. 39

Deg C

0. 0917

microns

0. 069

microns

6. Standard Uncen. due to Accuracy Master Equipment. Equipment. Slip gauge Considering half of the accuracy & assuming rectangular distribution

U6 

0.12

=

=

3

Combined Uncertainity:  Uc

=

Uc Degree of Freedom, (V eff )

=

2

 

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3)

microns

0.425 4

Veff  

uc(y)

=

4

ån(ui(y) )  j=1

  Vi

 

=

 

#DIV/0!

=

¥

Expanded Uncertainity of Overall Uncertainity or Uncertainity of Measureme Measurement nt : From thestudent's distribution ta ble, for the Confidence Level approximately 95%, the Coverage Factor, k =2.

 

U

=

k x Uc

Therefore uncertainty in above measurement measurement is

=+

 

=

2

x

0. 425

microns

0. 851

microns

0. 851

microns

 

Dial Thickness gauge Determination of Measurement Uncertainty 50 mm Least Count: Dial Gauge Range:

10

microns

50

mm

Set of Slip Gauge used f or calibration

Size (mm) :-

50

Uncertainty in measurement (mm): Unit of Measurement :

0.12

=

=

Reading Pionts :

microns

Uncertainty of Temperature Scanner =

0.39

Accuracy of master Equip.

0.1

Deg C

 

Type 'A' Evaluation Five Readings are taken and the deviation from the nominal value is as follows-

  Mean Deviation x

n

( xj)n

=

 j=1 2

Measured/Observed Readings

Standard Value

Average

(xj-x)

(xj-x)

mm

mm

mm

micron

microns

(xj) 49.990 49.990 49.990 49.990 49.990

0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000

0.000 0.000 0.000 0.000 0.000

49.990 49.990 49.990 49.990 49.990

0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000

0.000 0.000 0.000 0.000 0.000

0.0000

micron

0.000

microns

0.000

microns

 

(x)

Standard Deviation , S(X)

=

49.990

2

   (Xj - X) n-1

= 2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainty in Ty Type pe 'A' Evaluation, Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty uncertainty of Standard Equipment used i.e. Set of Slip Gauge

 

The value of Uncertainty Uncerta inty is taken from its calibration certifica certificate te Assuming Normal distribution Co Cov verage Factor of Calibrating Lab 0.12 U1  =  = 2

=2 0.059

microns

2.8868

microns

2. Standard Uncertainty Due to the Resolution of dial thickness gauge

Considering half of the least count & assuming reactangular distribution 10 U2  = 2x 3

=

3. Standard Uncertainty Due to Thermal Coefficient bitween Master Instrument & UUC

Assuming rectangular distribution. U3

=

L  X a  X dt 3

mm

Where

L

=

Length

=

 

a

=

  20% of ( a1 +a2)

 =

 

a1

=

Th. Coefficient of Expansion

=

11.5 X 10 / Deg C

 

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 / Deg C

50

-6 4.60 X 10 / Deg C -6

-6

 

 

d

U3

=

1

Control Limit or 10% of Temp. 20 °C

0.230

=

0.133

=

3

Deg C

microns

4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC

 

Assuming rectangular distribution. U4  Where

 

L

a

L  X a  X dt

=

3

=

Length

=

mm

50

=

-6

 (a1+a2)/2

11.5 X 10

 

a1

=

Th. Coefficient of Expansion

=

11.5 X 10-6 / Deg C

 

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 / Deg C

 

d

20% of Temp. Limit ± 1ºC

=

U4 

-6

0.115

=

0.2

0.066

=

3

5. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner   Assuming Normal distribution.   The value of Uncertainty Uncerta inty is taken from its calibration certifica certificate te i.e. = 0.39 L  X a  X dt U7  = 2 Where L = Length = 50

   

a d U7 

=

Deg C

Deg C

Deg C

mm

-6

= Th. Coefficient of of Expansion = = Uncertainty of temperature scanner 0.224 = 2

11.5 X 10 / Deg C 0.39

Deg C

0.112

Deg C

0. 058

microns

6. Standard Uncen. due to Accuracy Master Equipment. Equipment. Slip gauge Considering half of the accuracy & assuming rectangular distribution

U6 

0.10

=

=

3

Combined Uncertainty:

 

Uc

 

Uc

=

 

2

2

2

(UA) +(U1) +(U2) +(U3) 2.894

=

2……………………………………………

microns

Degree of Freedom, (Veff ) 4

Veff  

uc(y)

=

4

n(ui(y) )  j=1   Vi  

=

 

#DIV/0!



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement :

From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =. 2   U = k x Uc   = 2 x 2.894

microns

5.788

microns

Therefore uncertainty in above measurement is

=

±

5.8

microns

 

comparator stand Determination of Measurement Uncertainity of comparator stand comparator stand Rang

250*150

mm

Least Count:

microns

Size of S.G.

LTDG

Uncer. Of S.G.(micron)

1.51

Accyracy

3.0

Uncertainty Of Surface Plate(micron) Unit of Measurement :

0.00

=

microns

Uncertinty of Temperature Scaner =

Reading Point : 0.39

150

mm

o

 C

Wringing of Slip Gauges Accuracy Slip gauge

0 0

micron

Accuracy surface plate

0

micron

Type 'A' Evalution

Five Readings are taken and the deviation from the nominal value is as follows-

  Mean Devitation 

x

=

7.841

n

( xj)n  j=1 2

Measured/Observed Measured/Obser ved Readings

Standard Value

Avearge

(xj-x)

(xj-x)

mm

mm

mm

microns

microns

-0.6000 -2.6000 1.4000 -0.6000 -0.6000 -0.6000 1.4000 1.4000 1.4000 -0.6000

0.360 6.760 1.960 0.360 0.360 0.360 1.960 1.960 1.960 0.360

1.3499

microns

0.4269

microns

0.4269

microns

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.006 0.004 0.008 0.006 0.006 0.006 0.008 0.008 0.008 0.006

0.0066

   (Xj - X)

Standard Deviation =

2

  n-1

2

Stabdard Devitation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainity in Type 'A' Evalutation, UA 

=

Type 'B' Evalution  3. Standard Uncertainity Due to the uncertainty of Standard Equipment used i.e. Puppy Dial

 

The value of uncertainity is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab =

U3

=

1.51 2

 =

0.755

2

microns

4. Standard Uncertainity Due to the uncertainty of Standard Equipment used i.e. Surface Plate

 

The value of uncertainity is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab U4

=

0.00 2

 5. Standard Uncertainity Due toThermal Coefficient between UUC & Standard

 =

0.000

2 microns

 

  Assuming rectangular distribution.

U5 Where    

L a dt

L X a X dt

=

3

= Length = Th. Coefficient of Expansion = Control Limit or 10% of Temp. 20 °C

=

250.000

mm

11.5 X 10-6 / Deg C

=

Deg C

1.0

2.875

1.660

microns

3

7. Standard Uncertainity Due to the Temp. Variation in Master Instrument & UUC assumed as 0.5 deg C  

Assuming rectangular distribution.

U7 Where

L  X a  X dt

= L

 

a

 

d

U7

3 =

Length

=

Th. Coefficient of Expansion =

=

=

250

20% of Temp. Limit ± 1ºC

o

o

 C

0.2

0.575

=

mm -6

11.5 X 10 /  C

0.3320

 =

3

microns

8. Standard Uncertainity Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner

 

The value of uncertainity is taken from its calibration certificate U8 Where

L

   

L  X a  X dt

=

2 =

Length

= =

Th. Coefficient of Expansion o =

a d

U8

=

1.121

=

 =

2

mm -6

Uncertainty of temperature scaner

=

250 o

11.5 X 10 /  C 0.39

o

 C

0.6474

microns

=

1.732

microns

=

2.887

microns

12. Standard Uncen. due to Accuracy Accuracy Master Equipment. LTDG Considering half of the accuracy & assuming rectangular distribution

U12 

3.00

=

3

13. Standard Uncen. due to Accuracy Accuracy Master Equipment. Surface plate Considering 20% of the accuracy & assuming rectangular distribution

U13 

5.00

=

3

Combined Uncertainity:

Uc

=

 Uc

=

 

2

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3)

3.921

microns

Degree of Freedom, (V eff ) 4

Veff  

uc(y)

=

4 n(ui(y) )  j=1

 

=

  Vi  

64038.28194



=

Expanded Uncertainity Uncertainity of Overall Uncertainity or Uncertainity of Measurem Measurement ent : From thestudent's distribution table, f or the Confidence Level approxima approximately tely 95%, the Coverage Factor, k =2.  

Ue 

=

k e x Uc

  Therefore uncertainty in above measurement is = ±

 

=

2

x

3.921

microns

7.841

microns

 

Dial Gauge Determination of Measurement Uncertainty Range :

0.8

mm

Size of slip

0.8

Uncer. Of S.G.(micron)

0.09

Least Count:

=

microns

0. 8

mm

0

Uncertainty Of Comparator stand(micron) Unit of Measurement :

10

2. 85 microns

Reading Point :

Uncertainty of Temperature Scanner =

0.39

Accuracy

0.1

Slip Gauge

o

 C 6

Comparator

microns

 

Type 'A' Evaluation

Five Readings are taken and the deviation from the nominal value is as followsn

Mean Deviation x

( xj)n

=

 j=1 2

Measured/Observed Readings

Standard Value

Avearge

(xj-x)

(xj-x)

mm

mm

mm

microns

microns

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.0000

microns

0.0000 0.0000

microns microns

0.807 0.807 0.807 0.807 0.807 0.807 0.807 0.807 0.807 0.807

0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80 0.80

0.8070

   (Xj - X)

Standard Deviation =

2

  n-1 2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainty in Type 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Slip Gauge

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U1 

=

0.09 2

=2

 =

0. 045

microns

 =

0. 115

microns

 2. Standard Uncertainty Due to the wringing of Standard Equipment used i.e. Slips

 

The value of Uncertainty is taken from its calibration certificate Assuming Rectangular distribution

U2

=

0.2 1.732

3.Standard Uncertainty Due toThermal toThermal Coefficient between UUC & Standard   Assuming rectangular distribution. U3

= = =

L  X a  X dt 3

Where  

L a

engthof ( a1 +a2)  L20%

=  =

 

a1

=

Th. Coefficient of Expansion

=

4.7 X 10 /  C

 

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

0.80 0.0000032

mm -6

-6

O

O

 

 

d

=

U3 

Control Limit Limit or 10% of Temp. 20 °C 0.0026

=

3

1

Deg C

=

0.001

microns

=

2.887

microns

4.Standard Uncertainty Due to the Resolution of Dial gauge  

Considering half of the lleast east count & assuming rectangular distribution

U4

10

=

2x

1.732

5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC Assuming rectangular distribution. L  X a  X dt

5 L

 

a

=

d

Length

0.80

=

mm -6

 

 (a1+a2)/2

=

   

3

=

Where

8.1 X 10 -6

O

a1

=

Th. Coefficient of Expansion

=

4.7X 10 /  C

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

-6

20% of Temp. Limit ± 1ºC

=

U5

0.001

=

=

3

O

0.2

Deg C

0.0007

microns

6.Standard Uncertainty Due to the uncertainty o f Standard Equipment used i.e. Temp.Scanner

 

The value of Uncertainty is taken from its calibration certificate i.e. =0.39

U6 

L  X a  X dt

=

2

Where

L

=

Length

 

a

=

Th. Coefficient of Expansion of Caliper Checker =

=

 

d

1

mm -6 o

8.1X 10 /  C o

U6

=

=

Uncertainty of temperature scanner 0.003

=

0.39

=

2

 C microns

0.0013

 7.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Comparator Stand

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U7

2.85

=

 =

2

=2

1. 425

microns

=

0.058

micron

=

3.464

micron

8. Standard Uncertainty Due to the Accuracy of Master Equipment Equipment slip Gauge Considering half of the accuracy & assuming rectangular distribution

U8 

0.10

=

 

3

9. Standard Uncertainty Due to the Accuracy of Comparator stand Considering half of the accuracy & assuming rectangular distribution

U9

=

 

6.00

3

Combined Uncertainty:

Uc

=

 Uc

=

 

2

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3)

4.731

microns

Degree of Freedom, (V eff ) 4

Veff  

=

uc(y)

4

n(ui(y) )  j=1

  Vi

 

=

2.40412E+57

 



=

Expanded Uncertainty Uncertainty of Overall Uncertainty or Uncertainty of Measuremen Measurementt : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.   Ue  = k e x Uc   = 2 x 4.731

Therefore uncertainty in above above measurement measurement is =

±

9.46

microns microns

 

Dial Gauge Determination of Measurement Uncertainty Range :

50

mm

Size of slip

50.0

Uncer. Of S.G.(micron)

0.12

Least Count:

Uncertainty Of Comparator stand(micron) Unit of Measurement :

=

10

microns

50

mm

2. 85 microns

Reading Point :

Uncertainty of Temperature Scanner =

0.39

Accuracy

0.1

Slip Gauge

o

 C 6

Comparator

microns

 

Type 'A' Evaluation

Five Readings are taken and the deviation from the nominal value is as followsn

Mean Deviation x

( xj)n

=

 j=1 2

Measured/Observed Readings

UUC Value

Avearge

(xj-x)

(xj-x)

mm

mm

mm

microns

microns

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.0000

microns

0.0000 0.0000

microns microns

50.010 50.010 50.010 50.010 50.010 50.010 50.010 50.010 50.010 50.010

50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00 50.00

50.0100

   (Xj - X)

Standard Deviation =

2

  n-1 2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainty in Type 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Slip Gauge

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U1 

=

0.12 2

=2

 =

0. 060

microns

 =

0. 115

microns

 2. Standard Uncertainty Due to the wringing of Standard Equipment used i.e. Slips

 

The value of Uncertainty is taken from its calibration certificate Assuming Rectangular distribution

U2

=

0.2 1.732

3.Standard Uncertainty Due toThermal toThermal Coefficient between UUC & Standard   Assuming rectangular distribution. U3 Where  

   

= L a

a1 a2

= =

= =

L  X a  X dt 3 Length   20% of ( a1 +a2) Th. Coefficient of Expansion Th. Coefficient of Expansion

=  =

50.00 0.0000032

mm -6

O

=

4.7 X 10 /  C

=

11.5 X 10 /  C

-6

O

 

 

d

=

U3 

Control Limit Limit or 10% of Temp. 20 °C 0.1620

=

3

1

Deg C

=

0.094

microns

=

2.887

microns

4.Standard Uncertainty Due to the Resolution of Dial gauge  

Considering half of the lleast east count & assuming rectangular distribution

U4

10

=

2x

1.732

5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC Assuming rectangular distribution. L  X a  X dt

5 Where

L

 

a

=

d

Length

50.00

=

mm -6

 

 (a1+a2)/2

=

   

3

=

8.1 X 10 -6

O

a1

=

Th. Coefficient of Expansion

=

4.7X 10 /  C

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

-6

20% of Temp. Limit ± 1ºC

=

U5

0.081

=

=

3

O

0.2

Deg C

0.0468

microns

6.Standard Uncertainty Due to the uncertainty o f Standard Equipment used i.e. Temp.Scanner

 

The value of Uncertainty is taken from its calibration certificate i.e. =0.39

U6  Where

L  X a  X dt

= L

 

a

 

d

2

=

=

Length

=

50

mm -6 o

8.1X 10 /  C

Th. Coefficient of Expansion of Caliper Checker =

o

U6

=

=

Uncertainty of temperature scanner 0.158

=

0.39

=

2

 C microns

0.0790

 7.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Comparator Stand

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U7

2.85

=

 =

2

=2

1. 425

microns

=

0.058

micron

=

3.464

micron

8. Standard Uncertainty Due to the Accuracy of Master Equipment Equipment slip Gauge Considering half of the accuracy & assuming rectangular distribution

U8 

0.10

=

 

3

9. Standard Uncertainty Due to the Accuracy of Comparator stand Considering half of the accuracy & assuming rectangular distribution

U9

=

 

6.00

3

Combined Uncertainty:

Uc

=

 Uc

=

 

2

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3)

4.733

microns

Degree of Freedom, (V eff ) 4

Veff  

=

uc(y)

4

n(ui(y) )  j=1

  Vi

 

=

#DIV/0!

 



=

Expanded Uncertainty Uncertainty of Overall Uncertainty or Uncertainty of Measuremen Measurementt : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.   Ue  = k e x Uc   = 2 x 4.733

Therefore uncertainty in above above measurement measurement is =

±

9.47

microns microns

 

Dial Gauge Determination of Measurement Uncertainty Range :

25

mm

Least Count:

Size of slip

20.0

5

Uncer. Of S.G.(micron)

0.09

0.09

Uncertainty Of Comparator stand(micron) Unit of Measurement :

=

10

microns

25

mm

2. 85 microns

Reading Point :

Uncertainty of Temperature Scanner =

0.39

Accuracy

0.1

Slip Gauge

o

 C 6

Comparator

microns

 

Type 'A' Evaluation

Five Readings are taken and the deviation from the nominal value is as followsn

Mean Deviation x

( xj)n

=

 j=1 2

Measured/Observed Readings

Standard Value

Avearge

(xj-x)

(xj-x)

mm

mm

mm

microns

microns

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.0000

microns

0.0000 0.0000

microns microns

25.007 25.007 25.007 25.007 25.007 25.007 25.007 25.007 25.007 25.007

25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00 25.00

25.0070

   (Xj - X)

Standard Deviation =

2

  n-1 2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainty in Type 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Slip Gauge

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U1 

=

0.090 2

=2

 =

0. 045

microns

 =

0. 115

microns

 2. Standard Uncertainty Due to the wringing of Standard Equipment used i.e. Slips

 

The value of Uncertainty is taken from its calibration certificate Assuming Rectangular distribution

U2

=

0.2 1.732

3.Standard Uncertainty Due toThermal toThermal Coefficient between UUC & Standard   Assuming rectangular distribution. U3

= = =

L  X a  X dt 3

Where  

L a

Length   20% of ( a1 +a2)

=  =

 

a1

=

Th. Coefficient of Expansion

=

4.7 X 10 /  C

 

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

25.00 0.0000032

mm -6

-6

O

O

 

 

d

=

U3 

Control Limit Limit or 10% of Temp. 20 °C 0.0810

=

3

1

Deg C

=

0.047

microns

=

2.887

microns

4.Standard Uncertainty Due to the Resolution of Dial gauge  

Considering half of the lleast east count & assuming rectangular distribution

U4

10

=

2x

1.732

5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC Assuming rectangular distribution. L  X a  X dt

5 L

 

a

=

Length

d

25.00

=

mm -6

 

 (a1+a2)/2

=

   

3

=

Where

8.1 X 10 -6

O

a1

=

Th. Coefficient of Expansion

=

4.7X 10 /  C

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

-6

20% of Temp. Limit ± 1ºC

=

U5

0.041

=

=

3

O

0.2

Deg C

0.0234

microns

6.Standard Uncertainty Due to the uncertainty o f Standard Equipment used i.e. Temp.Scanner

 

The value of Uncertainty is taken from its calibration certificate i.e. =0.39

U6  Where

L  X a  X dt

= L

 

a

 

d

2

=

Length

=

=

25

mm -6 o

8.1X 10 /  C

Th. Coefficient of Expansion of Caliper Checker =

o

U6

Uncertainty of temperature scanner 0.079

=

=

=

0.39

=

2

 C

0.0395

microns

 7.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Comparator Stand

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U7

2.85

=

 =

2

=2

1. 425

microns

=

0.058

micron

=

3.464

micron

8. Standard Uncertainty Due to the Accuracy of Master Equipment Equipment slip Gauge Considering half of the accuracy & assuming rectangular distribution

U8 

0.10

=

 

3

9. Standard Uncertainty Due to the Accuracy of Comparator stand Considering half of the accuracy & assuming rectangular distribution

U9

=

 

6.00 3

Combined Uncertainty:

Uc

=

 Uc

=

 

2

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3)

4.732

microns

Degree of Freedom, (V eff ) 4

Veff  

uc(y)

=

4

n(ui(y) )  j=1

  Vi

 

=

 

#DIV/0!



=

Expanded Uncertainty Uncertainty of Overall Uncertainty or Uncertainty of Measuremen Measurementt : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.

 

Ue 

=

k e x Uc

Therefore uncertainty in above above measurement measurement is =

±

 

=

2

x

4.732

microns

9.46

microns

 

Measuring Pin Determination Determinati on of Measurement Measurement Uncertainty Range : Size of slip

20

mm 20.0

Uncer. Of S.G.(micron)

0.09

Least Count: 0

Uncertainty Of Comparator stand(micron) Unit of Measurement :

=

2.85 microns

Reading Point :

Uncertainty of Temperature Scanner = Accuracy

microns

0

0.39

Slip Gauge

0.1

mm

20

o

 C 6

Comparator

microns

 

Type 'A' Evaluation

Five Readings are taken and the deviation from the nominal value is as followsn

Mean Deviation x

( xj)n

=

 j=1 2

Measured/Observed Readings

Standard Value

Avearge

(xj-x)

(xj-x)

mm

mm

mm

microns

microns

-0.0400 0.1600 0.0600 -0.0400 -0.1400 -0.0400 0.1600 0.0600

0.002 0.026 0.004 0.002 0.020 0.002 0.026 0.004

-0.0400 -0.1400 0.0000

0.002 0.020

0.1075

microns

0.0340 0.0340

microns microns

20.0004 20.0006 20.0005 20.0004 20.0003 20.0004 20.0006 20.0005

20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00

20.0004 20.0003

20.00 20.00

20.0004

   (Xj - X)

Standard Deviation =

2

  n-1

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainty in Type 'A' Evaluation, UA

=

2

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Slip Gauge

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution

U1 

Coverage Factor of Calibrating Lab 0.09

=

2

=2

 =

0.045

microns

 =

0.000

microns

 2. Standard Uncertainty Due to the wringing of Standard Equipment used i.e. Slips

 

The value of Uncertainty is taken from its calibration certificate Assuming Rectangular distribution

U2

=

0 1.732

3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard   Assuming rectangular distribution. U3

= =

L  X a  X dt 3

Where

L

 

a =

Length   20% of ( a1 +a2)

 

a1 =

Th. Coefficient of Expansion

a2 =

Th. Coefficient of Expansion

 

d

Control Limit or 10% of Temp. Temp. 20 °C 0.0648

U3 

= =

4.Standard Uncertainty Due to the Resolution of Dial g auge

3

20.00 0.0000032

mm -6

O

4.7 X 10 /  C

=

 

=  =

-6

O

11.5 X 10 /  C

=

=

1

Deg C

0.037

microns

 

 

Considering half o off the least co count unt & assuming rectangular distribution

U4

0.2

=

2x

=

1.732

0.058

microns

5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC Assuming rectangular distribution.

5 Where

L

 

L  X a  X dt

=

3 =

Length

d

 

 (a1+a2)/2

a =

   

2 0. 00

=

mm

8.1 X 10 -6

-6 O

a1 =

Th. Coefficient of Expansion

=

4.7X 10 /  C

a2 =

Th. Coefficient of Expansion

=

11.5 X 10-6 / O C 0.2

20% of Temp. Limit ± 1ºC

=

U5

0.032

=

0.0187

=

3

Deg C

microns

6.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner

 

The value of Uncertainty is taken from its calibration certificate i.e. =0.39

U6  Where

L  X a  X dt

= L

2

=

Length

a =

Th. Coefficient of Expansion of Caliper Checker =

 

d

Uncertainty of temperature scanner

U6

=

20

=

 

=

0.39

=

0.063

=

2

mm -6 o

8.1X 10 /  C o

 C

0.0316

microns

 7.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Comparator Stand

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U7

2.85

=

 =

2

=2

1.425

microns

=

0.058

micron

=

3.464

micron

=

0.173

micron

=

0.231

micron

8. Standard Uncertainty Due to the Accuracy of Master Equipment slip Gauge Considering half of the accuracy & assuming rectangular distribution

U8 

0.10

=

 

3

9. Standard Uncertainty Due to the Accuracy of Comparator stand Considering half of the accuracy & assuming rectangular distribution

U9

6.00

=

 

3

9. Standard Uncertainty Due to the Accuracy of dial Indicator Considering half of the accuracy & assuming rectangular distribution

U9

0.30

=

 

3

9. Standard Uncertainty Due to the Uncertainity of dial Indicator Considering half of the accuracy & assuming Normal distribution 0.40

U9

=

2

Combined Uncertainty:

Uc

=

 Uc

=

 

2

2

2

2……………………………………………

(UA) +(U1) +(U2) +(U3)

3.759

microns

Degree of Freedom, (Veff ) 4

Veff  

uc(y)

=

n(ui(y)4)  j=1

  Vi

 

1345169092

=

 



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.

 

Ue 

=

k e x Uc

Therefore uncertainty uncertainty in above measurement measurement is =

±

 

=

2

x

3.759

microns

7.52

microns

 

ultra sonic gauge Determination of Measurement Uncertainty of ultra sonic gauge Up to 150 mm Range :

100

mm

Size of Caliper

100

Uncer. Of S.G.(micron)

0.17

Least Count:

microns

100

mm

0

Uncertainty Of surface plate(micron) Unit of Measurement :

10

4.6

=

microns

Reading Point :

Uncertainty of Temperature Scanner =

0.39

o

Accuracy

0.12

Surface Plate

Slip Gauge

 C 5

microns

 

Type 'A' Evaluation

Five Readings are taken and the deviation from the nominal value is as followsn

Mean Deviation x

( xj)n

=

 j=1 2

Measured/Observed Readings

Standard Value

Avearge

(xj-x)

(xj-x)

mm

mm

mm

microns

microns

-5.0000 5. 0 000 -5.0000 -5.0000 5 . 0 000 5. 0 000 -5.0000 5. 0 000 -5.0000 5. 0 000 0.0000

25 . 00 0 25.000 25 . 00 0 25 . 00 0 25.000 25.000 25 . 00 0 25.000 25 . 00 0 25.000

5.2705

microns

1.6667 1.6667

microns microns

99.45 99.46 99.45 99.45 99.46 99.46 99.45 99.46 99.45 99.46

1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00 1 00

99. 4 55 0

   (Xj - X)

Standard Deviation =

2

  n-1 2

Standard Deviation of the Mean, S ( X)

[S(X)] n

=

= Standard Uncertainty in Type 'A' Evaluation, UA

=

Type 'B' Evaluation  1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. slip gauge

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U 1 

=

0.17

 =

2

=2

0.085

microns

 =

0.000

microns

=

100.000

mm

 2. Standard Uncertainty Due to the wringing of Standard Equipment used i.e. slip gauge/Slips

 

The value of Uncertainty is taken from its calibration certificate Assuming Rectangular distribution

U2

=

0 1.732

3.Standard Uncertainty Due toThermal toThermal Coefficient between UUC & Standard   Assuming rectangular distribution. U3

=

L X a  X dt 3

Where      

L = Length 20 % of a1 a2 a  = a1  = Th. Coefficient of Expansion of DStandard a2  = Th. Coefficient of Expansion of UUC

3.24 X 10-6 / Deg C = =

4.7 X 10-6 / Deg C 11.5 X 10-6 / Deg C

 

 

dt

= Control Limit or 10% of Temp. 20 °C 0.320

1.0

Deg C

0.185

microns

2.887

microns

3 4.Standard Uncertainty Due to the Resolution of ultra sonic gauge  

Considering half half of the least least count & assuming rectangular distribution

U4

10

=

2x

=

1.732

5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC Assuming rectangular distribution. L  X a  X dt

5

=

Where

L

 

a

Length

d

100.00

=

mm -6

 

 (a1+a2)/2

=

   

3 =

11.5X 10

-6

O

-6

O

a1

=

Th. Coefficient of Expansion

=

11.5X 10 /  C

a2

=

Th. Coefficient of Expansion

=

11.5 X 10 /  C

20% of Temp. Limit ± 1ºC

=

U5

0.230

=

=

3

0.2

Deg C

0.1328

microns

6.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner

 

The value of Uncertainty is taken from its calibration certificate i.e. =0.35

U6  Where

L  X a  X dt

= L

 

a

 

d

2

=

Length

=

100

=

mm -6

o

11.5 X 10 /  C

Th. Coefficient of Expansion of slip gauge =

o

U6

=

=

Uncertainty of temperature scanner 0.449

0.39

= =

2

 C

0.2243

microns

 7.Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Surface Plate

 

The value of Uncertainty is taken from its calibration certificate Assuming Normal distribution Coverage Factor of Calibrating Lab

U7

4.60

=

2

=2

 =

2.300

microns

=

0.069

micron

=

2.887

micron

8. Standard Uncertainty Due to the Accuracy of Master Equipment Considering half of the accuracy & assuming rectangular distribution

U8 

0.12

=

 

3

8. Standard Uncertainty Due to the Accuracy of Master Equipment Considering half of the accuracy & assuming rectangular distribution 5.00

U8 

=

 

3

Combined Uncertainty:

Uc

=

 Uc

=

 

2

2

2

(UA) +(U1) +(U2) +(U3)

4.985

2……………………………………………

microns

Degree of Freedom, (V eff ) Veff  

=

uc(y) 4

n(ui(y) )  j=1

  Vi

 

=

720.2495681

 



=

Expanded Uncertainty of Overall Uncertainty or Uncertainty of Measurement : From the student's distribution table, for the Confidence Level approximately 95%, the Coverage Factor, k =2.   Ue   = k e x Uc 4.985   = 2 x

Therefore uncertainty in above measurement is =

±

10.0

microns microns