DEPTH Gauge

Determination of Measurement Uncertainty of Depth Gauge Up to 300 mm

Range : 300 mm Least Count: 10 microns
Size of Caliper 300
Uncer. Of S.G.(micron) 0.316069613 0
Uncertainty Of surface plate(micron) 4.6
Unit of Measurement : = microns Reading Point : 300 mm
o
Uncertainty of Temperature Scanner = 0.39 C
Accuracy Slip Gauge 0.12 Surface Plate 5 microns
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

2
Measured/Observed Readings Standard Value Avearge (xj-x) (xj-x)
mm mm mm microns microns

300.01 300 4.0000 16.000

300.00 300 -6.0000 36.000
300.01 300 4.0000 16.000
300.00 300 -6.0000 36.000
300.01 300 300.0060 4.0000 16.000
300.00 300 -6.0000 36.000
300.01 300 4.0000 16.000
300.01 300 4.0000 16.000
300.00 300 -6.0000 36.000
300.01 300 4.0000 16.000
0.0000
2
Standard Deviation =  (Xj - X)
n-1
5.1640 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 1.6330 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 1.6330 microns
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
0.32
U1 = = 0.158 microns
2
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
0.2
U2 = = 0.115 microns
1.732
3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard
Assuming rectangular distribution.
U3 = L X a X dt
3
Where L =Length = 300.000 mm
a = 20 % of a1+a2 3.24 X 10-6 / Deg C
a1 =Th. Coefficient of Expansion of DStandard = 4.7 X 10-6 / Deg C
a2 =Th. Coefficient of Expansion of UUC = 11.5 X 10-6 / Deg C
dt = Control Limit or 10% of Temp. 20 °C 1.0 Deg C
0.960 0.554 microns
3
4.Standard Uncertainty Due to the Resolution of Depth Gauge
 Considering half of the least count & assuming rectangular distribution
10
U4 = = 2.887 microns
2 x 1.732
5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
5 =
3
Where L = Length = 300.00 mm
-6
a = (a1+a2)/2 8.1X 10
-6 O
a1 = Th. Coefficient of Expansion = 11.5X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.486
U5 = = 0.2806 microns
3
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
L X a X dt
U6 =
2
Where L = Length = 300 mm
-6 o
a = Th. Coefficient of Expansion of slip gauge = 11.5 X 10 / C
o
d = Uncertainty of temperature scanner = 0.39 C
1.346
U6 = = 0.6728 microns
2
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
4.60
U7 = = 2.300 microns
2

8. Standard Uncertainty Due to the Accuracy of Master Equipment

Considering half of the accuracy & assuming rectangular distribution
0.12
U8 = = 0.069 micron
3
8. Standard Uncertainty Due to the Accuracy of Master Equipment
Considering half of the accuracy & assuming rectangular distribution
5.00
U8 = = 2.887 micron
3
8. Standard Uncertainty Due to the Accuracy of Master Equipment caliper
Considering half of the accuracy & assuming rectangular distribution
5.00
U8 = = 2.887 micron
3
8. Standard Uncertainty Due to the Uncertainityof Master Equipment caliper
Considering half of the accuracy & assuming rectangular distribution
3.90
U8 = = 1.950 micron
2

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 6.135 microns
Degree of Freedom, (Veff)
4
uc(y)
Veff = 4
n(ui(y) )
j=1
Vi
= 1793.317216 = 
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 = ke x Uc = 2 x 6.135 microns
Therefore uncertainty in above measurement is = ± 12.3 microns
 Feeler Gauge
Determination of Measurement Uncertainty of Feeler Gauge
Feeler Gauge Range : 1.00 mm
Reading Point = 1.00 mm
Uncer. in D. M. M. (mm): = 2.10 microns
Unit of Measurement : = microns
o
Uncertainty of Temperature Scanner = 0.39
C
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows :-
n

Mean Deviation x = ( xj)n

j=1

Measured/Observed Readings Standard Value Average (xj-x) (xj-x)2

mm mm microns microns
(xj) (x) (x)
1.002 0.000 -0.2000 0.0400
1.003 0.000 0.8000 0.6400
1.002 0.000 -0.2000 0.0400
1.002 0.000 -0.2000 0.0400
1.003 0.000 1.0022 0.8000 0.6400
1.001 0.000 -1.2000 1.4400
1.002 0.000 -0.2000 0.0400
1.002 0.000 -0.2000 0.0400
1.003 0.000 0.8000 0.6400
1.002 0.000 -0.2000 0.0400
Standard Deviation , S(X) =  (Xj - X)2
n-1
= 0.632 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.200 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.200 microns
Type 'B' Evaluation
1. Standard Uncertainty Due to the Digital Micro Meter
The value of Uncertainty is taken from its calibration certificate
Assuming Normal distribution Coverage Factor of Calibrating Lab = 2
2.10
U1 = = 1.050 microns
2
2. Standard Uncertainty Due to Half of least count of Digital Micro Meter
Assuming Rectangular distribution
U2 = 0.001
= 0.0003 microns
2x 3
3. Standard Uncertainty Due to thermal Coefficient between Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
U3 =
3
Where L = Length 1.000 mm
a = 20 % (a1+ a2)
a1 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
d = Control Limit or 10% of Temp. 20 °C 1 Deg C
 0.0046
U3 = = 0.0027 microns
3
4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
U4 =
3
Where L = Length = 1.00 mm
a = (a1+a2)/2 11.5 X 10-6
a1 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.002
U4 = = 0.0013 microns
3
5. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner
o
The value of Uncertainty is taken from its calibration certificate i.e. = 0.39 C
Assuming Normal distribution.
L X a X dt
U6 =
2
Where L = Length = 1.000 mm
a = Th. Coefficient of Expansion = 11.5 X 10-6 / o
C
o
d = Uncertainty of temperature Scanner = 0.39 C
0.00449
U6 = = 0.002243 microns
2
2. Standard Uncertainty Due to Accuracy of Digital Micro Meter
Assuming Rectangular distribution
U2 = 0.002
= 0.0012 microns
3
Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 1.069 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
n (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 = k x Uc = 2 x 1.069 microns
2.138 microns
Therefore uncertainty in above measurement is = ± 2.14 microns
 EXTERNAL MICROMETER
Determination of Measurement Uncertainty of Micrometer Range upto 0 to 100 mm
Micrometer Range : 100 mm Least Count: 1 microns
Slip Gauges used for calibration Reading Points 100 mm
Uncer.of std. = 0.17 microns No. Of Slip Used 1
Unit of Measurement : = microns
o
Uncertainty of Temperature Scanner = 0.39 C
Wringing of Slip Gauges 0.2 microns
Accuracy of Slip Gauges 0.12 microns
Type 'A' Evaluation
Five Readings are taken and the Deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

Measured/Observed Readings Standard Value Avearge (xj-x) (xj-x)2

99.997 100 0.0000 0.000
99.997 100 0.0000 0.000
99.997 100 99.9970 0.0000 0.000
99.997 100 0.0000 0.000
99.997 100 0.0000 0.000
99.997 100 0.0000 0.000
99.997 100 0.0000 0.000
99.997 100 0.0000 0.000
99.997 100 0.0000 0.000
99.997 100 0.0000 0.000
Standard Deviation =  (Xj - X)2
n-1
= 0.0000 microns

[S(X)]2
Standard Deviation of the Mean, S ( X) = n
= 0.0000 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.0000 microns
Type 'B' Evalution
1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Slip Gague
The value of Uncertainty is taken from its calibration certificate
Assuming Normal distribution =2
0.17
U1 = = 0.085 microns
2
2. Standard Uncertainty Due to the Resolution of External Micrometer
Considering half of the least count & assuming rectangular distribution
1
U2 = = 0.289 microns
2x 3
3. Standard Uncertainty Due toThermalCoefficient of UUC & Standard
Assuming rectangular distribution.
U3 = L X a X dt
3
Where L = Length = 100.000 mm
a = 20 % of a1+a2 3.24 X 10-6 / Deg C
a1 = Th. Coefficient of Expansion of DStandard = 4.7 X 10-6 / Deg C
a2 = Th. Coefficient of Expansion of UUC = 11.5 X 10-6 / Deg C
dt = Control Limit or 10% of Temp. 20 °C 1.0 Deg C
 0.0648 0.037 microns
3
4. Standard Uncertainty Due to the Wringing of Slip Gauge
Considering half of the least count & assuming rectangular distribution
0
U4 = = 0.000 microns
3
5. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC assumed as 0.5 deg C
Assuming rectangular distribution.
L X a X dt
U5 =
3
Where L = Length = 100.00 mm
a = (a1+a2)/2 8.1 X 10-6
a1 = Th. Coefficient of Expansion = 4.7 X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.162
U5 = = 0.0935 microns
3
6. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner
o
The value of Uncertainty is taken from its calibration certificate i.e. = 0.39 C
L X a X dt
U6 =
2
Where L = Length = 100.0 mm
a = Th. Coefficient of Expansion of Slip Gague = 8.1 X 10-6 /o C
o
d = Uncertainty of temperature scaner = 0.39 C
0.316
U6 = = 0.1580 Deg C
2

7. Standard Uncertainty Due to the Accuracy of Master Equipment

Considering half of the accuracy & assuming rectangular distribution
0.12
U7 = = 0.069 micron
3

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 0.361 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
n(ui(y)4)
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.
Ue = ke x Uc = 2 x 0.361 microns
0.722 microns
Therefore uncertainty in above measurement is =+ 0.7 microns
 INTERNAL MICROMETER
Determination of Measurement 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 micron
Accuracy of Slip Gauge 0.10 micron
Uncer. Of Slip Gauge Accessories 2.40 micron No. of Slip 1
Unit of Measurement : = microns Reading Point : 50 mm
o
Uncertinty of Temperature Scanner = 0.39 C
Accuracy of Master Equipment (Slip Gauge) 0.1 Surfaced plate 0
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

(xj-x) (xj-x)2
Measured/Observed Readings Standard Value Avearge
microns microns
49.998 50.000 -0.5000 0.250
49.999 50.000 0.5000 0.250
49.998 50.000 -0.5000 0.250
49.999 50.000 0.5000 0.250
49.999 50.000 49.9985 0.5000 0.250
49.999 50.000 0.5000 0.250
49.998 50.000 -0.5000 0.250
49.998 50.000 -0.5000 0.250
49.998 50.000 -0.5000 0.250
49.999 50.000 0.5000 0.250
Standard Deviation =  (Xj - X)2
n-1
= 0.5270 microns

[S(X)]2
Standard Deviation of the Mean, S ( X) = n
= 0.1667 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.1667 microns
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 =2
0.12
U1 = = 0.060 microns
2
2. Standard Uncertainty Due toThermal Coefficient of UUC & Standard
Assuming rectangular distribution.
L X a X dt
U2 =
3
Where L = Length = 100 mm
-6
a = 20% of ( a1 +a2) = 3.24 X 10 / Deg C
a1 = Th. Coefficient of Expansion = 4.7 X 10-6 / Deg C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / Deg C
d = Control Limit or 10% of Temp. 20 °C 1 Deg C
0.324
U2 = = 0.187 microns
3
3. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Slip Gauge Accessories
The value of Uncertainty is taken from its calibration certificate
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
2.40
U3 = = 1.200 microns
 U3 = = 1.200 microns
2
4. Standard Uncertainty Due to the Resolution of lnternal Micrometer
Considering half of the least count & assuming rectangular distribution
1
U4 = = 0.289 microns
2x 3
5. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
U5 =
3
Where L = Length = 100 mm
-6
a = (a1+a2)/2 8.1 X 10
a1 = Th. Coefficient of Expansion = 4.7 X 10-6 / Deg C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / Deg C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.162
U5 = = 0.094 microns
3

6. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner
o
The value of Uncertainty is taken from its calibration certificate i.e. = 0.39 C
Assuming rectangular distribution.
L X a X dt
U6 =
2
Where L = Length = 100 mm
a = Th. Coefficient of Expansion of Slip Gague = 4.7 X 10-6 / Deg C
o
d = Uncertainty of temperature Scanner = 0.39 C

0.183
U6 = = 0.1058 microns
1.732

7. Standard Uncertainty Due to the Accuracy of Master Equipment (Slip Gauge)

Considering half of the accuracy & assuming rectangular distribution
0.1
U7 = = 0.029 micron
2 3

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

Assuming rectangular distribution (20% of Full Accuracy)
0
U8 = = 0.000 micron
3

9. Standard Uncertainty Due to the Accuracy of Master Equipment (Slip GaugeAccessories)

Considering half of the accuracy & assuming rectangular distribution
0.1
U9 = = 0.029 micron
2 3
Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 1.266 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
n(ui(y)4)
j=1
Vi
= 29956.10739 = 
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 = ke x U c = 2 x 1.266 microns
2.532 microns
Therefore uncertainty in above measurement is =+ 2.53 microns
 Micrometer Setting Standard
Determination of Measurement Uncertainty of Micrometer Setting Standard
Range : 75 mm Reading points 75 mm
Range 25 75 100 50
Uncertainty in S.G. (mm): = 0.10 0.14 0.17 0.12
Uncer. in Comp Stand(micron) 2.85 microns
Unit of Measurement : = microns
Uncertinty of Temperature Scanner = 0.39 Deg C
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-
n
Mean Deviation x = (å xj)¸n
j=1

2
Measured/Observed Readings Value Average (xj-x) (xj-x)
mm mm microns microns
(xj) (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 75.0006 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
2
Standard Deviation , S(X) = å (Xj - X)
n-1
= 0.0000 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.000 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.000 microns
Type 'B' Evaluation
1. Standard Uncertainty Due to the uncertainty of Standard Comp Stand
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
2.85
U1 = = 1.425 microns
2
2. Standard Uncertainty Due to 50% of Resolution of Standard Dial Gauge
Assuming Rectangular distribution
0.2
U2 = = 0.289 microns
2 3
3. Standard Uncertainty Due to Thermal Coefficien of Master Instrument & UUC .
Assuming rectangular distribution. for Master
L X a X dt
U3 =
3
Where L = Length = 75.00 mm
a = 20% of ( a1 +a2) = 0.0000032
-6 O
a1 = Th. Coefficient of Expansion = 4.7 X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = Control Limit or 10% of Temp. 20 °C 1 Deg C
0.2430
U3 = = 0.140 microns
3
4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC.
Assuming rectangular distribution.
 L X a X dt
U4 =
3
Where L = Length = 75.00 mm
-6 O
a = (a1+a2)/2 8.1 X 10 / C
-6 O
a1 = Th. Coefficient of Expansion = 4.7 X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.122
U4 = = 0.0702 microns
3
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. = 0.39 Deg C
Assuming Normal distribution.
L X a X dt
U6 =
2
Where L = Length = 75.00 mm
-6
a = Th. Coefficient of Expansion = 8.1 X 10 / Deg C
d = Uncertainty of temperature Scanner = 0.32 Deg C
0.194
U6 = = 0.0972 microns
2
6 . Standard Uncertainty Due to the uncertainty of Standard Slip Gauge set
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
0.140
U7 = = 0.068 microns
2
7. Standard Uncertainty Due to the uncertainty of Standard Dial Indicator
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
0.30
U8 = = 0.150 microns
2
8. Standard Uncertainty Due to the Accuracy of Master Equipment
Considering half of the accuracy & assuming rectangular distribution
0.12
U8 = = 0.069 micron
3

9. Standard Uncertainty Due to the Accuracy of comparator

Considering half of the accuracy & assuming rectangular distribution
6
U8 = = 3.464 micron
3
10. Standard Uncertainty Due to the Accuracy of dial Indicator
Considering half of the accuracy & assuming rectangular distribution
0.4
U8 = = 0.231 micron
3

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 3.773 microns
Degree of Freedom, (Veff)
4
uc(y)
Veff = 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 2 x 3.773 microns
7.546 microns
Therefore uncertainty in above measurement is = ± 7.546 microns
 Plain Plug Gauge
Determination of Measurement Uncertainty of Plain Plug Gauge
PP Gauge Range : 100 mm Reading points 100 mm
Range 25 75 100 50
Uncertainty in S.G. (mm): = 0.09 0.14 0.17 0.12
Uncer. in Comp Stand(micron) 2.85 microns
Unit of Measurement : = microns
Uncertinty of Temperature Scanner = 0.39 Deg C
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-
n
Mean Deviation x = (å xj)¸n
j=1

2
Measured/Observed Readings Standard Value Average (xj-x) (xj-x)
mm mm microns microns
(xj) (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 99.9864 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
2
Standard Deviation , S(X) = å (Xj - X)
n-1
= 0.1989 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.063 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.063 microns
Type 'B' Evaluation
1. Standard Uncertainty Due to the uncertainty of Standard Comp Stand
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
2.85
U1 = = 1.425 microns
2
2. Standard Uncertainty Due to 50% of Resolution of Standard Dial Gauge
Assuming Rectangular distribution
0.2
U2 = = 0.289 microns
2 3
3. Standard Uncertainty Due to Thermal Coefficien of Master Instrument & UUC .
Assuming rectangular distribution. for Master
L X a X dt
U3 =
3
Where L = Length = 100.00 mm
a = 20% of ( a1 +a2) = 0.0000032
-6 O
a1 = Th. Coefficient of Expansion = 4.7 X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = Control Limit or 10% of Temp. 20 °C 1 Deg C
0.3240
U3 = = 0.187 microns
3
4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC.
Assuming rectangular distribution.
 L X a X dt
U4 =
3
Where L = Length = 100.00 mm
-6 O
a = (a1+a2)/2 8.1 X 10 / C
-6 O
a1 = Th. Coefficient of Expansion = 4.7 X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.162
U4 = = 0.0935 microns
3
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. = 0.39 Deg C
Assuming Normal distribution.
L X a X dt
U6 =
2
Where L = Length = 100.00 mm
-6
a = Th. Coefficient of Expansion = 8.1 X 10 / Deg C
d = Uncertainty of temperature Scanner = 0.32 Deg C
0.259
U6 = = 0.1296 microns
2
6 . Standard Uncertainty Due to the uncertainty of Standard Slip Gauge set
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
0.136
U7 = = 0.068 microns
2
7. Standard Uncertainty Due to the uncertainty of Standard Dial Indicator
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
0.30
U8 = = 0.150 microns
2
8. Standard Uncertainty Due to the Accuracy of Master Equipment slip gauge
Considering half of the accuracy & assuming rectangular distribution
0.12
U8 = = 0.069 micron
3

8. Standard Uncertainty Due to the Accuracy of Master Equipment dial indicator

Considering half of the accuracy & assuming rectangular distribution
0.4
U8 = = 0.231 micron
3

8. Standard Uncertainty Due to the Accuracy of Master Equipment comparator stand

Considering half of the accuracy & assuming rectangular distribution
6
U8 = = 3.464 micron
3

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 3.777 microns
Degree of Freedom, (Veff)
4
uc(y)
Veff = 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 2 x 3.777 microns
7.554 microns
Therefore uncertainty in above measurement is = ± 7.554 microns
 0.851
Snap Gauge
Determination of Measurement Uncertainity of Snap Gauge
Snap Gauge Range : 100 mm Reading Point : 100 mm
Uncertainity in S.G. (mm): = 20 75 100
Uncertainty due to Wringing of S.G. 0.09 0.14 0.17
Unit of Measurement : = 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-
n
Mean Devitation x = (å xj)¸n
j=1

Measured/Observed Readings Standard Value Average (xj-x) (xj-x)2

mm mm microns microns
(xj) (x)
119.150 0.000 0.0000 0.000
119.150 0.000 0.0000 0.000
119.150 0.000 0.0000 0.000
119.150 0.000 0.0000 0.000
119.150 0.000 0.0000 0.000
119.150 0.000 119.1500 0.0000 0.000
119.150 0.000 0.0000 0.000
119.150 0.000 0.0000 0.000
119.150 0.000 0.0000 0.000
119.150 0.000 0.0000 0.000
Standard Devitation , S(X) = å (Xj - X)2
n-1
= 0.000 microns
[S(X)]2
Stabdard Devitation of the Mean, S ( X) = n

= 0.000 microns
Standard Uncertainity in Type 'A' Evalutation, UA = 0.000 microns
Type 'B' Evalution
1. Standard Uncertainity Due to the uncertainty of Standard 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 =2
0.17
U1 = = 0.085 microns
2
2. Standard Uncertainity Due to Thermal Coefficient between UUC & Standard.
Assuming rectangular distribution.
L X a X dt
U2 =
3
Where L = Length = 100.0 mm
a = Th. Coefficient of Expansion of Slip Gague = 4.7X 10-6 / Deg C
dt = Temperature Variation or Temp. Difference = 1 Deg C
0.470
U2 = = 0.271 microns
3
3. Standard Uncertainity Due to the Wringing of Slip Gagues
Assuming Rectangular distribution
-0.20
U3 = = -0.115 microns
3
4. Standard Uncertainity Due to the Temp. Variation in Master Instrument & UUC assumed as 0.5 deg C
Assuming rectangular distribution.
L X a X dt
U4 =
3
 Where L = Length = 100.0 mm
a = Th. Coefficient of Expansion of Slip Gague = 6.8 X 10-6 / O C
dt = Temperature Variation or Temp. Difference = 1 Deg C
0.470
U4 = = 0.271 microns
3
5. Standard Uncertainity Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner
The value of uncertainity is taken from its calibration certificate i.e. = 0.39 Deg C
Assuming Normal distribution.
L X a X dt
U5 =
2
Where L = Length = 100.0 mm
a = Th. Coefficient of Expansion of Slip Gague = 4.7X 10-6 / Deg C
dt = Uncertainty of temperature scaner = 0.39 Deg C
0.183
U5 = = 0.0917 microns
2

6. Standard Uncen. due to Accuracy Master Equipment. Slip gauge

Considering half of the accuracy & assuming rectangular distribution

0.12
U6 = = 0.069 microns
3

Combined Uncertainity:
Uc = (UA)2+(U1)2+(U2)2+(U3)2……………………………………………
Uc = 0.425 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
ån(ui(y)4)
j=1
Vi
= #DIV/0! = ¥
Expanded Uncertainity of Overall Uncertainity or Uncertainity of Measurement :
From thestudent's distribution table, for the Confidence Level approximately 95%, the Coverage
Factor, k =2.
U = k x Uc = 2 x 0.425 microns
0.851 microns
Therefore uncertainty in above measurement is =+ 0.851 microns
 Dial Thickness gauge
Determination of Measurement Uncertainty
Dial Gauge Range: 50 mm Least Count: 10 microns
Set of Slip Gauge used for calibration
Size (mm) :- 50 Reading Pionts : 50 mm
Uncertainty in measurement (mm): = 0.12
Unit of Measurement : = microns
Uncertainty of Temperature Scanner = 0.39 Deg C
Accuracy of master Equip. 0.1
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n
Mean Deviation x = ( xj)n
j=1

2
Measured/Observed Readings Standard Value Average (xj-x) (xj-x)
mm mm mm micron microns
(xj) (x)
49.990 0.0000 0.0000 0.000
49.990 0.0000 0.0000 0.000
49.990 0.0000 0.0000 0.000
49.990 0.0000 0.0000 0.000
49.990 0.0000 0.0000 0.000
49.990 0.0000 49.990 0.0000 0.000
49.990 0.0000 0.0000 0.000
49.990 0.0000 0.0000 0.000
49.990 0.0000 0.0000 0.000
49.990 0.0000 0.0000 0.000

2
Standard Deviation , S(X) =  (Xj - X)
n-1
= 0.0000 micron
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.000 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.000 microns
Type 'B' Evaluation
1. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Set of Slip Gauge
The value of Uncertainty is taken from its calibration certificate
Assuming Normal distribution Coverage Factor of Calibrating Lab =2
0.12
U1 = = 0.059 microns
2
2. Standard Uncertainty Due to the Resolution of dial thickness gauge
Considering half of the least count & assuming reactangular distribution
10
U2 = = 2.8868 microns
2x 3
3. Standard Uncertainty Due to Thermal Coefficient bitween Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
U3 =
3
Where L = Length = 50 mm
-6
a = 20% of ( a1 +a2) = 4.60 X 10 / Deg C
a1 = Th. Coefficient of Expansion = 11.5 X 10-6 / Deg C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / Deg C
 d = Control Limit or 10% of Temp. 20 °C 1 Deg C
0.230
U3 = = 0.133 microns
3
4. Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
U4 =
3
Where L = Length = 50 mm
-6
a = (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 10-6 / Deg C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.115
U4 = = 0.066 Deg C
3
5. Standard Uncertainty Due to the uncertainty of Standard Equipment used i.e. Temp.Scanner
Assuming Normal distribution.
The value of Uncertainty is taken from its calibration certificate i.e. = 0.39 Deg C
L X a X dt
U7 =
2
Where L = Length = 50 mm
a = Th. Coefficient of Expansion = 11.5 X 10-6 / Deg C
d = Uncertainty of temperature scanner = 0.39 Deg C
0.224
U7 = = 0.112 Deg C
2

6. Standard Uncen. due to Accuracy Master Equipment. Slip gauge

Considering half of the accuracy & assuming rectangular distribution

0.10
U6 = = 0.058 microns
3

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 2.894 microns
Degree of Freedom, (Veff)
4
uc(y)
Veff = 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 Range : 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) 0.00
Unit of Measurement : = microns Reading Point : 150 mm
o
Uncertinty of Temperature Scaner = 0.39 C
Wringing of Slip Gauges 0
Accuracy Slip gauge 0 micron
Accuracy surface plate 0 micron
Type 'A' Evalution
Five Readings are taken and the deviation from the nominal value is as follows-
n 7.841

Mean Devitation x = ( xj)n

j=1

Measured/Observed Readings Standard Value Avearge (xj-x) (xj-x)2

mm mm mm microns microns

0.006 0.000 -0.6000 0.360

0.004 0.000 -2.6000 6.760
0.008 0.000 1.4000 1.960
0.006 0.000 -0.6000 0.360
0.006 0.000 -0.6000 0.360
0.006 0.000 0.0066 -0.6000 0.360
0.008 0.000 1.4000 1.960
0.008 0.000 1.4000 1.960
0.008 0.000 1.4000 1.960
0.006 0.000 -0.6000 0.360

Standard Deviation =  (Xj - X)2

n-1

1.3499 microns

[S(X)]2
Stabdard Devitation of the Mean, S ( X) = n

= 0.4269 microns

Standard Uncertainity in Type 'A' Evalutation, UA = 0.4269 microns

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 = 2

1.51
U3 = = 0.755 microns
2
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 2
0.00
U4 = = 0.000 microns
2
5. Standard Uncertainity Due toThermal Coefficient between UUC & Standard
 Assuming rectangular distribution.

L X a X dt
U5 =
3
Where L = Length = 250.000 mm
a = Th. Coefficient of Expansion = 11.5 X 10-6 / Deg C
dt = Control Limit or 10% of Temp. 20 °C 1.0 Deg C
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.

L X a X dt
U7 =
3
Where L = Length = 250 mm
a = Th. Coefficient of Expansion = 11.5 X 10-6 / o C
o
d = 20% of Temp. Limit ± 1ºC 0.2 C

0.575
U7 = = 0.3320 microns
3

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

L X a X dt
U8 =
2
Where L = Length = 250 mm
a = Th. Coefficient of Expansion o = 11.5 X 10-6 / o C
o
d = Uncertainty of temperature scaner = 0.39 C

1.121
U8 = = 0.6474 microns
2
12. Standard Uncen. due to Accuracy Master Equipment. LTDG
Considering half of the accuracy & assuming rectangular distribution

3.00
U12 = = 1.732 microns
3

13. Standard Uncen. due to Accuracy Master Equipment. Surface plate

Considering 20% of the accuracy & assuming rectangular distribution

5.00
U13 = = 2.887 microns
3

Combined Uncertainity:

2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)

Uc = 3.921 microns

Degree of Freedom, (Veff)

uc(y)4
Veff =
n(ui(y)4)
j=1
Vi
= 64038.28194 = 

Expanded Uncertainity of Overall Uncertainity or Uncertainity of Measurement :

From thestudent's distribution table, for the Confidence Level approximately 95%, the Coverage
Factor, k =2.

Ue = ke x Uc = 2 x 3.921 microns

Therefore uncertainty in above measurement is = ± 7.841 microns

 Dial Gauge
Determination of Measurement Uncertainty
Range : 0.8 mm Least Count: 10 microns
Size of slip 0.8
Uncer. Of S.G.(micron) 0.09 0
Uncertainty Of Comparator stand(micron) 2.85
Unit of Measurement : = microns Reading Point : 0.8 mm
o
Uncertainty of Temperature Scanner = 0.39 C
Accuracy Slip Gauge 0.1 Comparator 6 microns
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

Measured/Observed Readings Standard Value Avearge (xj-x) (xj-x)2

mm mm mm microns microns

0.807 0.80 0.0000 0.000

0.807 0.80 0.0000 0.000
0.807 0.80 0.0000 0.000
0.807 0.80 0.0000 0.000
0.807 0.80 0.8070 0.0000 0.000
0.807 0.80 0.0000 0.000
0.807 0.80 0.0000 0.000
0.807 0.80 0.0000 0.000
0.807 0.80 0.0000 0.000
0.807 0.80 0.0000 0.000
0.0000
2
Standard Deviation =  (Xj - X)
n-1
0.0000 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.0000 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.0000 microns
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
0.09
U1 = = 0.045 microns
2
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
0.2
U2 = = 0.115 microns
1.732
3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard
Assuming rectangular distribution.
L X a X dt
U3 =
3
Where L = Length = 0.80 mm
a = 20% of ( a1 +a2) = 0.0000032
a1 = Th. Coefficient of Expansion = 4.7 X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
 d =
Control Limit or 10% of Temp. 20 °C 1 Deg C
0.0026
U3 = = 0.001 microns
3
4.Standard Uncertainty Due to the Resolution of Dial gauge
Considering half of the least count & assuming rectangular distribution
10
U4 = = 2.887 microns
2 x 1.732
5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
5 =
3
Where L = Length = 0.80 mm
-6
a = (a1+a2)/2 8.1 X 10
-6 O
a1 = Th. Coefficient of Expansion = 4.7X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.001
U5 = = 0.0007 microns
3
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
L X a X dt
U6 =
2
Where L = Length = 1 mm
a = Th. Coefficient of Expansion of Caliper Checker = 8.1X 10-6 /o C
o
d = Uncertainty of temperature scanner = 0.39 C
0.003
U6 = = 0.0013 microns
2
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 =2
2.85
U7 = = 1.425 microns
2

8. Standard Uncertainty Due to the Accuracy of Master Equipment slip Gauge

Considering half of the accuracy & assuming rectangular distribution
0.10
U8 = = 0.058 micron
3
9. Standard Uncertainty Due to the Accuracy of Comparator stand
Considering half of the accuracy & assuming rectangular distribution
6.00
U9 = = 3.464 micron
3

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 4.731 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
n(ui(y)4)
j=1
Vi
= 2.40412E+57 = 
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 = ke x Uc = 2 x 4.731 microns
Therefore uncertainty in above measurement is = ± 9.46 microns
 Dial Gauge
Determination of Measurement Uncertainty
Range : 50 mm Least Count: 10 microns
Size of slip 50.0
Uncer. Of S.G.(micron) 0.12
Uncertainty Of Comparator stand(micron) 2.85
Unit of Measurement : = microns Reading Point : 50 mm
o
Uncertainty of Temperature Scanner = 0.39 C
Accuracy Slip Gauge 0.1 Comparator 6 microns
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

Measured/Observed Readings UUC Value Avearge (xj-x) (xj-x)2

mm mm mm microns microns

50.010 50.00 0.0000 0.000

50.010 50.00 0.0000 0.000
50.010 50.00 0.0000 0.000
50.010 50.00 0.0000 0.000
50.010 50.00 50.0100 0.0000 0.000
50.010 50.00 0.0000 0.000
50.010 50.00 0.0000 0.000
50.010 50.00 0.0000 0.000
50.010 50.00 0.0000 0.000
50.010 50.00 0.0000 0.000
0.0000
2
Standard Deviation =  (Xj - X)
n-1
0.0000 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.0000 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.0000 microns
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
0.12
U1 = = 0.060 microns
2
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
0.2
U2 = = 0.115 microns
1.732
3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard
Assuming rectangular distribution.
L X a X dt
U3 =
3
Where L = Length = 50.00 mm
a = 20% of ( a1 +a2) = 0.0000032
a1 = Th. Coefficient of Expansion = 4.7 X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
 d =
Control Limit or 10% of Temp. 20 °C 1 Deg C
0.1620
U3 = = 0.094 microns
3
4.Standard Uncertainty Due to the Resolution of Dial gauge
Considering half of the least count & assuming rectangular distribution
10
U4 = = 2.887 microns
2 x 1.732
5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
5 =
3
Where L = Length = 50.00 mm
-6
a = (a1+a2)/2 8.1 X 10
-6 O
a1 = Th. Coefficient of Expansion = 4.7X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.081
U5 = = 0.0468 microns
3
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
L X a X dt
U6 =
2
Where L = Length = 50 mm
a = Th. Coefficient of Expansion of Caliper Checker = 8.1X 10-6 /o C
o
d = Uncertainty of temperature scanner = 0.39 C
0.158
U6 = = 0.0790 microns
2
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 =2
2.85
U7 = = 1.425 microns
2

8. Standard Uncertainty Due to the Accuracy of Master Equipment slip Gauge

Considering half of the accuracy & assuming rectangular distribution
0.10
U8 = = 0.058 micron
3
9. Standard Uncertainty Due to the Accuracy of Comparator stand
Considering half of the accuracy & assuming rectangular distribution
6.00
U9 = = 3.464 micron
3

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 4.733 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
n(ui(y)4)
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.
Ue = ke x Uc = 2 x 4.733 microns
Therefore uncertainty in above measurement is = ± 9.47 microns
 Dial Gauge
Determination of Measurement Uncertainty
Range : 25 mm Least Count: 10 microns
Size of slip 20.0 5
Uncer. Of S.G.(micron) 0.09 0.09
Uncertainty Of Comparator stand(micron) 2.85
Unit of Measurement : = microns Reading Point : 25 mm
o
Uncertainty of Temperature Scanner = 0.39 C
Accuracy Slip Gauge 0.1 Comparator 6 microns
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

Measured/Observed Readings Standard Value Avearge (xj-x) (xj-x)2

mm mm mm microns microns

25.007 25.00 0.0000 0.000

25.007 25.00 0.0000 0.000
25.007 25.00 0.0000 0.000
25.007 25.00 0.0000 0.000
25.007 25.00 25.0070 0.0000 0.000
25.007 25.00 0.0000 0.000
25.007 25.00 0.0000 0.000
25.007 25.00 0.0000 0.000
25.007 25.00 0.0000 0.000
25.007 25.00 0.0000 0.000
0.0000
2
Standard Deviation =  (Xj - X)
n-1
0.0000 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.0000 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.0000 microns
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
0.090
U1 = = 0.045 microns
2
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
0.2
U2 = = 0.115 microns
1.732
3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard
Assuming rectangular distribution.
L X a X dt
U3 =
3
Where L = Length = 25.00 mm
a = 20% of ( a1 +a2) = 0.0000032
a1 = Th. Coefficient of Expansion = 4.7 X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
 d =
Control Limit or 10% of Temp. 20 °C 1 Deg C
0.0810
U3 = = 0.047 microns
3
4.Standard Uncertainty Due to the Resolution of Dial gauge
Considering half of the least count & assuming rectangular distribution
10
U4 = = 2.887 microns
2 x 1.732
5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
5 =
3
Where L = Length = 25.00 mm
-6
a = (a1+a2)/2 8.1 X 10
-6 O
a1 = Th. Coefficient of Expansion = 4.7X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.041
U5 = = 0.0234 microns
3
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
L X a X dt
U6 =
2
Where L = Length = 25 mm
a = Th. Coefficient of Expansion of Caliper Checker = 8.1X 10-6 /o C
o
d = Uncertainty of temperature scanner = 0.39 C
0.079
U6 = = 0.0395 microns
2
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 =2
2.85
U7 = = 1.425 microns
2

8. Standard Uncertainty Due to the Accuracy of Master Equipment slip Gauge

Considering half of the accuracy & assuming rectangular distribution
0.10
U8 = = 0.058 micron
3
9. Standard Uncertainty Due to the Accuracy of Comparator stand
Considering half of the accuracy & assuming rectangular distribution
6.00
U9 = = 3.464 micron
3

Combined Uncertainty:
2 2 2 2……………………………………………
Uc = (UA) +(U1) +(U2) +(U3)
Uc = 4.732 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
n(ui(y)4)
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.
Ue = ke x Uc = 2 x 4.732 microns
Therefore uncertainty in above measurement is = ± 9.46 microns
 Measuring Pin
Determination of Measurement Uncertainty
Range : 20 mm Least Count: microns
Size of slip 20.0 0
Uncer. Of S.G.(micron) 0.09 0
Uncertainty Of Comparator stand(micron) 2.85
Unit of Measurement : = microns Reading Point : 20 mm
o
Uncertainty of Temperature Scanner = 0.39 C
Accuracy Slip Gauge 0.1 Comparator 6 microns
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

Measured/Observed Readings Standard Value Avearge (xj-x) (xj-x)2

mm mm mm microns microns

20.0004 20.00 -0.0400 0.002

20.0006 20.00 0.1600 0.026
20.0005 20.00 0.0600 0.004
20.0004 20.00 -0.0400 0.002
20.0003 20.00 20.0004 -0.1400 0.020
20.0004 20.00 -0.0400 0.002
20.0006 20.00 0.1600 0.026
20.0005 20.00 0.0600 0.004
20.0004 20.00 -0.0400 0.002
20.0003 20.00 -0.1400 0.020
0.0000
2
Standard Deviation =  (Xj - X)
n-1
0.1075 microns
2
[S(X)]
Standard Deviation of the Mean, S ( X) = n
= 0.0340 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 0.0340 microns
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
0.09
U1 = = 0.045 microns
2
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
0
U2 = = 0.000 microns
1.732
3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard
Assuming rectangular distribution.
L X a X dt
U3 =
3
Where L = Length = 20.00 mm
a = 20% of ( a1 +a2) = 0.0000032
a1 = Th. Coefficient of Expansion = 4.7 X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
d = Control Limit or 10% of Temp. 20 °C 1 Deg C
0.0648
U3 = = 0.037 microns
3
4.Standard Uncertainty Due to the Resolution of Dial gauge
 Considering half of the least count & assuming rectangular distribution
0.2
U4 = = 0.058 microns
2 x 1.732
5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
5 =
3
Where L = Length = 20.00 mm
a = (a1+a2)/2 8.1 X 10-6
a1 = Th. Coefficient of Expansion = 4.7X 10-6 / O C
a2 = Th. Coefficient of Expansion = 11.5 X 10-6 / O C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.032
U5 = = 0.0187 microns
3
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
L X a X dt
U6 =
2
Where L = Length = 20 mm
a = Th. Coefficient of Expansion of Caliper Checker = 8.1X 10-6 /o C
o
d = Uncertainty of temperature scanner = 0.39 C
0.063
U6 = = 0.0316 microns
2
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 =2
2.85
U7 = = 1.425 microns
2

8. Standard Uncertainty Due to the Accuracy of Master Equipment slip Gauge

Considering half of the accuracy & assuming rectangular distribution
0.10
U8 = = 0.058 micron
3
9. Standard Uncertainty Due to the Accuracy of Comparator stand
Considering half of the accuracy & assuming rectangular distribution
6.00
U9 = = 3.464 micron
3
9. Standard Uncertainty Due to the Accuracy of dial Indicator
Considering half of the accuracy & assuming rectangular distribution
0.30
U9 = = 0.173 micron
3
9. Standard Uncertainty Due to the Uncertainity of dial Indicator
Considering half of the accuracy & assuming Normal distribution
0.40
U9 = = 0.231 micron
2

Combined Uncertainty:
Uc = (UA)2+(U1)2+(U2)2+(U3)2……………………………………………
Uc = 3.759 microns
Degree of Freedom, (Veff)
uc(y)4
Veff =
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 = ke x Uc = 2 x 3.759 microns
Therefore uncertainty in above measurement is = ± 7.52 microns
 ultra sonic gauge
Determination of Measurement Uncertainty of ultra sonic gauge Up to 150 mm
Range : 100 mm Least Count: 10 microns
Size of Caliper 100
Uncer. Of S.G.(micron) 0.17 0
Uncertainty Of surface plate(micron) 4.6
Unit of Measurement : = microns Reading Point : 100 mm
o
Uncertainty of Temperature Scanner = 0.39 C
Accuracy Slip Gauge 0.12 Surface Plate 5 microns
Type 'A' Evaluation
Five Readings are taken and the deviation from the nominal value is as follows-
n

Mean Deviation x = ( xj)n

j=1

2
Measured/Observed Readings Standard Value Avearge (xj-x) (xj-x)
mm mm mm microns microns

99.45 100 -5.0000 25.000

99.46 100 5.0000 25.000
99.45 100 -5.0000 25.000
99.45 100 -5.0000 25.000
99.46 100 99.4550 5.0000 25.000
99.46 100 5.0000 25.000
99.45 100 -5.0000 25.000
99.46 100 5.0000 25.000
99.45 100 -5.0000 25.000
99.46 100 5.0000 25.000
0.0000
Standard Deviation =  (Xj - X)2
n-1
5.2705 microns

[S(X)]2
Standard Deviation of the Mean, S ( X) = n
= 1.6667 microns
Standard Uncertainty in Type 'A' Evaluation, UA = 1.6667 microns
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
0.17
U1 = = 0.085 microns
2
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
0
U2 = = 0.000 microns
1.732
3.Standard Uncertainty Due toThermal Coefficient between UUC & Standard
Assuming rectangular distribution.
U3 = L X a X dt
3
Where L = Length = 100.000 mm
a = 20 % of a1+a2 3.24 X 10-6 / Deg C
a1 = Th. Coefficient of Expansion of DStandard = 4.7 X 10-6 / Deg C
a2 = Th. Coefficient of Expansion of UUC = 11.5 X 10-6 / Deg C
 dt = Control Limit or 10% of Temp. 20 °C 1.0 Deg C
0.320 0.185 microns
3
4.Standard Uncertainty Due to the Resolution of ultra sonic gauge
Considering half of the least count & assuming rectangular distribution
10
U4 = = 2.887 microns
2 x 1.732
5.Standard Uncertainty Due to the Temp. Variation in Master Instrument & UUC
Assuming rectangular distribution.
L X a X dt
5 =
3
Where L = Length = 100.00 mm
-6
a = (a1+a2)/2 11.5X 10
-6 O
a1 = Th. Coefficient of Expansion = 11.5X 10 / C
-6 O
a2 = Th. Coefficient of Expansion = 11.5 X 10 / C
d = 20% of Temp. Limit ± 1ºC 0.2 Deg C
0.230
U5 = = 0.1328 microns
3
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
L X a X dt
U6 =
2
Where L = Length = 100 mm
-6 o
a = Th. Coefficient of Expansion of slip gauge = 11.5 X 10 / C
o
d = Uncertainty of temperature scanner = 0.39 C
0.449
U6 = = 0.2243 microns
2
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
4.60
U7 = = 2.300 microns
2

8. Standard Uncertainty Due to the Accuracy of Master Equipment

Considering half of the accuracy & assuming rectangular distribution
0.12
U8 = = 0.069 micron
3
8. Standard Uncertainty Due to the Accuracy of Master Equipment
Considering half of the accuracy & assuming rectangular distribution
5.00
U8 = = 2.887 micron
3

Combined Uncertainty:
Uc = (UA)2+(U1)2+(U2)2+(U3)2……………………………………………
Uc = 4.985 microns
Degree of Freedom, (Veff)
4
uc(y)
Veff = 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 = ke x Uc = 2 x 4.985 microns
Therefore uncertainty in above measurement is = ± 10.0 microns