Training Material for Balances (2)Prepared by R&D Division 1

A&D Company,Company Limited1

Contents
 Measuring Repeatability, Linearity & Sensitivity Drift - P.3– Specifications of GX-2000 -------------------- P.4– Repeatability ------------------------------------- P.5– Linearity ------------------------------------------ P.10
– Sensitivity Drift --------------------------------- P.122

Measuring Repeatability
Repeatability,,Linearity & Sensitivity Drift3Specifications of GXGX-2000
WeighingW
i hi Capacity
CitMinimum Weighing Value(1 digit)

Repeatability(Standard Deviation)

Linearity
Sensitivity Drift(10 ~ 30ºC)

2100
2100g
0.01g
0.01g
±0.02g0.02g±2ppm/ºC(Automatic self calibration is not used)4

Repeatability
 Repeatability indicates the variation in measurement when

the same mass is loaded several times
times. Repeatability isexpressed using standard deviation (  : sigma).
 As theh repeatability
bili off GX-2000 isi 0.01g, whenh a 2kg
k massis loaded repeatedly, the results will be*– 1999.99g ~ 2000.01g with the probability of 68% (Mean  1 )– 1999.98g ~ 2000.02g with the probability of 95% (Mean  2 )– 1999.97g
1999 97g ~ 2000
2000.03g
03g with
ith the probabilit
probability of 99.7%
99 7% (Mean(M 3 )* supposing that the mean value is 2000.00g
2000 00g
5Repeatability
Normal Distribution
Frequency

68%

Mean

2000.00g

1999.99g

2000.01g-1σ+1σ2000.02g

1999.98g

99.7%
2000.03g

1999.97g-1σ-2σ3σ-3σ

95%+1σ+2σ-2σ+2σ-3σ+3σ+3σ
3σ

6RepeatabilityCalculating Repeatability ( )Measured Value  Mean 2Formula:Ex)

Standard Deviation  n 1

Number of Measurements  1

We measured a 2kg mass five times with GX-2000 (minimum weighing
value 0.01g). The results were as follows:

1st
2nd
3rd
4th
5th

2000.01g
2000 00g
2000.00g
1999.98g
1999.99g
g
2000.02g
7

Repeatability
Measured Minimum Weighing
Value
Value (digit)
1
1st2000 01
2000.01g
1 dig
di2nd 2000.00g
0 dig
3rd
1999.98g-2 dig1999.99gg-1 digg
4th
5th
2000.02g
2 dig
Mean 2000.00g
0 dig

Measured Value - Mean
0.01g
0.00g
-0.02g
0 02-0.01g
0.02g

As the minimum weighing value of GX-2000 is 0.01g,
1 digit = 0.01g
0 01g

 Measured Value  Mean 2 n 1

2(Measured Value -Mean)
0.00010.00000 00040.00040.00010.0004

Number of Measurements  1

 Measured Value  Mean   0.0010
2Md ValueV l  Mean
M  Measured2

Number of Measurements  1

0.00025

 Measured Value  Mean   0.01588  0.016 g
2

 n 1

Number of Measurements  18Repeatability
Alternatively,
Measured Value - Mean
1 dig
0 dig
di-2 dig-1 dig2 digg2(Measured Value -Mean)
10412

 Measured Value  Mean   102

 Measured Value  Mean  
2Number of Measurements  12.5

 Measured Value  Mean   1.588 ≒1.6digg  0.016 g
Number of Measurements 1
12

 n 1Since the repeatability of GX
GX-2000
2000 is 00.01g,
01g the performance of this balance
would be unsatisfactory.
9Linearity
 Linearity refers to the deviation in the measured value

from the ideal (linear) curve between 0g and the maximum
capacity.
 It isi necessary to correct theh slope
loff theh measurement

curve by conducting a calibration first, because theweighing results will vary depending on the acceleration ofgravity at the point of use or can be influenced bytemperaturepchanges.
g10Linearity
Sensitivity and linearity errors are zero
There are sensitivity and linearity errors、

Displayed
value

2000g

Sensitivity and linearity errors are zero

Error: -0.04g

1500g

Linearity error: -0.01g

1000g

Error: -0.04g

500g

There are sensitivity and linearity errors

1500g

Error: -0.04g

1000g

2000g

Displayed
value

CAL

Error: -0.02g

Linearity error: -0.02g

500g

Linearity error: -0.01g

Weight0g




500g

1000g

1500g

2000g

Weight0g

500g

1000g

1500g

2000g

When calibrated
Whlibd withi h a 2000g
2000 weight,
i h theh measurement curve will
ill beb correctedd by
b –0.04g
0 04 atthe point of 2000g.
Likewise, it will be corrected by –0.01g, -0.02g, and –0.03g at 500g, 1000g, and 1500g
respectively The maximum linearity error after the calibration will thus be –0.02g
respectively.
–0 02g (at 1000g).
1000g)
Since the specification of linearity for GX-2000 is ±0.02g, the performance is judged to besatisfactory in this case.

11

Sensitivity Drift Sensitivity drift is the increase or decrease in the measured

value that occurs when the same mass is weighed atdifferent ambient temperatures.
 The
h rate off variationi i isi expressedd ini “ppm (Parts(PerMillion).” For example, the sensitivity drift of GX-2000 is±2ppm/ºC. This means that the measured value can varyb up tobyt “±2/1,000,000”
2/1 000 000” withith a 1ºC change
hiin temperature.
tt

12Sensitivity DriftEx 1)

We calibrated GX-2000 so that it would display 2000.00g at 20ºC. If the ambient
temperature later became 30ºC, what would be the maximum error ofmeasurement caused by sensitivity drift?

Measured Value (Referential Value)  (ppm / º C)  Variation in Temperature
2000.00( g )  {2(ppm / º C)} {30(º C)  20(º C)}
 2000.00 2
101000000

 0.04( g )This indicates that there can be a variation of up to ±0.04g (1999.96 ~2000.04g) from the initial value of 2000.00g when the temperature changes
by 10ºC.
13

Sensitivity DriftEx 2)

The following results were obtained using GX-2000. What is the sensitivity drift(ppm/ºC)?
W i htWeightA bi t Temperature
Ambient
Tt
20ºC
2000.00g
30ºC

MeasuredMdVValuel2000.00g
1999.97g

 Result B (after change)  Result A (before change)  1000000  (ppm)Result A (before change)ppm
 (ppm / º C)
Variation in Temperature
1999.97  2000.00
1000000  15(ppm)2000.00
 15
 1.5(ppm / º C)
30  20

This satisfies the specification
off sensitivity
i i i drift
d if forf GX-2000,
GX 2000
which is ±2ppm/ºC.
14