Measuring Repeatability, Linearity & Sensitivity Drift - P.3

Transcription

1 Training Material for Balances () Prepared by R&D Division 1 A&D Company, Limited 1

2 Contents Measuring Repeatability, Linearity & Sensitivity Drift - P.3 Specifications of GX P.4 Repeatability P.5 Linearity P.10 Sensitivity Drift P.1

3 Measuring Repeatability, Linearity & Sensitivity Drift 3

4 Specifications of GX-000 Wihi Weighing Capacity 100g Minimum Weighing Value (1 digit) 0.01g Repeatability (Standard Deviation) 0.01g Linearity ±0.0g Sensitivity Drift (10 ~ 30ºC) ±ppm/ºc (Automatic self calibration is not used) 4

5 Repeatability Repeatability indicates the variation in measurement when the same mass is loaded several times. Repeatability is expressed using standard deviation ( : sigma). As the repeatability of GX-000 is 0.01g, when a kg mass is loaded repeatedly, the results will be* g ~ g with the probability of 68% (Mean 1 ) g ~ 000.0g with the probability of 95% (Mean ) g 97g ~ g 03g with the probability of 99.7% (Mean 3 ) * supposing that the mean value is g 00g 5

6 Repeatability Normal Distribution Frequency g Mean 68% g g -1σ +1σ g 000.0g 99.7% g g 95% -1σ +1σ -σ +σ -3σ +3σ -σ +σ -3σ +3σ 6

7 Calculating Repeatability ( ) Repeatability Formula: Standard Deviation n 1 Measured Value Mean Number of Measurements 1 Ex) We measured a kg mass five times with GX-000 (minimum weighing value 0.01g). The results were as follows: 1st g nd g00g 3rd g 4th g 5th 000.0g 7

8 Repeatability Measured Value Minimum Weighing Value (digit) 1st g01 1 dig nd g 0 dig 3rd g - dig 4th g -1 dig 5th 000.0g dig Mean g 0 dig As the minimum weighing value of GX-000 is 0.01g, 1 digit = 0.01g01g n 1 Measured Value Mean Number of Measurements 1 Measured Value - Mean (Measured Value -Mean) 0.01g g g g g Measured Value Mean MeasuredVl Value Mean Number of Measurements n 1 Measured Value Mean Number of Measurements g 8

9 Repeatability Alternatively, Measured Value - Mean (Measured Value -Mean) 1 dig 1 0 dig 0 - dig 4-1 dig 1 dig Measured Value Mean Measured Value Mean Number of Measurements n1 Measured Value Mean Number of Measurements dig gg Since the repeatability of GX-000 is 0.01g, 01g the performance of this balance would be unsatisfactory. 9

10 Linearity Linearity refers to the deviation in the measured value from the ideal (linear) curve between 0g and the maximum capacity. It is necessary to correct the slope of the measurement curve by conducting a calibration first, because the weighing results will vary depending on the acceleration of gravity at the point of use or can be influenced by temperature changes. 10

11 Linearity Sensitivity and linearity errors are zero Sensitivity and linearity errors are zero 000g Displayed value There are sensitivity and linearity errors Error: -0.04g 000g Displayed value There are sensitivity and linearity errors 1500g Error: -0.04g 1500g Linearity error: -0.01g 1000g 500g Error: -0.0g Error: -0.04g CAL 1000g 500g Linearity error: -0.0g Linearity error: -0.01g Weight Weight 0g 500g 1000g 1500g 000g 0g 500g 1000g 1500g 000g When calibrated with a 000g weight, the measurement curve will be corrected by 0.04g 004 at the point of 000g. Likewise, it will be corrected by 0.01g, -0.0g, and 0.03g at 500g, 1000g, and 1500g respectively. The maximum linearity error after the calibration will thus be 0.0g 0g (at 1000g). Since the specification of linearity for GX-000 is ±0.0g, the performance is judged to be satisfactory in this case. 11

12 Sensitivity Drift Sensitivity drift is the increase or decrease in the measured value that occurs when the same mass is weighed at different ambient temperatures. The rate of variation is expressed in ppm (Parts Per Million). For example, the sensitivity drift of GX-000 is ±ppm/ºc. This means that the measured value can vary by up to ±/1,000, with a 1ºC change in temperature. t 1

13 Sensitivity Drift Ex 1) We calibrated GX-000 so that it would display g at 0ºC. If the ambient temperature later became 30ºC, what would be the maximum error of measurement caused by sensitivity drift? Measured Value (Referential Value) (ppm /º C) Variation in Temperature ( g) { (ppm /º C)} {30(º C) 0(º C)} ( g) This indicates that there can be a variation of up to ±0.04g ( ~ g) from the initial value of g when the temperature changes by 10ºC. 13

14 Sensitivity Drift Ex ) The following results were obtained using GX-000. What is the sensitivity drift (ppm/ºc)? Wiht Weight Ambient Temperature Measured dvalue 0ºC g g 30ºC g Result B (after change) Result A (before change) Result A (before change) ppm (ppm /º C) Variation in Temperature (ppm) (ppm) (ppm /º C) 30 0 This satisfies the specification of sensitivity i i drift for GX-000, which is ±ppm/ºc. 14