Proper Platinum Resistance Thermometer Calibration Uncertainty Analysis

Transcription

1 Proper Platinum Resistance Thermometer Calibration Uncertainty Analysis Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 1

2 Introduction Uncertainty quantification is a primary task of the metrologist The uncertainty analysis must reflect our best understanding of the measurement and the instrument being calibrated If a calibration process is not fully understood, the uncertainty analysis is almost certainly flawed If the uncertainties do not reflect some aspects of UUT behavior, it will not reflect the UUT in use Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 2

3 Introduction Incomplete uncertainty analysis Thorough uncertainty analysis is often more complex than it appears Ignorance is bliss - the less we know, the better our numbers look Although our assessors are very good, some do not possess sufficient current understanding to notice omissions in the uncertainty analysis Philosophical viewpoint Should the calibration be considered as an isolated experiment or as part of a process? Should the uncertainty analysis include only those components present at the time of calibration? Should the uncertainty analysis include additional components to reflect UUT short term behavior? Should the uncertainty analysis include additional components to reflect UUT long term behavior? Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 3

4 Introduction Consequently, it is easy to underestimate the real measurement uncertainty Some omissions are insignificant to the final result and amount to a minor embarrassment or controversy when discovered Other omissions may result in a noticeable, substantive underestimation of the final uncertainty Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 4

5 Categorization Often categorization helps us see things more clearly Platinum resistance thermometer calibration uncertainties can be categorized into two areas: Uncertainties in temperature Uncertainties in resistance measurement Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 5

6 Categorization Thermal uncertainties Temperature stability Temperature uniformity Determination of the temperature Temperature equilibrium Self heating caused by excitation current* Resistance measurement uncertainties Readout accuracy Readout linearity Electrical noise Electrical interference Self heating caused by excitation current* *Evaluate only once (avoid double counting) Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 6

7 Uncertainty Budget Uncertainty Evaluation Type A Evaluation Category LN2 tn100 Hg TPW FPIn FPSn FPZn t500 mk mk mk mk mk mk mk mk Readout Noise (1σ) E Total A A Type B Evaluation SPRT accuracy (calibration and drift) T Bath uniformity T Thermometer readout (6 ppm, SPRT) E Thermometer readout (6 ppm, UUT) E Total B B Total Standard Uncertainty U Total Expanded Uncertainty (k =2) U' Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 7

8 Additional Components Some components are missing Reference SPRT R TPW propagation Reference SPRT self heating correction Reference SPRT immersion error UUT noise contribution UUT short term repeatability UUT immersion error UUT insulation resistance Mathematical model uncertainties Process repeatability Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 8

9 SPRT Uncertainties SPRT R TPW measurement (or ambiguity allowance) during use propagates to uncertainty in determination of W T90 Example, R TPW uncertainty of 0.5 mk becomes 1.4 mk at 500 C SPRT self heating is different in different thermal environments Fixed point cells (SPRT cal) and comparison baths (use) SPRT has immersion requirements which may or may not be satisfied in the application For example, calibration of short sensors Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 9

10 UUT Uncertainties UUT noise allowance The noise influences the precision of the average obtained during the calibration mk Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 10

11 UUT Uncertainties UUT short term repeatability Hysteresis Hysteresis of 5 Industrial Probes Deviation From Average ( C) Reference Temperature ( C) Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 11

12 UUT Uncertainties UUT short term repeatability R TPW repeatability (average = , spread = C) R TPW Repeatability RTPW measurement Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 12

13 UUT Uncertainties UUT immersion error Immersion Curves in a Liquid Bath at 80 C 0.01 Temperature Difference from the Bottom, C L+20D L+17.5D L+15D L+12.5D L+10D L+7.5D Immersion Depth, Sensor Length L + X Diameters in Length PROBE 1 PROBE 2 PROBE 3 PROBE 4 PROBE 5 Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 13

14 UUT Uncertainties UUT insulation resistance effects (worst case) 1) R total ( Ω) = 1 R R R n = 1 256Ω MΩ 2) R total ( Ω) = Ω 3) R = 256Ω Ω Ω 4) Ω 0.36 Ω C = C = 18.2mK 5) 18.2mK 3 = 10.5mK Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 14

15 Mathematical Model U t t temperature temperature t t temperature Curve Fit temperature Magnitude of Residuals Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 15

16 Process Repeatability Comparison Process Check 420 C Standard Deviation = C T(SPRT) - T(Check Standard) /1/ /6/2003 6/28/2003 3/20/ /10/2002 8/1/2004 4/23/2004 1/14/2004 Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 16

17 Revised Uncertainty Budget Uncertainty Evaluation Type A Evaluation Category LN2 tn100 Hg TPW FPIn FPSn FPZn t500 mk mk mk mk mk mk mk mk Process variability P Precision of UUT measurement T&E Propagated repeatability of RTPW (UUT) UUT Total A A Type B Evaluation SPRT accuracy (calibration and drift) T SPRT RTPW propagation T SPRT self heating correction T Insulation resistance (UUT) Bath uniformity T Thermometer readout (6 ppm, SPRT) E Thermometer readout (6 ppm, UUT) E Total B B Total Standard Uncertainty U Total Expanded Uncertainty (k =2) U' Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 17

18 Difference Original Uncertainty Evaluation U' Revised Uncertainty Evaluation U' Difference Absolute % Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 18

19 Conclusions Uncertainty evaluation involves variables that may not be readily apparent Some variables are difficult to quantify and may vary from UUT to UUT Underestimating the uncertainties in this manner may lead to significant errors Incomplete uncertainty analyses are very common among both unaccredited and accredited laboratories Thomas Wiandt Fluke Corporation, Hart Scientific Division NCSLI 2007 Session 8B 19