1. 2007 NCSL International Workshop and Symposium 1 NCSLI Determination of Temperature Probability Distribution by Diagrams National Measurement Laboratory CMS/ITRI, Taiwan Chen-Yun Hung

2. 2 2007 NCSL International Workshop and Symposium Introduction Precision dimensional measurement is highly sensitive to environmental temperature Usually, we evaluate the uncertainty of temperature by Type B evaluation Several kinds of scatter diagrams by simulated data are provided to help users find the probability distributions of temperature quickly

3. 3 2007 NCSL International Workshop and Symposium Temperature changes in a sine function with time Probability distribution of temperature U-shaped distribution Probability Distribution of Temperature Changes in a Sine Function with Time Time in measurement Rectangular distribution

4. 4 2007 NCSL International Workshop and Symposium Find the Probability Distribution of Temperature by the Histogram Described from Simulated Data We collect one measured temperature data every minute for 8 hours The data of temperature are all within (20.0  1.0)  C 4 cycles in 8 hours

5. 5 2007 NCSL International Workshop and Symposium Type I Temperature Changes in a Sine Function with Time U-shaped distribution Derivation of mathematical models Verified by histogram Standard deviation equals half-width (1.0  C) divided by

6. 6 2007 NCSL International Workshop and Symposium Type II Temperature Changes in a Linear Function with Time Rectangular distribution Verified by histogram Standard deviation equals half-width (1.0  C) divided by Probability distribution of temperature which ascends quickly (slowly) but descends slowly (quickly) is the same as Type II Higher relative uncertainty of uncertainty (R %)

7. 7 2007 NCSL International Workshop and Symposium Type III Temperature Changes in a Trapezoid Function with Time U-shaped distribution Verified by histogram Standard deviation more than half-width (1.0  C) divided by Higher relative uncertainty of uncertainty (R %)

8. 8 2007 NCSL International Workshop and Symposium Type IV Temperature Contracts Cyclically with Time Normal distribution or Triangular distribution Verified by histogram Normal distribution: Standard deviation equals Triangular distribution: Standard deviation equals Decide the relative uncertainty of uncertainty subjectively

9. 9 2007 NCSL International Workshop and Symposium Type V Temperature Expands or Contracts Cyclically with Time Normal distribution or Triangular distribution Verified by histogram Normal distribution: Standard deviation equals Triangular distribution: Standard deviation equals Decide the relative uncertainty of uncertainty subjectively

10. 10 2007 NCSL International Workshop and Symposium Type VI Temperature is Irregular Cyclically with Time Normal distribution or Triangular distribution Verified by histogram Normal distribution: Standard deviation equals Triangular distribution: Standard deviation equals Decide the relative uncertainty of uncertainty subjectively

11. 11 2007 NCSL International Workshop and Symposium Short Summary Normal distribution or Triangular distribution Most of data center around the central temperature Type IV, V, VI U-shaped distribution Most of data center on the upper bound and lower bound Temperature changes in a sine function with time Type I, III Rectangular distribution Temperature changes in a linear function cyclically and regularly with time Type II

12. 12 2007 NCSL International Workshop and Symposium Example Type VI

13. 13 2007 NCSL International Workshop and Symposium The Difference Between the Histogram and the Bar Chart Temperature belongs to the continuous random variable An incorrect statistical chart will cause an incorrect assumption of the probability distribution Type I for example U-shaped distribution Resolution of 0.1  C ─ U-shaped distribution

14. 14 2007 NCSL International Workshop and Symposium The Difference Between the Histogram and the Bar Chart (Cont’d) Resolution of 0.01  C ─ Rectangular distribution or Two-peaked distribution

15. 15 2007 NCSL International Workshop and Symposium The Difference Between the Histogram and the Bar Chart (Cont’d) Resolution of 0.00001  C ─ Rectangular distribution or trapezoid distribution

16. 16 2007 NCSL International Workshop and Symposium Suggestions Evaluate the uncertainty of temperature by Type A evaluation if users expect a smaller uncertainty Short period of measured time Sometimes, scatter diagrams of actual data do not belong to any types in this paper

17. 17 2007 NCSL International Workshop and Symposium References 1. ISO, Guide to the expression of uncertainty in measurement, 1995. 2. C. Y. Fang, C. K. Sung, C. Y. Hung, and K. W. Lui, “Determination of Temperature Probability Distribution in Measurement Uncertainty”, Proceeding of ASPE 2006 Annual meeting. 3. ISA RP52.1, Recommended Environments for Standards Laboratories, 1975. 4.

18. 2007 NCSL International Workshop and Symposium 18 Thank you for your attention