ME 322: Instrumentation Lecture 2

1. ME 322: InstrumentationLecture 2 January 24, 2014 Professor Miles Greiner

2. Reminders • HW 1 due Monday • Use ME 322 ID number (from WebCampus) • not name • We have moved some students to Lab Section 5 (W 1-3:45 PM). Please check MyNevada to know your current Lab assignment.

3. Results of the Quad Measurements • Data is on Lab 2 website • Today I’ll show you how to process that data, which you will need to repeat and present in Lab 2, Analysis of Quad Measurement • Spreadsheet had Measured Data and Calculations • H, DC , NCi, NCA, F = DC/NCA • NSi, NSA, S=F*NSA • NLi, NLA, L=F*NLA • A = LS • C = A*($3.49/200 ft2) • How to Plot • F versus H; L vs S (scatter plots) • Cost Estimate Histogram • Questions • Is stride length F highly correlated with height, H? • What is the sample mean and standard deviation of the cost estimates? • Are the measured values of L and S correlated? • If you budget the amount of your cost estimate, you are only 50% sure to have enough to cover quad (be above the average value, which we assume is the most accurate estimate) • How much money should you budget to be 90% sure to have enough

4. Randomly Varying Processes • The output of a measurement instrument is affected by the measurand (the quantity being measured) and many uncontrolled (undesired) factors • Consider a process (such as a measurement) that has a very large number of factors that can, independently, increase or decrease the value of the outcome • Its not likely that all or a large majority of the factors will push the outcome in the same direction. • Its more likely that “most” of the factors will cancel each other, and push the outcome only “slightly” in one direction or the other. • This describes how uncontrolled factors affect the output of measurement systems (instruments)

5. Gaussian (Normal) Probability Distribution Function • Describes Randomly Varying Processes • Looks like the pattern observed from the cost estimate histogram in Labs 1 and 2 • We were able to estimate m ~ and s ~ for that data

6. How can we use this? • If a sample is very large, and if the process variations are “normally” distributed, • Then expect sample histogram to take a bell shape, • And, if we know s and m, the probability that the next measurement x will be in the range x1 < x < x2 is • Note, for any s and m :

7. Non-Dimensionalization • Define • Number of standard deviations x is above the mean • We can show that the probability that the next measurement is between z1 and z2 is: • Where • This integral is tabulated on page 146, for z > 0

9. Graphical RepresentationArea from center (z = 0) to z For z > 0 : Note:

10. Negative values of z For z1 < 0 :

11. Symmetric Example Find the Probability a measurement is within one standard deviation (s) of the mean (m). = = -1 = = 1

12. Page 146

13. Next measurement is within 2s and 3s of the mean

15. One-sided example • From Lab 2, what seed cost will cover (be greater than) 90% of all future estimates? • One-sided example • P=0.9= I(z2)-I(z1) • z2 = ? But z1-∞, so I(-∞)= -I(∞)=-0.5 • So P = 0.9 = I(z2) – [-0.5] • 0.4 = I(z2) • Interpolate between z2 = 1.28 and 1.29 • Get z2 = 1.282

17. Lab 2 • If you make a measurement, there is a 50% likelihood it is below the mean (best) value. • How much should you add to your best estimate to be 90% you are above the mean? • Answer: 1.282 standard deviations

18. Extra Slides

19. Area of UNR Quad • Find Short Side (S) • NSi • NSA • Find Long Side (L) • NLi • NLA