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# 4 - TEXAS A&M UNIVERSITY Statistical Data Processing...

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TEXAS A&M UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING TEXAS A&M UNIVERSITY COLLEGE STATION, TX 77843-3123 979 845 1251 FAX 979 845 3081 1 of 15 Statistical Data Processing R. Langari, 9/10/10 Statistical Data Analysis Purpose of Experiments Exploratory : Collected data so one can later find correlations among measured quantities - Examples: Validation : Given a theoretical model, perform experiments that validate or invalidate the model. This includes design validation/qualification as well! - Examples: Other? --> Need to ensure that we have meaningful data! What is meaningful data? -->Data always has error in it! DEPARTMENT OF MECHANICAL ENGINEERING TEXAS A&M UNIVERSITY COLLEGE STATION, TX 77843-3123 979 845 1251 FAX 979 845 3081 2 of 15 Statistical Data Processing R. Langari, 9/10/10 How to assess the source and magnitude of errors? Error Sources Systematic or Bias Errors , e.g. sensor calibration errors, certain set-up errors Precision or Random Errors , e.g. sensor resolution errors, some human errors, noise x s x t x t x t True value Sensed value x s t x

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TEXAS A&M UNIVERSITY DEPARTMENT OF MECHANICAL ENGINEERING TEXAS A&M UNIVERSITY COLLEGE STATION, TX 77843-3123 979 845 1251 FAX 979 845 3081 3 of 15 Statistical Data Processing R. Langari, 9/10/10 Review of Statistical Distributions Let us denote the quantity to be determined; e.g. temperature in a room by . The true value of , which we denote by or , is, and will remain, unknown , although we can find a close estimate of following the discussion given below. First consider the hypothetical case that infinite number of measurements of can be made. These measurements will have some “mean” or average value which we denote by or more accurately by . If these measurements are not biased and are only affected by random or precision errors, then it is generally the case that is the closest possible approximation of . Moreover, the distribution of around this mean value is Gaussian , i.e. follows the so called normal or Gaussian probability distribution function discussed next. x x x true x t x t x μ μ x μ x x t x DEPARTMENT OF MECHANICAL ENGINEERING TEXAS A&M UNIVERSITY COLLEGE STATION, TX 77843-3123 979 845 1251 FAX 979 845 3081 4 of 15 Statistical Data Processing R. Langari, 9/10/10
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4 - TEXAS A&M UNIVERSITY Statistical Data Processing...

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