chap05 - Learn by writing methods are valuable for...

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“Learn by writing” methods are valuable for developing understanding of a new concept. Questions 5.1 – 5.4 provide some topics for “Learn to Write” exercises. PROBLEM 5.1 SOLUTION Systematic error is a constant error that shifts all measured values of a variable by a fixed amount. In effect, the sample mean value will be offset from the true mean value by this fixed amount. Randomization methods break up some of the trends brought on by interference, a result of systematic errors, Randomization makes systematic errors behave as random errors, which are more easily quantified using statistics. Calibration is an excellent way to isolate, identify, quantify and thereby reduce systematic errors. Random error leads to scatter in the measured values obtained during the measurement of a variable under otherwise fixed operating conditions. Unlike systematic errors, random errors will change in magnitude between repeated measurements bringing on the noted scatter. Both systematic and random errors are present in any measurement to some degree. For the engineer, the difficult task is assigning the probable values of these errors. That‟s where the test plan comes into importance. By incorporating repetition into a test plan, random errors can be statistically estimated with some amount of predictability. Incorporating replication strengthens the random error estimates and allows estimates of control to be made, which may include some of the systematic errors. PROBLEM 5.2 SOLUTION Systematic errors are usually estimated by comparison methods. These methods include: (i) calibration, (ii) concomitant methods, (iii) interlaboratory or different facility comparisons, or (iv) experience. Random errors are manifested by measured data scatter and their effects on the estimate of the true value of the measured variable can be estimated statistically using the methods discussed previously in Chapter 4. ERRORS ARE NOUNS; UNCERTAINTIES ARE NUMBERS. An error refers to a difference between the measured value and the true value. Because this exact amount is unknown, a probable range of the error is estimated. This numerical estimate is the uncertainty.
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PROBLEM 5.3 SOLUTION TRUE VALUE: The actual value of the measured variable. The value sought by measurement. Most often refers to the true mean value of the variable which would result from an infinite sampling under perfect test control. BEST ESTIMATE: The nearest approximation of the true value that can be made with the data set available. It is based on the data set and the precision and the bias errors involved in the measurement. It is usually offered by the sample mean value and qualified by its precision interval. MEAN VALUE: Exact statement of the mean or central tendency of a measured data set. The mean value of a finite data set is given by its sample mean value.
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This note was uploaded on 10/31/2009 for the course MECH 420 taught by Professor M.s during the Spring '09 term at American University of Beirut.

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chap05 - Learn by writing methods are valuable for...

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