Test plan parameter design system and tolerance design data reduction Independent dependent extraneous variables Random ordering Test blocks Let s return to the general measurement system What about this When would be need this Calibration Apply a known input value measure output Can be static or dynamic input We end up with a calibration curve in this case static Output Span FSO Key points 1 Often fit with functional form Choose based on physics 2 Slope gives static sensitivity What type of slope is good Input range 3 Linear relationship desirable simple sensitivity constant Calibration done with a calibration standard Primary Standard Absolute Standard NIST National Labs Transfer Standard calibrate local standards Local Standard calibrate working standards Working Standard calibrate lab equipment A majority of lab equipment undergoes periodic calibration Now we need to consider error The exact value of some physical variable is called the true value The absolute error is defined as uabs vtrue vmeasured We can also present a deviation plot as uabs The relative error is defined as urel uabs x100 vtrue Measures deviation in value from true value vmeasured Two types of errors that we deal with 1 Systematic or bias errors measured value mean is off from the true value by a fixed amount 2 Random errors measured value is off by a random amount from the true value by a fixed amount but measured mean approaches the true value Related to the concept of Accuracy and Precision All of the errors combine leading to measurement uncertainty Measurement system Data collected Measurement technique What type of instrumentation errors might we see Resolution smallest physically indicated division that the instrument indicates or is marked Time in seconds Uncertainty associated with resolution generally set to resolution Hysteresis error greatest deviation between two output values for a given input value that occurs performing upscale and downscale calibration yup ydown uHmax MAX x100 uH x100 FSO FSO Linearity error measure of how linear the best fit of the instruments calibration data is y yL uLmax MAX x100 uL FSO FSO x100 Thermal Drift greatest deviation in the output value for a fixed input value that could occur due to variations in environmental temperature uTmax x100 uT FSO Sensitivity error greatest change in the slope static sensitivity of the calibration fit x100 output y ynom MAX uK x100 uK FSO FSO uK input MAX Zero shift error greatest change in the intercept of the calibration fit x100 uZ output y ynom MAX uZmax x100 uZ FSO FSO input Repeatability related to the precision of the calibration statistical measure 2S x uR x100 FSO Sx is the standards deviation of the data measured at a given x How are these errors assessed Hysteresis and linearity errors typically found using a single upscale and downscale calibration Other errors found through analyzing multiple calibration curves Once the errors are determined we can determine the by combining them through uI 2 2 2 2 u u u u j L K T j If more than one instrument is used uI 1 v uI 2 uT uI21 uI22 v uT
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