Calculating Linearity Error
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of the device. In order to measure the linearity of a device, we must take repeated measurements of parts or samples that cover its entire range. So that we don't introduce reproducibility error into the picture, the same operator must make all the measurements. To check linearity, measure at full scale deflection error least 5 samples that cover the full the range of the instrument. Reference measurements for each
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of the samples (made by your quality group or by an outside laboratory) will be needed to determine linearity. The reference measurements will be compared
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to the results from the instrument whose linearity is being studied. Measure each of the samples randomly at least 10 times. For each of the parts, calculate the average and the range of the measurements made. The sample averages and ranges
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will be used with the reference values to determine linearity either graphically or by calculations. Graphical Method: Plot the average measured values (on the y-axis) for each sample against the reference value (on the x-axis). If the resulting line is approximates a straight line with a 45-degree slope, the measurement device is linear. If the measured values do not form a straight line, or the line diverges from the optimal 45-degree slope, you may have a problem with linearity. Calculating Linearity: A how to calculate linearity in method validation technique does exist that provides a precise mathematical evaluation of the linearity. The evaluation is based on the equation of a line that defines the relationship between the bias and the reference values of the parts or samples. The bias is the value of the sample measurement minus the reference measurement. To calculate the line of best fit, use the equation: y = ax + b where:y = bias valuea = slope of the linex = reference valueb = the y-intercept To calculate the slope, a: where:n = total number of measurements made To calculate the y-intercept, b: With values for a and b, we can complete the regression equation (y = ax + b); it gives us the line of best fit. Using the results of the regression equation, we can determine the goodness of fit by calculating the Coefficient of Determination, R2. R2 lets us know what amount of the variation in the bias values the regression line explains. If R2 is 0.6 (60%) or more, the regression line is an adequate representation of the line of best fit. Calculating the linearity and bias. Linearity = a, slope of the line of best fit Bias = b, y-intercept of the line of best fit Test the linearity State the hypothesis H0: a = 0 Calculate t for linearity Determine the critical value of t. Use a t-table or spreadsheet program to determine tcritical. Typically an α risk of 0.05 is used. Acce
Федерация 中国 (China) 日本 (Japan) 대한민국 (Korea) 台灣 (Taiwan) See All Countries Toggle navigation INNOVATIONS SHOP SUPPORT COMMUNITY United States Sensor Terminology Publish Date: Sep 23, 2013 | 5 Ratings linearity error definition | 4.60 out of 5 | Print Overview This tutorial is part linearity formula of the National Instruments Measurement Fundamentals series. Each tutorial in this series, will teach you a specific topic y a bx calculator of common measurement applications, by explaining the theory and giving practical examples. This tutorial will cover sensors and the terminology associated with them. For the complete list of tutorials, http://www.qualitytrainingportal.com/resources/msa/type_a_uncertainty.htm return to the NI Measurement Fundamentals Main page. Table of Contents Sensitivity Range Precision Resolution Accuracy Offset Linearity Hysteresis Response Time Dynamic Linearity 1. Sensitivity The sensitivity of the sensor is defined as the slope of the output characteristic curve (DY/DX in Figure 1) or, more generally, the minimum input of physical parameter that will create a detectable output http://www.ni.com/white-paper/14860/en/ change. In some sensors, the sensitivity is defined as the input parameter change required to produce a standardized output change. In others, it is defined as an output voltage change for a given change in input parameter. For example, a typical blood pressure transducer may have a sensitivity rating of 10 mV/V/mm Hg; that is, there will be a 10-mV output voltage for each volt of excitation potential and each mm Hg of applied pressure. Sensitivity Error The sensitivity error (shown as a dotted curve in Figure 1) is a departure from the ideal slope of the characteristic curve. For example, the pressure transducer discussed above may have an actual sensitivity of 7.8 mV/V/mm Hg instead of 10 mV/V/mm Hg. Back to Top 2. Range The range of the sensor is the maximum and minimum values of applied parameter that can be measured. For example, a given pressure sensor may have a range of -400 to +400 mm Hg. Alternatively, the positive and negative ranges often are unequal. For example, a certain medical blood pressur
and Error (Squareroot Function) Math Videos from Heather SubscribeSubscribedUnsubscribe168168 Loading... Loading... Working... Add to Want to watch this again later? Sign in to add this video https://www.youtube.com/watch?v=roiH4fWyfdo to a playlist. Sign in Share More Report Need to report the video? Sign in to report inappropriate content. Sign in Transcript Statistics 6,667 views 14 Like this video? Sign in to make your opinion count. Sign in 15 4 Don't like this video? Sign in to make your opinion count. Sign in 5 Loading... linearity error Loading... Transcript The interactive transcript could not be loaded. Loading... Loading... Rating is available when the video has been rented. This feature is not available right now. Please try again later. Published on Sep 25, 2013Linear approximation of sqrt(1.1) and error. Category Education License Standard YouTube License Show more Show less Loading... Autoplay When autoplay how to calculate is enabled, a suggested video will automatically play next. Up next Linear Approximation/Netwon's Method | MIT Highlights of Calculus - Duration: 31:41. MIT OpenCourseWare 41,862 views 31:41 Linear Approximation - Duration: 48:19. slcmath@pc 2,974 views 48:19 Linearization and Error - Duration: 7:09. John McAllen 126 views 7:09 Differentials Tangent Line Approximation Propagated Error - Duration: 58:11. ProfRobBob 8,806 views 58:11 Approximation of Error in Hindi - Duration: 42:24. Bhagwan Singh Vishwakarma 3,991 views 42:24 Differentials: Propagated Error - Duration: 9:31. AllThingsMath 9,147 views 9:31 Linear Approximation Using Differentials - Duration: 6:12. RightAngleTutor 14,865 views 6:12 3.7 Linear Approximation - Duration: 7:55. rootmath 70,192 views 7:55 Linear Approximation Square Root Example - Duration: 13:50. Brandon Craft 9,267 views 13:50 Linear Approximation - Calculus (Worked Example) - Duration: 6:24. AcademicLeadersEd 23,838 views 6:24 Linear Approximation: Example on Errors in Measurement - Duration: 6:22. Math Easy Solutions 991 views 6:22 Multivariable calculus 2.2.7: Linear approximation of functions of two variables - Duration: 6:36. Michael Hutchings 1,914 vie