Measurement Uncertainty. Overview Factors which decide System Performance Types of Error in Measurement Mean, Variance and Standard Deviation.

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Presentation transcript:

Measurement Uncertainty

Overview Factors which decide System Performance Types of Error in Measurement Mean, Variance and Standard Deviation

Error = Xm - Xtrue Xm-> Measured Value Xtrue->Actual Value What is the “true” value? Is it possible to take measurement data without any error? What is the source of error? How can we minimize the impact of these errors ?

System Performance Depends on the following factors : ->System accuracy is the magnitude of the maximum expected error. Usually specified as percentage of full scale. ->System precision is an estimate of repeatability.The more precise a system, the less random error affects the result. ->System resolution is the smallest possible discernible increment.Higher the resolution, smaller the smallest increment !

Types of Error Systematic errors (or “bias” errors): Occur in a repeatable fashion (i.e., every time a measurement is made under similar conditions). Offset error: is a constant error which occurs every time a measurement is taken. Offset Error: Xm = Xtrue ± Constant Xm=Measured value Xtrue=Actual value

Types of Error contd. Scale error: Xm = Xtrue x Constant implies Xtrue = Xm / Constant Nonlinear errors: Can result from poor design or from inappropriate system use Ex: y= x 2, y = cos xt, or y = log x

Types of Error contd. Drift Errors: Ambient temperature, humidity and aging can change the characteristics of an electronic component. Random errors: Absolutely random in nature !

Definitions Sample median - The middle value when the measurements are arranged from smallest to largest. Sample mean: (Sum / No. of Samples)

Definitions contd. Sample Mean: Xmean=sum(Xi)/n Sample deviation: Difference between the measured value and the sample mean Deviation = X – Xmean Sample variance = sum(Xi-Xmean)²/(n-1)

Definitions contd. Sample Standard Deviation: s=sqrt(sum(Xi-Xmean)²/(n-1)) Sample standard deviation gives us an estimate of the variability of the sample in the same units as the data. Components manufactured with a small standard deviation, cost more than components that are manufactured to a looser standard.

clear all R1=5.1 V=24 R2=13.8:0.1:15.2 V1=(R1/(R1+R2))* V I1=V / (R1+R2) figure(1) subplot(2,1,1) plot(R2,V1) subplot(2,1,2) plot(R2,I1)