uncertainty analysis

Uncertainty Analysis : 

Uncertainty Analysis Presented by: Eng: Mohamed Mahmoud Ismail Presented to: Dr : Sadek Z Kassab

Uncertainty Analysis: 

Uncertainty Analysis Introduction : why we talk about uncertainty analysis ? What is the importance of uncertainty analysis ?

Uncertainty Analysis: 

Uncertainty Analysis What is Uncertainty Analysis? Uncertainty analysis is the procedure used to quantify data validity and accuracy Types of error: fixed error Random error

Uncertainty Analysis: 

Uncertainty Analysis The following assumptions are used in the above analysis: Equipment has been constructed correctly and calibrated properly to eliminate fixed errors. Instrumentation has adequate resolution and that fluctuations in readings are not excessive. Care is used in making and recording observations so that only random errors remain.

Uncertainty Analysis: 

Uncertainty Analysis Uncertainty Calculations Examples are given to illustrate how the High-Low method is used to estimate errors

Uncertainty Analysis: 

Uncertainty Analysis

Uncertainty Analysis: 

Uncertainty Analysis

Uncertainty Analysis: 

Uncertainty Analysis

Uncertainty Analysis: 

Uncertainty Analysis

Uncertainty Analysis: 

Uncertainty Analysis Error Calculations using Standard Deviation

Uncertainty Analysis: 

Uncertainty Analysis (σ) the standard deviation ( N ) the number of observations made ( t ) factor values obtained from statistical table depends on no of observations and level of confidence The normally accepted confidence level is 95%

Uncertainty Analysis: 

Uncertainty Analysis Analyzing the propagation of uncertainty in calculations Suppose that measurements of independent variables x1, x2, … , xn are made in the lab .The relative uncertainty of each independently estimated as ui R result for experiment mathematically as R= R(x1, x2 , ….., xn ) ∂Ri = ∂R/∂xi * δxi Divide R by the equation ∂Ri / R = 1/R * ∂R/∂xi * δxi = xi/R * ∂R/∂xi * δxi/xi ------- (1) substitute the uncertainty interval from xi URi = xi/R * ∂R/∂xi * UXi UR = ± [ (x1/R * ∂R/∂x1 * UX1)^2 + (x2/R * ∂R/∂x2 * UX2)^2 + - - - - - - - - - - +(xn/R * ∂R/∂xn * UXn)^2 ]^½