What is uncertainty analysis ?

It is the analysis that we carry out to estimate the range (upper and lower value) in which a given measurement value can be varied (without being wrong). It is related to the resolution of a measurement setup. The calculation is more “attractive” in the case we provide a value for a property that is occurring as a function of the fundamental measures (that have been measured via distinct measuring arrangements). For example, the tensile stress can be estimated by measuring force and length. The uncertainty of the stress value can be calculated taking into account the uncertainty of the apparatuses used for the measurement of (1) the force and (2) the length, as well as the mathematic expression that correlates them. You can have an overview on the site: http://en.wikipedia.org/wiki/Measurement_uncertainty,

However, from a practical point of view you should take into account the calibration certificate of the measuring apparatus and a series of testing measurements around the specific value you would like to present and that has been measured by the same apparatus, by the same person, under the same methodology and environmental conditions.

Dear Pathak,

when we calculate a value depending on other measured values (which are not 100% exact). we need to calculate the max possible error could be occur.

Check the attached file, please.

Regards!

Azd.

You may calculate uncertaintity by different methods (Classical method based on the Taylor series, Monte Carlo Simulation method, Bootstrap method, etc). If you want to go deeper on the subject take a look at:

where you can find GUM (Guide of Uncertainty in Measurement).

Best Regards

@ Manuel Carlos Gamerio da Silva

Thanks for info

@Azad Zayoud

Thanks for info

@ Maciej Mikulski

Thanks for info.

@ P.Psyllaki 

Thanks for info.

And as of now i have only equation from the paper.

No answer

Dear colleague

For another issue, I just made a summary on uncertainty analysis, inspired from the GUM andVIm quoted in former answers. Seee attached file.  

Your equations are uncertainty propagation equation for several quantities involved in heat transfer.

Best regards

One more comment on the answer of Maciej Mikulski, who provides a propagation equation that is different of the statistical one I used in my summary, but which is also often used. The equations you show in your question are of the statistical type. 

Since the square root of a sum of squares is always smaller than the sum itself, the statistical method results in an estimate of the uncertainty that is smaller than the exact differential method. This latter method provides the maximum possible uncertainty, when deviations from all the causes go in the same direction. This is seldom the case, in particular when the variables are not correlated, and this is why the statistical method is of a more common use. 

please refer to my articles, you can find out a way to calculate uncertainty analysis

Abhishek,

From a philosophical perspective, uncertainty analysis represents an attempt to characterize the 'true' value of an unknown parameter (usually a stochastic/random parameter).  For example, if I attempt to measure the concentration of an air pollutant at a particular location (spatial coordinate) and at a particular time (temporal coordinate), I can do so with an air pollution monitor.  Any air pollution monitor that I use to measure the concentration of an air pollutant will have an inherent bias (offset measurement), that can be displayed when the monitor displays a non-zero concentration (positive or negative) when the substance I am attempting to measure is not present at the monitor.

The measurement process, even with a monitor that has a theoretical zero bias can only provide an approximate measurement of the 'true' concentration of the air pollutant, because the precise concentration value is unknown or uncertain.  Therefore, I calibrate the air pollution monitor to calculate its bias so that when I use it to measure the concentration of the air pollutant, I can provide an approximate measurement of the concentration, based on the bias at each point of the monitor's calibration curve (usually linear for most instruments and measurement ranges).

Uncertainty analysis is when I attempt to determine what the 'true' concentration is, based on the estimate of the monitor bias, to provide a confidence interval/range within which the 'true' concentration value lies.  Uncertainty analysis recognizes the fact that we can not know the precise value of  each measurement, but we can characterize each measurement point statistically within a defined range or confidence interval.  A philosopher would call this an epistemological issue/problem (determining what we know, how valid is our knowledge about what we know, and what is the range/limits of what we know).

Although uncertainty analysis uses the tools of statistics to find its answers, it is not to be confused with variability, which attempts to measure the natural variation inherent in any system due to changes in state or local conditions.  Variability is also determined using the tools of statistics. 

I attached a summary I have recently written.