Assignment on Uncertainty analysis exercise 3- Using GUM method to estimate uncertainty

A food factory produces a cylindrical confectionary product of variable length, depending on the required product size

Table 1: Replicate values of the diameter of product

Table 2: Variation of product mass a function of length            

Approximate density of the extruded material based on the value

Expanded uncertainty in density estimation, based on diameter and mass uncertainties using 9% of confidence interval

Solution

The density of the material is;                             

But in this case, we know that δ = 0.1mm. The uncertainty is type B.

Since this could either be +ve or –ve, the most likely value is Z = 0.

Length versus mass

Now the residual plot is

Conclusion

            Summing up all the discussion it is concluded that the problem statement is about the uncertainty which is used the GUM method. In this statement first of all determine the density of the extruded material, and find its expanded uncertainty by using the GUM methods which is also shown in the above calculation. Then plot the length versus mass . Moreover, the discussion also concluded length and mass are increasing from the starting point of above 250 (20 for mass) to the 750 (65 for mass). Although, the calculated values of veff is 8.29 which represent the combined uncertainty. However, opposite to this value, the calculated value of standard uncertainty is 0.02. Thus discussion and calculation represent that standard uncertainty is below the value of combined uncertainty. Furthermore, the density of the material is also calculated to find out the final value of extruded materials. The calculations concluded that the density of the material is limited to the p-value of 0.001077 for the materials.