Simple Examples and Problem Statement

As is common in illustrative textbook examples, also the following are not just from industrial practice. Generally, the reconciliation problem is multidimensional and if nonlinear, such detailed analysis as follows is hard or impossible. 

Recall the example 3 (heating furnace) in Chapter 6, Section 6.3. Having simplified the scheme according to Fig. 6-12 we have 

We make abstraction from how the named quantities are actually measured. Formally, we consider as measured the mass flowrates (mj) 

We suppose that the measurement errors in m, wij, y are uncorrelated, with standard deviations a, Cj respectively. With the san motivation as in Section 9.1, the adjustments will be subjected to the condition 

Let us try to find some values Xj = Xj obeying the solvability conditions (10.1.16) and minimizing the criterion (10.1.14b) as we have seen, is arbitrary hence we can set directly in (10.1.14b). We thus have to minimize 

---