Error propagation, multiplicative

It is important to note that the error propagation in taking a number to a power is different from the error propagation in multiplication. For example, consider the uncertainty in the square of 4.0 ( 0.2). Here, the relative error in the result (16.0) is given by Equation 6-13 ... 

An important consideration has been omitted in [3-5], which are devoted to this approach, and that is the usually rather large experimental errors associated with microarray measurements. It is important to know how such errors propagate in the calculations and their effects on the proper identification of the connectivity matrix. A simple example worked out in detail in section 12.5 shows the possible multiplicative effects of such errors in nonlinear kinetic equations. Until this problem is addressed, the approach of linearization must be viewed with caution. 

In a forward-marching method such as Euler s method, we are more interested in the total error propagation over multiple usage of the algorithm than in the local one-step error. If we let Cj be the error between the approximate solution, rcj, and exact solution, x ti) to the differential equation, then... 

Fig. 4. 38 Examples of an error propagation through multiple levels (Source Inspired by ISO 26262, part 10)...

If we arrange FMEA hierarchically beyond the classical sequence based on cause of failure, type of failure, failure effect, multiple system levels could be considered. In that different hierarchical system levels, error propagations could be avoided within the different level for example in the implementation, the component and system design, but also on vehicle level, for example between different ITEMS or vehicle systems (Fig. 4.47). 

Experiments with the oxidation of benzyl alcohol by NAD+, catalyzed by yeast alcohol dehydrogenase, yielded (fccat/XM)D/(fccat/XM)x = 1.72 — 1.76 (standard deviations about 0.03-0.06). These experiments involved multiple labeling so an exact interpretation must take into account Huskey s rules for this situation (Chart 7 below). Application of the Swain-Schaad relationship predicts an H/T effect of 5.9-6.3 (propagated errors 0.2-0.6). The observed H/T effects are 7.0-7.2 (standard deviations about 0.1), providing a very strong indication of the importance of tunneling in this reaction. 

The estimation of the error of a computed result R from the errors of the component terms or factors A, B, and C depends on whether the errors are determinate or random. The propagation of errors in computations is summarized in Table 26-2. The absolute determinate error e or the variance V = s for a random error is transmitted in addition or subtraction. (Note that the variance is additive for both a sum and a difference.) On the other hand, the relative determinate error ejx or square of the relative standard deviation (sJxY is additive in multiplication. The general case R = f A,. ) is valid only if A, B,C,... are independently variable it is... 

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