**4.6 Iterative logic for individual distribution of applications**

After classifying all applications to be distributed during the selected period, an iterative sequence of steps for their distribution is then proposed, seeking to prioritize the choice of applications based, whenever possible, on the IGC classification of each application being distributed, in addition to the ZAE of each examiner.

	- i. If the Current Application pertains to the Current Examiner's ZAE, then select the Current Application and proceed to Step 2;
	- ii. If there is no application pertaining to the Current Examiner's ZAE, look for the next application in line that does not pertain to any other Examiner's ZAE and, only after that, proceed to Step 2.
	- i. If an Application with the same Classification has not yet been distributed to the Current Examiner, then distribute the Current Application and proceed to Step 3;
	- ii. Otherwise, search for the next available Application and return to Step 1.


**Figure 3.** *Time for examination form.*

i. If there are no more applications with any of the Classifications, repeat Steps 1 through 5 for the remaining Classifications until there are no more Applications available for distribution.

#### **4.7 Final redistribution sample and calculation of the distribution balancing ratio (IBD)**

In order to evaluate the distribution of the patent applications, a new data sample was obtained, referred to as Final Redistribution Sample. As the Standard Sample (with time) used to validate the model was obtained using examination data that, on their turn, were also based on international searches, this new redistribution sample was necessary to harmonize the examination process carried out by the examiners evaluated therein with the process implemented by the examiner, from which the Standard Sample with time was obtained. Based on this new sample, the proposed model and distribution logic are applied, and a Distribution Balancing Ratio (IBD) is then calculated, both for the original distribution and the new one, according to Eq. (12):

$$IBD = \frac{\sqrt{\sum\_{i} \sum\_{j} \left(\frac{m\_{adj}}{\mathcal{M}\_{el\_j}}\right)^2}}{\sqrt{\sum\_{i} \sum\_{j} \left(\frac{m\_{adj}}{\mathcal{M}\_{el\_j}}\right)^2 + \sum\_{i} \sum\_{j} \left(\frac{m\_{adj} - \mathcal{M}\_{el\_j}}{\mathcal{M}\_{el\_j}}\right)^2}}\tag{12}$$

Where: medij is the median of variable j of patent applications distributed to examiner i; and Medj is the median of variable j for all applications in the final redistribution sample.

In a first analysis of the IBD equation, it can be verified that the ratio seeks to capture and measure the influence of the differences between the medians of the variables of each examiner's samples and the general medians of the division's variables (complete sample). It is important to note that all medians of the variables composing the IBD are normalized (divided) by the general values of the respective medians of the complete sample. With that, we seek to avoid further distortions caused by different orders of magnitude of certain variables.

Additionally, as the several medians calculated can be higher or lower than the respective median of the division, the differences in these values can be positive or negative. Hence, as we wish to obtain an accumulated measurement of all differences in medians with no loss of information and without having a negative deviation in a certain variable compensating a positive deviation in another, we choose to square the differences and then add and extract the square root.

More specifically, when the numerator and the denominator of the IBD equation are analyzed, it can be noticed that both have the same first term, which is the sum of the squares of the normalized medians of all variables of interest from the examiners'samples. However, the denominator has a second additional term presenting the sum of the squares of the normalized differences between the medians of each examiner's individual samples and the medians of the corresponding variables from the complete sample.

It is important to highlight that, in an ideal distribution, the medians of the variables from all examiners'samples would be equal to the medians of the general variables of the division, i.e., the sum of the squares of the differences of the medians (second term of the IBD denominator) would be zero and, consequently, the IBD would be equal 1. On the other hand, a random distribution in which the examiners'samples have great differences in median values, when compared to the *A Methodology for Evaluation and Distribution of Patent Applications to INPI-BR Patent… DOI: http://dx.doi.org/10.5772/intechopen.98400*

general division medians, would lead to very high denominator values, thus greatly reducing the IBD and, ultimately, making it tend to zero. Thereafter, we have that, the closer the medians of the variables from the examiners' individual samples are to the general medians of the division's variables, the greater and closer to 1 the IBD value will be and, consequently, better balanced the distribution will be.
