## 4 Results
### Sizing of Estimable Items  
As already mentioned in Section 2, the authors' estimation framework uses NDE as a measure of development efforts. NDE is a time-based unit expressing the amount of work in man-hours, man-days, etc. Such time-based measuring ensures seamless translation of the estimated efforts into the project schedule. However, it is worth highlighting that the NDE itself is defined in a way that makes it independent from neither the project schedule nor the team composition. In essence, sizing is aimed at designating each EI as an NDE. For the preliminary estimation, a two-step sizing approach is proposed: (a) designate each LEI using such attributes as an estimable item point (EIP) and an estimable item uncertainty (EIU); (b) then, obtain optimistic and pessimistic NDEs from the corresponding EIP and EIU. Let \(x\in X\) be an LEI belonging to EIBS \(X\). The _estimable item point_ (EIP) of \(x\), \(x[\text{EIP}]\), is a positive number representing the relative measure of development efforts required to implement \(x\). In turn, the _estimable item uncertainty_ (EIU), \(x[\text{EIU}]\), is a non-negative dimensionless number expressing how much is unknown with regard to \(x\); in other words, the bigger the \(x[\text{EIU}]\), the less definitive the \(x[\text{NDE}]\) and vice versa. It is worth emphasizing that EIPs and EIUs are supposed to be designated for LEIs (not CEIs). EIPs and EIUs are based on experts' judgment. In Figure 4, an example is shown of EIP and EIU estimation based on the idea of affinity grouping [5]: the LEIs are placed on a coordinate plane where the horizontal axis corresponds to the size (EIP), and the vertical axis defines the level of uncertainty (EIU). One of the strengths of the described approach is its visual representation of the project scope on a two-dimensional plain, allowing a relative comparison of EIs' sizes and uncertainties. \begin{table}
\begin{tabular}{l c l} \hline \hline
**Name** & **Shortcut** & **Description** \\ \hline Identifier & ID & Uniquely identifies an EI in an EIBS. \\ Title & TITLE & Several words of summary of an EI. \\ Description & DESC & Explanation of what an EI is about. \\ Assumptions & ASHP & Assumptions associated with an EI. \\ Risks & RISK & Risks associated with an EI. \\ Dependencies & DEPN & Dependencies of an IE. \\ Functional requirements & FR & Functional requirements associated with an EI. \\ Nonfunctional requirements & NFR & Nonfunctional requirements associated with an EI. \\ Constraints & CON & Constraints associated with an EI. \\ Architecture considerations & ARCH & Architecture ideas, patterns, tactics. \\ Out of scope & OOS & Explicitly stated what is out of the project scope. \\ Normalized development estimate & NDE & NDE associated with an EI. \\ Questions & Q & Questions associated with an EI. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Most common types of estimable item attributes. Figure 3: Treelike representation of EIBS for RTBPM-E.  
After estimating EIPs and EIUs, it is necessary to transform them into NDEs. Define the relationship between NDE and EIP as follows:  
\[x[\mathrm{NDE}_{\mathrm{basic}}]=p\cdot x[\mathrm{EIP}], \tag{5}\]  
where \(p>0\) is the NDE corresponding to one EIP. In turn, optimistic and pessimistic NDEs are related to the EIU as follows:  
\[ \begin{split} x\big{[}\mathrm{NDE}_{\mathrm{opt}}\big{]}& =(1-u_{1}\cdot x[\mathrm{EIU}])\cdot x[\mathrm{NDE}_{\mathrm{basic }}],\\ x\big{[}\mathrm{NDE}_{\mathrm{psm}}\big{]}&=(1+u_{2 }\cdot x[\mathrm{EIU}])\cdot x[\mathrm{NDE}_{\mathrm{basic}}],\end{split}  \tag{6}\]  
where \(x\big{[}\mathrm{NDE}_{\mathrm{opt}}\big{]}\) and \(x\big{[}\mathrm{NDE}_{\mathrm{psm}}\big{]}\) are the optimistic and pessimistic NDEs, respectively; \(0\leq u_{1}<1\) and \(u_{2}\geq 0\) are the coefficients defining deviation of the optimistic and pessimistic estimates from the basic NDE. Values of parameters \(p\), \(u_{1}\), \(u_{2}\) can be either based on experts' judgment or defined statistically from past projects.