# OSS Project Stability Assessment Support Tool Considering EVM Based on Wiener Process Models
## 3 Assessment Measures for EVM  
The method of EVM has been used for the project management under various IT companies. Generally, the EVM is applied to commonly software development projects [20]. However, it is difficult to directly apply the EVM to the actual OSS project, because the development cycle of OSS project is different from the traditional software development paradigm. Considering the characteristic of the OSS operation phase, the OSS development project is managed by using the bug tracking system. The method of EVM will be helpful for OSS managers to assess QCD (Quality, Cost, Delivery) of OSS [21]. This paper proposes the method of earned value analysis for OSS projects by using the data sets obtained from bug tracking system. Considering the earned value analysis for OSS, we assume the following terms as the EVM for OSS:  
* Actual Cost (AC): Cumulative maintenance effort up to operational time \(t\) considering the reporter and assignee. * Earned Value (EV): Cumulative maintenance effort up to operational time \(t\) considering the reporter. * Cost Variance (CV): Fixing effort required for OSS maintenance up to operational time \(t\), \(\mathrm{E}[\Theta_{e}\left(t\right)]\) and \(\mathrm{E}[\Theta_{s}\left(t\right)]\). * Cost Performance Index (CPI): \(\mathrm{E}[CPI_{e}\left(t\right)]\) and \(\mathrm{E}[CPI_{s}\left(t\right)]\) obtained from AC and EV. * Estimate at Completion (EAC): \(\mathrm{E}[EAC_{e}\left(t\right)]\) and \(\mathrm{E}[EAC_{s}\left(t\right)]\) obtained from AC, EV, CPI, and BAC. * Estimate to Completion (ETC): \(\mathrm{E}[ETC_{e}\left(t\right)]\) and \(\mathrm{E}[ETC_{s}\left(t\right)]\) obtained from AC, EV, CPI, BAC, and EAC. * Budget at Completion (BAC): Planned Value (PV) in the end point as the specified goal of OSS project. Then, the expected fixing effort required for OSS maintenance up to operational time \(t\) in case of \(\Psi_{e}\left(t\right)\) and \(\Psi_{s}\left(t\right)\) can be formulated as:  
\[\mathrm{E}[\Theta_{e}\left(t\right)] = \mathrm{E}[\Psi_{re}^{r}\left(t\right)]-\mathrm{E}[\Psi_{re}^{ra} \left(t\right)], \tag{15}\] \[\mathrm{E}[\Theta_{s}\left(t\right)] = \mathrm{E}[\Psi_{rs}^{r}\left(t\right)]-\mathrm{E}[\Psi_{rs}^{ra} \left(t\right)], \tag{16}\]  
where \(\mathrm{E}[\Psi_{re}^{ra}\left(t\right)]\) and \(\mathrm{E}[\Psi_{rs}^{ra}\left(t\right)]\) are the maintenance effort considering the reporter and assignee until the end of operation. Also, \(\mathrm{E}[\Psi_{re}^{r}\left(t\right)]\) and \(\mathrm{E}[\Psi_{rs}^{r}\left(t\right)]\) mean the maintenance effort considering the reporter until the end of operation. Similarly, the sample path of fixing effort required for OSS project maintenance up to operational time t in case of \(\Psi_{e}\left(t\right)\) and \(\Psi_{s}\left(t\right)\) are given by  
\[\Theta_{e}\left(t\right) = \Psi_{re}^{r}\left(t\right)-\Psi_{re}^{ra}\left(t\right), \tag{17}\] \[\Theta_{s}\left(t\right) = \Psi_{rs}^{r}\left(t\right)-\Psi_{rs}^{ra}\left(t\right). \tag{18}\]  
The zero point of fixing effort \(\mathrm{E}[\Theta_{e}\left(t\right)]\) and \(\mathrm{E}[\Theta_{s}\left(t\right)]\) mean the starting point of surplus effort. On the other hand, the zero point of fixing effort \(\mathrm{E}[\Theta_{e}\left(t\right)]\) and \(\mathrm{E}[\Theta_{s}\left(t\right)]\) is the end point of effort required in OSS project. Therefore, the OSS project managers will be able to judge the necessity of fixing effort and stability of OSS from the starting point of surplus effort.