## 5 Sensitivity Analysis  
The purpose of a sensitivity analysis is to investigate which parameters have an important influence on the model. In general, sensitivity analysis refers to changing one parameter in a model while keeping the other parameters unchanged. In other words, we analyze a parameter's variation in the model to see how it affects the model's performance. For software developers, when estimating model parameters, they can focus on the changes in the sensitivity parameters of the model, reduce the impact of the model parameters on the performance of the software RM, and improve the accuracy of evaluating software reliability.  
We conducted sensitivity analysis experiments using a fault data set (DS1-3) and estimated the parameter values of the PM using LSE. As can be seen from Figure 5a, we changed the parameter \(a\) of the PM while ensuring that the other parameters of the PM do not change. When parameter \(a=150.02\) becomes \(a=300\), \(a=100\), or \(a=10\), the cumulative number of faults estimated by the PM is subject to significant changes. Thus, we believe that parameter \(a\) is has significant impact on the PM, that is, it is a sensitivity parameter. Similarly, we conducted sensitivity analysis experiments on other parameters of the PM and found that parameters \(b\), \(\beta\), \(\theta\), \(d\), and \(\sigma\) of the PM have a major impact. We analyze the reasons as follows:  
Figure 4: The 95% confidence intervals for fault data. (**a**,**c**,**e**) represent 95% confidence intervals using 100% of the data for DS-1, DS4-2, and DS4-3, respectively. (**b**,**d**,**f**) represent 95% confidence intervals using 80% of the data for DS4-1, DS4-2, and DS4-3, respectively.  
1. The total number of original faults (_a_) in an OSS has an important impact in the process of the OSS development. Because the number of faults in the OSS directly affects and determines the quality and reliability of the OSS, it is a necessary factor to be considered when establishing the RM of OSS.
2. The FD rate (_b_) is also an important factor during OSS development and testing. It determines the probability that faults in an OSS will be detected. Its change directly affects the number of faults detected in the OSS. It also determines the number of remaining faults in the OSS. Therefore, it is necessary to consider the influence of the FD rate when establishing the RM of OSS.
3. The inflection factor (_b_) affects the curve shape change in an OSS model. Its changes are related to learning phenomena in the OSS FD. Due to the complexity of OSS FD, community contributors need to continuously learn software in order to continue the development and testing of OSS. So, it has an important impact on OSS reliability modeling.
4. Fault introduction (_th_) also affects the reliability modeling of an OSS. Its changes are related to changes in OSS functions and features. At the same time, its changes also reflect the efficiency of the OSS to completely remove faults.
5. Parameter \(d\) of the PM is also an important parameter. Its changes reflect complicated changes in the introduced faults of an OSS. Its complex changes show the complexity, uncertainty, and randomness of fault introduction for OSS. For example, the PM fits well with the shape of the actual cumulative number of detected faults.
6. The irregular fluctuation factor \(s\) is also an important parameter. In the process of OSS development, testing, and debugging, fault introduction presents random changes. The fault introduction intensity function changes irregularly over time. Its changes also reflect the complexity, uncertainty, and randomness of fault introduction.  
In summary, all of the PM's parameters are significant. The PM can well adapt to complicated and uncertain changes in the process of OSS development. The sensitivity analysis of parameters also shows that many factors need to be considered in the establishment of the OSS RM, especially factors that affect random changes in fault introduction during the development of OSS.  
Figure 5: _Cont._