Towards Confidence with Capture-recapture Estimation: An Exploratory Study of Dependence within Inspections

Background: Capture-ReCapture (CRC), as a technique for post-inspection defect estimation, has been studied in Software Engineering (SE) community since 1990s. While most studies focused on the performance evaluation of various CRC models and estimators, few have been done on the assessment of the credibility of estimation results, rendering the difficulty of decision-making for quality management when applying CRC for defect estimation. Objective: This research aims to explore and investigate a reliable and practical approach to assess the credibility of CRC based defect estimation. Method: One fundamental assumption of applying CRC method is the statistical independence of samples that can be measured by 'Coefficient of CoVariation' (CCV). We applied CCV as an indicator of the statistical dependence between the observations (i.e., the defects detected by inspectors), and assessed the estimation results of CRC with the published datasets in SE literature by examining the correlation between Relative Error (RE) and CCV. Based on the observed correlation, we further propose CĈV, which replaces the unknown N (the actual number of defects) with the estimated number (N), to assess the credibility of CRC estimates. Results: We found that most datasets are with non-zero CCVs and the R2 (Coefficient of Determination) of non-linear curve-fitting for their CCVs and REs is higher than 0.8. Conclusions: Our study shows the evidence that the statistical dependence among inspectors is ubiquitous in the existing CRC-related studies. Besides, the significant correlation between CCV (by CĈV in practice) and RE may enable the possibility of the assessment of CRC-based estimation in support of quality management.