在軟體系統發展過程中，當瑕疵或錯誤愈早被發現，更正此錯誤所付出的成本就愈少。反之，如果在整個軟體系統已經接近完成，常需要付出巨大的成本，來修復錯誤或瑕疵。也因此，儘可能在設計階段找出錯誤，是相當軟體發展中相當重要的一環。而本研究提供一個預測需求文件的瑕疵數的方法。藉著估計出瑕疵數，可以保證需求文件的品質。品質不良文件，需要重新被設計；瑕疵數較少的文件，則可以進入實作系統的階段。瑕疵數的估計，更可以提供管理階層，決策文件品質時的依據。

　　估計文件瑕疵數的數學模型主要可分成兩大類：１）標幟再捕法（capture-recapture model）；２）瑕疵找出曲線模型（detection profile method）。本研究提出一改良式標幟再捕法，運用標幟再捕法的基本假設。藉著兩次的標幟再捕法，增加估計所需的資訊。用最大概似估計量（Maximum Likelihood Estimator，MLE）的數學方法，求得當瑕疵數為多少時，使前後兩次同時發生機率為最大值。

　　參與實驗的人員是，成功大學資訊工程系物件導向軟體工程的修課學生，實驗所用的文件是NASA的自動提款機（automated teller machine ，ATM）文件。在實驗結果中，我們與未改良前的標幟再捕法，及其他的數學模型相比較，觀察在相對誤差（Relative Error ，RE）和整體的變異性（Variability）上的優劣。都可以清楚看出，改良式標幟再捕法有著不錯的表現。

　Defect prediction is an important process in the evaluation of software quality. Software defect estimation plays an important role for evaluating the quality of work products. Many defect estimation models have been proposed to increase the accuracy of the estimation, but it is not a easy job for project manager to decide if the work product reach the required quality, and can be passed to the next stage. To accurately predict the rate of software defects can not only facilitate software review decisions, but can also improve software quality. In this paper, we have provided a defect estimation approach, which uses defective data from sequential inspections to increase the accuracy of estimating defects. To demonstrate potential improvements, the results of our approach were compared to those of two other popular estimation approaches, the Capture-Recapture model and the Re-inspection model. By using the proposed approach, software organizations may increase the accuracy of their defect predictions and reduce the effort of subsequent inspections. By applying this estimation model, an estimation framework based in the model will be presented at the end of this paper. The framework can be used to develop a defect estimation system to estimate the number of defects in any kind of work products. The information provided by this system not only facilitates the defect estimation process for the project manager, but also increase the accuracy of the results.

[1] A. A. Porter and L. G. Votta, “An experiment to assess different defect detection methods for software requirements inspections,”Int’l Conf. Software Eng. (ICSE),pp. 103 – 112,1994.
[2] Adam A. Porter, Lawrence G. Votta, Jr.,and Victor R. Basili, “Comparing Detection Methods For Software Requirements Inspections: A Replicated Experiment,” Empirical Software Engineering. ISSN, Volume 3, pp. 355-379, December 1998.
[3] A. A. Porter, H. P. Siy, C. A. Toman, and L. G. Votta, “An Experiment to Assess the Cost-Benefits of Code Inspections in Large Scale Software Development,” IEEE Trans. Software Eng., vol. 23, no. 6, pp. 329-346, June 1997.
[4] A. Chao, “Estimating the Population Size for Capture- Recapture Data with Unequal Catchability.” Biometrics 43, pp. 783-791, Dec. 1987.
[5] A. Chao, “Estimating Population Size for Sparse Data in Capture-Recapture Experiments.” Biometrics 45, pp. 427-438, June 1989
[6] A. Chao, S-M. Lee, and S-L. Jeng, ”Estimating Population Size for Capture-Recapture Data when Capture Probabilities Vary by Time and Individual Animal.” Biometrics 48, pp. 201-216, March 1992.
[7] Claes Wohlin and Per Runeson “Defect Content Estimations from Review Data” Proc. Int’l Conf. Software Eng. ICSE, pp. 400-409, 1998 DPMmodel
[8] D.L. Otis, K.P. Burnham, G.C. White, and D.R. Anderson, “Statistical Interference from Capture Data on closed animal populations,” A Publication of the Wildlife Society, Wildlife Monographs 62, 1978.
[9] Frank Padberg, “Empirical interval estimates for the defect content after an inspection,” Int’l Conf. Software Eng. ICSE, pp.58-68,2002.
[10] Frank Padberg, Thomas Ragg, and Ralf Schoknecht, “Using Machine Learning for Estimating the Defect Content After an Inspection,” IEEE Trans. Software Eng, Vol. 30, No. 1, pp. 17-28, January 2004.
[11] IBM Corporation, Implementation Software Inspections, course notes, 1981
[12] IEEE Standards Collection–Software Engineering, Std 830-1993, 1994.
[13] James Miller, “Estimating the number of remaining defects after inspection,” Technical Report, ISERN-98-24, 1998
[14] J. Miller, M. Wood, and M. Roper ,“Further Experiences with Scenarios and Checklists,” Source Empirical Software Engineering, Volume 3 , Issue 1, pp.37 – 64,1998.
[15] Jay L. Devore, “PROBABILITY AND STATISTICS FOR ENGINEERING AND THE SCIENCES” 5th Edition, pp.40-43, California Polytechnic State University, San Luis Obispo,2000
[16] K. E. Emam and O. Laitenberger, “Evaluating Capture-Recapture Models with Two Inspectors,” IEEE Trans. Software Eng., vol. 27, no. 9, pp. 851-864, June 2001.
[17] Kai-Yuan Cai, “On Estimating the Number of Defects Remaining in Software”, Journal of Systems and Software, Volume 40 Issue 2, February 1998.
[18] L.C. Briand, K. El-Emam, and B.G. Freimut, “A Comparison and Integration of Capture-Recapture Models and the Detection Profile Method”, Proc. Int’l Symp. Software Reliability Eng. (ISSRE), vol. 9, pp. 32-41, 1998.
[19] L.C. Briand, K. El-Emam, B.G. Freimut, and O. Laitenberger, “A Comprehensive Evaluation of Capture-Recapture Models for Estimating Software Defect Content,” IEEE Trans. Software Eng., vol. 26, no. 6, pp. 518-540, June 2000.
[20] O. Laitenberger, and J.M. DeBaud, “An Encompassing Life-Cycle Centric Survey of Software Inspection”, Journal of Systems and Software, Volume 50 Issue 1, pp. 5 - 31, January 2000.
[21] P. Runeson and C. Wohlin, “An Experimental Evaluation of an Experience-Based Capture-Recapture Method in Software Code Inspections,” Empirical Software Eng., vol. 3, no. 3, pp. 381-406, 1998
[22] Roger S. Pressman, “Software Engineering: A Practitioner’s Approach,” Mc Graw Hill, 2001
[23] S.A. Vander Wiel and L.G. Votta, “Assessing Software Designs Using Capture-Recapture Methods,” IEEE Trans. Software Eng., vol. 19, no. 11, pp. 1045-1054, Nov. 1993.
[24] S. Biffl and W. Grossmann, “Evaluating the Accuracy of Defect Estimation Models Based on Inspection Data from Two Inspection Cycles”, Proc. Int’l Conf. Software Eng. (ICSE), vol. 23, pp. 145-154, 2001.
[25] S.G. Eick, C.R. Loader, M.D. Long, L.G. Votta, and S.A. Vander Wiel, “Estimating Software Fault Content before Coding, “ Proc. Int’l Conf. Software Eng. ICSE, vol. 14, pp. 59-65, 1992.