在軟體測試以及其被釋出後的後續維護中，軟體錯誤的偵測與移除皆扮演著舉足輕重的角色。過去三十年來，許多研究人員主要使用被假設為非齊次卜瓦松過程的軟體可靠度成長模型來研究此類偵錯與除錯的活動。此外，許多軟體可靠度成長模型為了簡化模型，在除錯過程中有著一個共通的假設，亦即忽略除錯的所需時間。然而，在實際軟體開發過程中除錯的所需時間應該被納入考量，這是因為當軟體失效發生的時候，開發者需要時間識別出這些軟體失效，進而除去其形成原因。
在此學位論文中，我們將應用排隊理論來推導有限伺服器排隊模型，進而使用這個模型當作軟體可靠度量化的指標；同時，此種模型也會將除錯的時間納入考量。我們也會證明此模型能夠幫助開發者預測對於每一個偵測到錯誤之回應時間，也能夠知道除錯的效率。以上這些指標能夠幫助計畫經理設立合理的開發時程以及妥善的人力資源配置。實驗的結果也證明結合偵錯與除錯過程的有限伺服器排隊模型具有準確地預估能力以及高度的適應性。

Fault detection and removal play major roles in software testing as well as follow-up maintenance after software release. Over the past three decades, researchers have been studying fault detection removal using mainly the software reliability growth models (SRGMs) that are assumed to be a non-homogeneous Poisson process. In addition, many of the SRGMs simplify the models by ignoring the fault correction time in the software debugging process. However, the fault correction time should be considered in practical software development because when failures occur in the test phase, it takes time for the developers to identify the failures and remove the corresponding root causes.
This thesis applied the queueing theory and introduced a finite server queueing (FSQ) model that took the fault correction time into consideration. The model was adopted to predict the possible fault detection and removal behavior as a quantitative method. We verified that the FSQ model helps developers to anticipate in the possible response time of each detected fault and the fault correcting efficiency. This assists project managers to set up reasonable schedules and allocate proper personnel resources. The obtained result showed that the FSQ model which incorporated the detection and removal processes exhibited an accurate prediction ability and high adaptability.

Contents
Abstract in Chinese I
Abstract II
Acknowledgement III
Contents IV
List of Figures VII
Notation 1
Chapter 1 2
Introduction 2
Chapter 2 5
Background and Related Works 5
Chapter 3 10
Software Reliability Modeling 10
3.1 The FSQ model 10
3.2 The fault removal process 12
3.3 The relationship between FSQ model and traditional SRGMs 17
Chapter 4 20
Data Analysis and Numerical Examples 20
4.1. Failure data 20
4.1.1. Maximum Likelihood Estimation 23
4.1.2. Least Square Estimation 23
4.2. Criteria for model comparison 24
4.3. Performance analysis 31
4.3.1. Parameter estimation of system T1 32
4.3.2. Parameter estimation of system P1 36
4.3.3. Parameter estimation of system R1 39
4.3.4. Performance comparison of the systems 42
Chapter 5 63
Software Project Management 63
5.1. Case study on target system 63
5.2. Management Analysis 63
5.2.1. The efficiency of correcting faults 63
5.2.2. The response time of each fault 64
Chapter 6 67
Conclusions 67
Appendix 69
Appendix A. Detailed information of the system T1 69
Appendix B. Detailed information of the system P1 70
Appendix C. Detailed information of the system R1 71
Reference 72

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