一类软件可靠性模型的统计分析

论文总字数：22612字

摘 要

随着社会复杂性的增加，系统软件的可靠性工程领域面临着越来越复杂的关键挑战。本文在大量的文献阅读基础上，首先简单介绍了可靠性模型理论的相关概念理论。接着对非齐次泊松过程模型作了详细的介绍，说明了其中包含的多种情况。然后分别举例说明了对于两类数据的使用不同模型来拟合的效果以及比较，在计算时主要运用了极大似然估计方法来估计各个参数，比如初始错误数、错误检测率等。在得出这些基本参数之后，利用了现有数据对未来一段时间内可能出现的错误数目、接下来出现错误的时间都进行了预测。由于各个模型特点不同，还将各个模型进行了比较，采用了公认的误差平方和准则以及赤池信息量准则。接下来，基于个人对可靠性模型理论的理解，对于Yamada不完美排错模型2提出了四种猜想，并且从理论和实际检验中比较了猜想和已有理论的区别，得到了自己的结果。最后，介绍了可靠性模型的一些相关应用，可以看出可靠性建模给我们检测软件带来了极大的便利。

关键词：软件可靠性 模型 极大似然 非齐次泊松过程

Statistical Analysis Of System Software Reliability

Abstract

With the increase of social complexity, the reliability engineering of the system is faced with more and more complex and key challenge .On the basis of a lot of literature reading, this paper briefly introduces the relevant concepts of the reliability model theory. Then, the model of non-homogeneous Poisson process is introduced, and the variety of cases is described. And then an example is given to illustrate the for different uses of the two kinds of data model to fitting effect and comparison, in the calculation mainly uses the maximum likelihood estimation method to estimate the parameters, such as initial error number, error detection rate.After these basic parameters are drawn, the possible errors of the existing data over the next period of time are used, and the time of the error is predicted. Because of the different characteristics of each model, the different models are compared, and the accepted error square and criterion and the criterion of pool information are adopted. Next, personal understanding on the theory of reliability model based on, for Yamada imperfect debugging model 2 proposed four kind of conjecture, and from the theoretical and practical test compares the distinction conjecture and the existing theories, their results are obtained. At last, some related applications of the reliability model are introduced, which can be seen that the reliability modeling has brought us great convenience for testing software.

Key word:software， reliability model， MLE， NHPP

目 录

摘要.......................................................................2

Abstract.....................................................................3

1. 可靠性模型简介......................................................7

1.1选题背景和意义......................................................7

1.2系统可靠性概念......................................................7

1.2.1可靠度........................................................7

1.2.2失效率........................................................8

1.3软件可靠性建模......................................................9

1.3.1概述..........................................................9

1.3.1.1、错误播种模型..........................................9

1.3.1.2、失效率模型............................................9

1.3.1.3、曲线拟合模型..........................................9

1.3.1.4、可靠性增长模型........................................9

1.3.1.5、马尔科夫结构模型......................................9

1.3.1.6、时间序列模型.........................................10

1.3.1.7、非齐次泊松过程模型...................................10

1.3.2可靠性增长模型...............................................10

1.3.2.1 Coutinho模型..........................................10

1.3.2.2 Wall-Ferguson模型......................................10

1.3.3非齐次泊松过程模型...........................................10

1.3.3.1、Musa指数模型.........................................10

1.3.3.2、Goel-Okumoto NHPP模型................................11

1.3.3.3、S形增长模型...........................................11

1.3.3.4、超指数增长模型........................................11

1.3.3.5、离散可靠性增长模型...................................11

1.3.3.6、测试努力相关的可靠性增长模型.........................11

1.3.3.7、广义NHPP模型.......................................11

1. 可靠性模型的应用实例分析...........................................12

2.1预备知识...........................................................12

2.1.1相关符号.....................................................12

2.1.2两类数据的参数估计...........................................12

2.1.2.1第一类数据：间隔域数据.................................12

2.1.2.2第二类数据：时间域数据.................................13

2.1.3 模型选取的标准...............................................13

2.1.3.1 SSE（误差平方和）准则..................................13

2.1.3.2 MSE（均方误差）准则....................................14

2.1.3.3 AIC（赤池信息量）准则..................................14

2.1.3.4 PRR（预测比率）准则....................................14

2.2 两类数据的五种不同模型的应用与比较.................................14

2.2.1 第一类数据：间隔域数据.......................................14

2.2.1.1 Goel-Okumoto模型.......................................17

2.2.1.2 变点S形模型（inflection S-shaped).........................17

2.2.1.3 Yamada 不完美排错模型1................................18

2.2.1.4 Yamada 不完美排错模型2................................19

2.2.1.5 Pham指数不完美排错模型................................20

2.2.1.6 一些NHPP模型对于表1数据的极大似然估计和SSE...........22

2.2.2 第二类数据：时间域数据.......................................24

2.2.2.1 Goel-Okumoto模型.......................................25

2.2.2.2 变点S形模型（inflection S-shaped)......................26

2.2.2.3 Yamada 不完美排错模型1.................................26

2.2.2.4 Yamada 不完美排错模型2.................................26

2.2.2.5 Pham指数不完美排错模型.................................27

2.2.2.6 一些NHPP模型对于数据集#2的极大似然估计和SSE、AIC......27

2.3 本章小结............................................................29

1. 可靠性模型的拓展与比较................................................30

3.1 关于Yamada不完美排错模型2的猜想1..................................30

3.1.1对两类数据的讨论...............................................30

3.1.1.2 第一类数据...............................................30

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