An integration of fault detection and correction processes in software reliability analysis

Abstract

Software reliability is defined as the probability of failure-free software operation for a specified period of time in a specified environment and is widely recognized as one of the most significant aspects of software quality. Over the past 30 years, many software reliability growth models (SRGMs) have been proposed and they can greatly help us to estimate some important measures such as the mean time to failure, the number of remaining faults, defect levels, and the failure intensity, etc. Besides, SRGMs can also help to determine person power needed to support the desired reliability requirements. However, from our studies, most of SRGMs only focus on describing the behavior of fault detection process and assume that faults are fixed immediately upon detection. In fact, this assumption may not be realistic. Thus, in this paper, we will propose a general framework for modeling the software fault detection and correction processes. We will also show that the proposed approaches cover a number of well-known SRGMs. Two numerical examples based on two real software failure data sets are presented and discussed in detail.

Introduction

Over the past decade, the deployment of computer systems has grown dramatically. People in the modern society are increasingly dependent on both hardware and software systems. Since software is embedded in everything and permeates our daily life, the correct performance of a software system becomes an important issue of many critical systems. Software reliability can be viewed as a good measure of quantifying software failures and is defined as the probability of failure-free software operation for a specified period of time in a specified environment (Lyu, 1996). Numerous software reliability growth models (SRGMs) have been developed to measure software reliability, and some of them are based on NHPP (Lyu, 1996, Musa et al., 1987, Pham, 2000, Xie, 1991). These SRGMs are very useful to describe the error-detection process as a discrete or continuous process at a time-dependent error-detection rate (Goel and Okumoto, 1979, Lo et al., 2001, Lo et al., 2003, Yamada et al., 1983, Yamada et al., 1993). The common assumption of conventional SRGMs is that the detected faults will be immediately removed. However, this assumption may not be very realistic, that is, it is rare to see that the detected faults are immediately corrected (Gokhale et al., 1998, Schneidewind, 1975, Schneidewind, 2003, Ohba, 1984, Xie and Zhao, 1992).

Schneidewind (1975) first modeled the fault-correction process by using a constant delayed fault-detection process. Later, Xie and Zhao (1992) extended the Schneidewind model to a continuous version by substituting a time-dependent delay function for the constant delay. A key factor of the continuous version of Schneidewind model is the time-dependent delay function, which measures the expected time lag to correct a detected fault. Actually, software debugging is a science. Fault correction personnel have to formulate a hypothesis and make predictions based on the hypothesis. Furthermore, they should run the software, observe its output, and confirm the hypothesis. We know that the time to remove a fault depends on the complexity of the detected faults, the skills of the debugging team, the available manpower, and the software development environment, etc. (Lyu, 1996, Musa et al., 1987, Musa, 1998). Therefore, it is very important for us to have different software reliability models for modeling the fault detection and correction processes. In this paper, we will propose a new software reliability model considering both the fault detection and correction processes. Some numerical examples are performed based on two real software failure data sets. Experimental results show that the proposed framework to incorporate debugging time lag for SRGM has a fairly accurate prediction capability.

This paper is organized as follows. In Section 2, the properties of the related models are reviewed and a description of characteristics of the NHPP models is discussed. An integration model of fault detection and correction processes is proposed in Section 3. Also, we show how some existing NHPP models are re-evaluated from the viewpoint of correction process and make some observations between the original NHPP models and the integrated models. The numerical examples and comparison results are presented in Section 4. Finally, the conclusions are made in Section 5.