Evaluation of software availability for the imperfect software debugging model

Abstract

To evaluate the software-related measure such as the first passage time and software availability, we consider in this paper an imperfect software debugging model incorporating two types of fault, one being easily detected and the other difficult to detect. When a software failure occurs, the fault that causes the failure either is removed from the fault contents or still remained in the system even after the debugging is completed. In this sense, the debugging model is referred to as an imperfect model. In this paper, we first define the transition probabilities of the debugging process and use it to derive several parameters of interest measuring the software performance, including the expected numbers of perfect debuggings. The availability function of a software system, which is defined as the probability that the software is in a working state at a given time, is also derived. We assume that the length of time necessary for debugging the failure is random in all evaluations. Numerical examples are given to illustrate the methods discussed.

Keywords:

• Imperfect debugging
• Markov process
• Fault removals
• Transition probability
• Software debugging model

Acknowledgements

We are grateful to the associate editor and anonymous referees for valuable comments which improved the earlier version significantly. This work was supported by Korea Research Foundation grant KRF-2000-015-DS0005.

Chong Hyung Lee received his BS(1993), MS(1995) and PhD(2001) in Statistics from Hallym University, Korea and is currently an assistant professor at Konyang University. His research areas include computation of system reliability, software reliability and quality control.

Seung Min Lee received his BS(1976) in Computer Science and Statistics from Seoul National University, and PhD(1987) in Statistics from State University of New York at Stony Brook. He is a full professor at Hallym University, Korea. His research interests include probability models, reliability theory and its applications.

Dong Ho Park is a full professor at Hallym University since 1993. He received his BS(1968) in Applied Mathematics from Seoul National University, and MS(1980) and PhD(1982) in Statistics from Florida State University. He was formerly an associate professor at University of Nebraska-Lincoln, USA, until 1995 and was president of the Korean Reliability Society. He has published on reliability theory, accelerated life testing, software reliability and system maintenance policy in a wide variety of international journals. He is a member of ASA, IMS, ASQ, ISI, IEICE, and IEEE.