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This paper proposes a special redundant model for describing the s-dependency of multi-version programming software during testing and debugging. N-version programming (NVP) is one of the most important software fault tolerance techniques. Many papers have studied the issue of fault correlation among versions. However, only a few of them consider this issue during the testing and debugging part of the software development life cycle. During testing and debugging, faults may not be successfully removed. Imperfect debugging may result in unsuccessful removal, and the introduction of new faults. Different from existing NVP models, the model proposed in this paper allows an assessment of s-dependency when correlated failures may not necessarily occur at the same execution time point. The model focuses on 2 VP systems. It is developed to be a bivariate counting process by assuming positive s-dependency among versions. Considering imperfect debugging, this bivariate process characterizes dynamic changes of fault contents for each version during testing and debugging. The system reliability, expected number of faults, probability of perfect debugging, and parameter estimation of model parameters are presented. An application example is given to illustrate the proposed model. The paper provides an alternative approach for evaluating the reliability of 2 VP software systems when there is positive s -dependency between versions.
Date of Publication: June 2012