Reliability growth modeling and optimal release policy under fuzzy environment of an N-version programming system incorporating the effect of fault removal efficiency

Failure of a safety critical system can lead to big losses.Very high software reliability is required for automating the working of systems such as aircraft controller and nuclear reactor controller software systems.Fault-tolerant softwares are used to increase the overall reliability of software systems.Fault tolerance is achieved using the fault-tolerant schemes such as fault recovery (recovery block scheme),fault masking (N-version programming (NVP)) or a combination of both (Hybrid scheme).These softwares incorporate the ability of system survival even on a failure.Many researchers in the field of software engineering have done excellent work to study the reliability of fault-tolerant systems.Most of them consider the stable system reliability.Few attempts have been made in reliability modeling to study the reliability growth for an NVP system.Recently,a model was proposed to analyze the reliability growth of an NVP system incorporating the effect of fault removal efficiency.In this model,a proportion of the number of failures is assumed to be a measure of fault generation while an appropriate measure of fault generation should be the proportion of faults removed.In this paper,we first propose a testing efficiency model incorporating the effect of imperfect fault debugging and error generation.Using this model,a software reliability growth model (SRGM) is developed to model the reliability growth of an NVP system.The proposed model is useful for practical applications and can provide the measures of debugging effectiveness and additional workload or skilled professional required.It is very important for a developer to determine the optimal release time of the software to improve its performance in terms of competition and cost.In this paper,we also formulate the optimal software release time problem for a 3VP system under fuzzy environment and discuss a the fuzzy optimization technique for solving the problem with a numerical illustration.