Modeling and Optimization of Software Reliability using Fuzzy-Algorithmic Approach

Abstract

An approach to software reliability modeling and optimization based on the algebra of processes and fuzzy logic is proposed. The software development events related to the introduction, detection and removal of errors is modeled using logical-algorithmic structures "work - control - correction", which correspond to the processes of development, testing and debugging. The logical-algorithmic model corresponds to the fuzzy knowledge base, which connects correctness levels of the working, testing and debugging stages with the decision classes interpreted as correct or incorrect execution of the task. To provide the best quality product within a limited time (cost), improving substitutions are embedded into the logicalalgorithmic model. Improving substitutions aimed at selecting patterns of the development stages determine the structure and parameters of the software reliability model. Controllable variables associated with improving substitutions are interpreted as identifiers of implementation options of the development stages. Each variant is a logical algorithmic structure with controllable variables related to the quality of execution of the working, control and correction operations. Then the optimization problem arises, which is formulated in a direct and dual statement. It is necessary to find the implementation options, as well as controllable variables related to the quality of execution of logic-algorithmic structures, which ensure the constrained or extreme levels of software reliability and development time. A method of software reliability optimization based on multi-criteria analysis of variants is proposed. Software faultlessness criteria are considered as fuzzy sets defined on a universal set of variants using membership functions. For each stage, membership functions of fuzzy reliability estimates are constructed by means of a pairwise comparison of variants using the Saaty scale. Ranking of implementation options is carried out by intersecting fuzzy sets of criteria corresponding to the Bellman-Zadeh scheme. The ranks of the criteria which define the parameters of concentration of fuzzy sets correspond to the quality indicators of working, checking and correction operations. The synthesis of the logical-algorithmic model that ensures acceptable levels of software reliability and development time is carried out by selecting controllable variables associated with improving substitutions. The genetic algorithm is used to determine the structure of the reliability model by selecting the implementation options of the development stages. To ensure compliance with the requirements, the gradient method is used to adjust the parameters of the reliability model by selecting the ratios of repeated inspections and corrections.