Research On Industrial Software Reliability Models Based On Bayesian Model Averaging Method

With the development of the industrial 4.0 revolution,great changes have taken place in the fate of industrial software.With the increasing importance of software,software has become the main driving force of many industrial product innovation.industrial software products’ quality can be guaranteed by improving the prediction accuracy of software reliability model.Model selection can be used to determine the optimal model,thus supporting a specific assumption.The model average considers the model uncertainty caused by the model selection activities.This paper mainly studies the application of Bayesian method in software reliability model selection and model average to prove that Bayesian model average method can improve the accuracy of model prediction.The specific research contents are as follows:(1)Modeling and parameter estimation of software reliability.The system learns the software reliability related content,selects three non-homogeneous Poisson process(NHPP)models as candidate model sets,and gives the specific assumptions and the process of mathematical deduction of the model.The candidate models’ unknown parameters are calculated based on the least square method and Bayesian posterior inference.(2)Model selection based on Bayesian method and fitting performance method.Before reliability evaluation,it is necessary to select suitable method to model specific objects according to actual situation.For this reason,mean square error,Akaike information criterion and Bayesian information criterion of candidate models are calculated respectively.Mean square error and Akaike information criterion are used as performance indexes to evaluate the accuracy of the model prediction,and the model is selected based on the fitting performance method.At the same time,how to approximate Bayesian factor based on Bayesian information criterion value is deduced,and Bayesian model selection method is carried out on this basis.Two different selection methods are used to select the best performance model.(3)Software reliability combination prediction modeling.To consider the uncertainty of parameters and models,this paper utilizes Bayesian inference to obtain the candidate models’ posterior probabilities as their weights for the combination forecasting method.To realize the Bayesian method using the Markov Chain Monte Carlo method.In addition,this paper proposes that the candidate models’ weights can be calculated by expectation-maximization algorithm,which is often used in mixed Gaussian model.And different weights can be given to candidate models according to different performance indexes.Then,the hybrid model can be obtained by weighted average of the candidate models by arithmetic weighting method.Finally,compared with the combination predictive model based on the Bayesian model average method,mean square error,Akaike information criterion and Bayesian information criterion are utilized as evaluation methods’ performance indicators,and the Bayesian model average method’ merits and demerits for software reliability modeling are analyzed.