EM Algorithm for Estimating Reliability of Multi-Release Open Source Software Based on General Masked Data

Multi-release is critical for modern open source software product in order to satisfy more customer requirements. Masked data, a kind of missing data, is the system failure data when the exact cause of the failures might be unknown. That is, the cause of the system failures may be any one of the objects. However, due to the influence of the test strategy in real project, the cause of the system failures may be a subset of the system objects, not any one of the objects. In this paper, the mathematical description of general masked data is presented based on the traditional masked data. Furthermore, a novel multi-release open source software (OSS) reliability model based on general masked data is proposed. Different from traditional multi-release OSS reliability model, the proposed approach is based on additive model with general masked data other than change point model. And then, the maximum likelihood estimation (MLE) process of the model parameters is derived in detail, and expectation maximization (EM) algorithm is used to solve the extremely complicated problem of the log-likelihood function. Finally, two data sets from real open source software project are applied to the proposed approach, and the results show that the proposed reliability model is useful and powerful.