Investigating Trend/Cyclic/Clustering Decomposition in Software Fault Detection

In this paper we consider a self-exciting Hawkes process with four components to represent reliability growth, long-term trend, periodicity and clustering effects in software fault-detection processes, and investigate whether there exists the above decomposition for the actual software fault count data. The model parameters are estimated by means of the maximum likelihood estimation method. Ushiroda et al. (2019) suppose the Legendre and Fourier polynomial functions in the intensity function to represent the long-term effect and periodicity effect in the software fault-detection process. In this paper, we introduce an additional component which depends on the past event-occurence times up to the present time to describe the clustering effect in the self-exciting Hawkes processes. Through the empirical study with actual software fault-count data sets, we identify the existence of trend/cyclic/clustering effects in the software fault-detection processes.