Two new stochastic models of the failure process of a series system

Consider a series system consisting of sockets into each ofwhich a component is inserted: if a component fails, it is replaced witha new identical one immediately and system operation resumes. Aninteresting question is: how to model the failure processof the systemas a whole when the lifetime distribution of each component is unknown?This paper attempts to answer this question by developing two new models,for the cases of a specified and an unspecified number of sockets,respectively. It introduces the concept of a virtual component, and inthis sense, we suppose that the effect of repair corresponds toreplacement of the most reliable component in the system. It thendiscusses the probabilistic properties of the models and methods forparameter estimation. Based on six datasets of artificially generatedsystem failures and a real-world dataset, the paper compares theperformance of the proposed models with four other commonly used models:the renewal process, the geometric process, Kijima's generalised renewalprocess, and the power law process. The results show that the proposedmodels outperform these comparators on the datasets, based on the Akaikeinformation criterion