Estimation in α-Series Processes with Exponential Inter-Arrival Times under Censored Data

Abstract

The α-series process is an important counting process commonly used to model data sets having monotonic trend. It is especially utilized in reliability analysis of deteriorating systems and warranty analysis of repairable systems. When a data set is compatible with the α-series process, it is important to make inference for model parameters of the process. All the studies in the literature only consider single realization of the process which only has complete samples. However, multi-sample of the process may be observed. In this situation, the data set includes both complete and censored samples. In this study, estimation problem for an α-series process under censored data is studied by assuming inter-arrival times of the process have exponential distribution and all samples are homogeneous. Maximum likelihood estimators of the model parameters are obtained and their asymptotic properties such as asymptotic normality and consistency are proved. Also, their small sample performances have been investigated by a simulation study.