A Reliability Modeling Method Based on Phase-Type Distribution Aiming at Shock Model

The traditional shock model generally describes the magnitude of the cumulative damage caused by a random shock sequence and compares the magnitude with a predetermined threshold to obtain the failure time of a component. There are two limitations in this kind of models in practice: First, the statistical characteristics of the damage due to a single shock may be difficult to obtain, which means the magnitude of the damage may not be described by an appropriate distribution; Second, the cumulative shock magnitude may be difficult to measure, or it may be difficult for a failure mode to be described by a threshold, meaning that the magnitude of the damage and the threshold may not be compared with each other. Considering both failure and censored samples, a reliability modeling method is proposed in this work to address the above problems. The shock model is first established by using both continuous and discrete phase-type (PH) distributions. Then the parameter estimation method of the shock model is derived based on EM method and the identifiability of the parameters in PH distributions is also given. Finally, the adaptability of the model is analyzed using three different types of simulation cases.