Power-law process and its applications on repairable systems

Abstract

Most of the complex systems in use nowadays such as communication systems, software systems, automobile engines, helicopters, aircraft generators, etc., are repairable systems that can be repaired by replacing or repairing system components other than replacement of the entire system after failing. Before a repairable system is used or handed over to the customer, system testing is usually conducted in the development phase to explore all aspects of functionality and system reliability. Moreover, early prototypes will often contain design flaws when a system is in the development stage, so that system testing is performed to correct such problems and this will affect the final design. Also, system reliability obtained during the development phase is essential to establish a warranty period or determine a maintenance phase for repairable systems. In this paper, we consider the basic concepts and statistical inferences for the power-law process which is the special type of nonhomogeneous Poison process, and it is widely used in the study and analysis of the system reliability. In addition, this paper also presents applications of the power-law process on repairable systems using two real data sets, failure times of an aircraft generator, and failure times of the Boeing air-conditioning system.