A lot of mechanical parts are subject to failure due to the deterioration. Usually the preventive maintenance is taken to ensure the safety and reliability. Therefore, it is very important to study the gradual reliability design of the mechanical part for improving the gradual reliability of the mechanical system under the condition of considering the preventive maintenance. Beta distribution is employed to describe the randomness of the mechanical part state after the preventive maintenance. The deterioration process of the mechanical part is modeled using the nonstationary Gamma process. The gradual reliability model before the first preventive maintenance is proposed according to the gradual failure principle and using the initial state distribution and the properties of Gamma process. Then, the gradual reliability model between any two times of preventive maintenance is also derived. Subsequently, the sensitivity equations of the proposed gradual reliability model to each parameter are given. The application process and practicality of the proposed approach are described by a numerical example. This work solved the problem where the maintenance has not been well considered in the reliability design of the mechanical part and contributed to the theory and method of improving the safety and reliability operation of the mechanical system.
Poisson generalized gamma process and its properties
