The purpose of this study was to propose useful suggestion by analyzing preventive replacement policy under which there are minor and major failure. Here, major failure is defined as the failure of system which causes the system to stop working, however, the minor failure is defined as the situation in which the system is working but there exists inconvenience for the user to experience the degradation of performance. For this purpose, we formulated an expected cost rate as a function of periodic replacement time and the number of system update cycles. Then, using the probability and differentiation theory, we analyzed the cost rate function to find the optimal points for periodic replacement time and the number of system update cycles. Also, we present a numerical example to show how to apply our model to the real and practical situation in which even under the minor failure, the user of system is not willing to replace or repair the system immediately, instead he/she is willing to defer the repair or replacement until the periodic or preventive replacement time. Optimal preventive replacement timing using two variables, which are periodic replacement time and the number of system update cycles, is provided and the effects of those variables on the cost are analyzed.

This paper presents a periodic replacement policy for a system subject to shocks when the system is operating for a finite random horizon. The system is subject to shocks during operation, and each shock causes downgrading of the system performance and makes it more expensive to run by the additional running cost. Shocks arrive according to a nonhomogeneous or a renewal process, and we develop periodic replacement policies under a finite random operating horizon. The optimum periodic replacement interval which minimizes the total operating cost during the horizon is found. Numerical examples are presented to demonstrate the results.

Systems such as database and socal network systems have been broadly used, and their unexpected failure, with great losses and sometimes a social confusion, has received attention in recent years. Therefore, it is an important issue to find optimal maintenance plans for such kind of systems from the points of system reliability and maintaining cost. However, it is difficult to maintain a system during its working cycle, since stopping works might incur users some troubles. From the above viewpoint, this paper discusses minimal repair maintenance policy with periodic replacement, while considering the random working cycles. The random working cycle and periodic replacement policies with minimal repair has been discussed in traditional literatures by usually analyzing cases for the nonstopping works. However, maintenance can be more conveniently done at discrete time and even during the working cycle in real applications. So, we propose that periodic replacement is planned at discrete times while considering the random working cycle, and moreover provide a model in which system, with a minimal repair at failures between replacements, is replaced at the minimum of discrete times KT and random cycles Y. The average cost rate model is used to determine the optimal number of periodic replacement.