Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (3): 631-641.doi: 10.23919/JSEE.2021.000054

• SYSTEMS ENGINEERING • Previous Articles     Next Articles

A generalized geometric process based repairable system model with bivariate policy

Ning MA1,*(), Jimin YE1(), Junyuan WANG2()   

  1. 1 College of Mathematics and Statistics, Xidian University, Xi’an 710071, China
    2 College of Sciences, China Jiliang University, Hangzhou 310018, China
  • Received:2020-06-20 Online:2021-06-18 Published:2021-07-26
  • Contact: Ning MA E-mail:chumnxi@163.com;jmye@mail.xidian.edu.cn;junyuanyc@163.com
  • About author:|MA Ning was born in 1994. She received her B.S. degree of statistics from the College of Mathematical Science in Shanxi University in 2017, M.S. degree of statistics from the College of Mathematics and Statistics, Xidian University in 2020. Her research interests include applied stochastic processes, maintenance theory and reliability analysis. E-mail: chumnxi@163.com||YE Jimin was born in 1967. He received his Ph.D. degree in signal and information processing from Xidian University in 2005. Currently, he is a professor and doctoral supervisor in the College of Mathematics and Statistics, Xidian University. His research interests are risk theory, stochastic operation research and applied probability. E-mail: jmye@mail.xidian.edu.cn||WANG Junyuan was born in 1987. He received his B.S. degree of mathematics and applied mathematics in 2011, Ph.D. degree of probability theory and mathematical statistics in 2020. He is a lecturer in China Jiliang University. His research interests include applied stochastic processes, maintenance theory and reliability analysis. E-mail: junyuanyc@163.com
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (61573014) and the Fundamental Research Funds for the Central Universities (JB180702)

Abstract:

The maintenance model of simple repairable system is studied. We assume that there are two types of failure, namely type I failure (repairable failure) and type II failure (irrepairable failure). As long as the type I failure occurs, the system will be repaired immediately, which is failure repair (FR). Between the $(n - 1)$ th and the $n$ th FR, the system is supposed to be preventively repaired (PR) as the consecutive working time of the system reaches ${\lambda ^{n - 1}}T$ , where $\lambda $ and $T$ are specified values. Further, we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the $N$ th type I failure or the occurrence of the first type II failure, whichever occurs first. In practice, the system will degrade with the increasing number of repairs. That is, the consecutive working time of the system forms a decreasing generalized geometric process (GGP) whereas the successive repair time forms an increasing GGP. A simple bivariate policy $(T, N)$ repairable model is introduced based on GGP. The alternative searching method is used to minimize the cost rate function $C(N, T)$ , and the optimal ${(T, N)^*}$ is obtained. Finally, numerical cases are applied to demonstrate the reasonability of this model.

Key words: renewal reward theorem, generalized geometric process (GGP), average cost rate, optimal policy, replacement