A bivariate optimal replacement policy with cumulative repair cost limit for a two-unit system under shock damage interaction

作者：Lai Min Tsai^*; Chen Chung Ho; Hariguna Taqwa

来源：Brazilian Journal of Probability and Statistics (Brazilian Stat. Assoc.), 2017, 31(2): 353-372.

DOI：10.1214/16-BJPS317

• Two-unit system
• shock damage interaction
• cumulative repair cost limit
• bivariate replacement policy

In this paper, a bivariate (n, k) replacement policy with cumulative repair cost limit for a two-unit system is studied, in which the system is subjected to shock damage interaction between units. Each unit 1 failure causes random damage to unit 2 and these damages are additive. Unit 2 will fail when the total damage of unit 2 exceed a failure level K, and such a failure makes unit 1 fail simultaneously, resulting in a total failure. When unit 1 failure occurs, if the cumulative repair cost till to this failure is less than a predetermined limit L, then unit 1 is corrected by minimal repair, otherwise, the system is preventively replaced. The system is also replaced at the nth unit 1 failure, or at damage level k (<K) of unit 2, or at total failure. The explicit expression of the long-term expected cost per unit time is derived and the corresponding optimal bivariate replacement policy can be determined analytically or numerically. Finally, a numerical example is given to illustrate the theoretical results for the proposed model.

• 出版日期2017-5