A Two-Threshold Replacement Policy for a Two-Unit System with Failure Interaction

• Activity Number: 612
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Shey-Huei Sheu* and Tzu-Hsin Liu and Zhe-George Zhang and Hsin-Nan Tsai
• Companies: Providence Univesrity and Providence University and Western Washington University and Providence University
• Keywords: Optimization ; minimal repair ; Cumulative damage model ; Shock model ; Replacement policy

Abstract

In this paper, we study a two-unit system with failure interactions. The system is subject to shocks which arrive according to a nonhomogeneous Poisson process. The shock can be classified into two types. Each type I shock causes a unit A minor failure which is rectified by a minimal repair, whereas a type II shock causes a complete system failure that calls for a corrective replacement. Each unit A minor failure also results in a random amount of damage to unit B and such a damage to unit B can be accumulated to trigger a preventive replacement or a corrective replacement action. In addition, unit B with damage of level z may become minor failed with probability at each unit A minor failure and rectified by a minimal repair. The probability of type II shock is permitted to depend on the number of shocks since the last replacement. In this paper, we consider a more general replacement policy. Under such a policy, the system is replaced at age T, or at the time which the total damage to unit B exceeds a pre-specified level Z (but less than the failure level K) or at first type II shock or when the total damage to unit B exceeding a failure level K, whichever comes first.