A RELATIONSHIP OF COMPONENTS IN THE OPTIMAL ARRANGEMENT PROBLEMS FOR THE MULTI-STATE CONSECUTIVE-k-OUT-OF-n:F SYSTEM IN CASE OF maxkj=2 - Yoshida, Naoki; Yamamoto, Hisashi; Akiba, Tomoaki; Shingyochi, Koji; Xiao, Xiao (International Journal of Industrial Engineering: Theory, Applications and Practice, 2017)
In a multi-state consecutive-k-out-of-n:F system, both the components and the system are allowed to be M+1 possible states for o,1,...,M. State M represents the perfectly working state, 0 represents the completely failed state, and the others represent the degraded states. k is an M-dimensional vector as a parameter k_j (j=1,2,...,M) which decides the system states. A multi-state system reliability model provides more flexibility for the modeling of equipment conditions. One of the most important problems in the multi-state consecutive-k-out-of-n:F system is the optimal arrangement problem. The optimal arrangement problem is defined to obtain the arrangement as minimizing the system state probabilities for any j. The previous researches have been studied the characteristic of optimal arrangements. Malon showed that the characteristic of invariable optimal arrangements depended on the magnitude relation of the failure probability of each component in a binary-state consecutive-k-out-of-n:F system. However, in the multi-state consecutive-k-out-of-n:F system, previous studies have shown that the optimal arrangement cannot be specified only by the magnitude relation of failure probability of each component. In this study, we discuss a layout of the optimal arrangement for a multi-state consecutive-k-out-of-n:F system by the distribution of a system state probabilities when maxk_j=2. The purpose of this paper is to investigate the hypothesis of optimal arrangement in a multi-state consecutive-k-out-of-n:F system as similar layout of Malon’s proved characteristic optimal arrangement of the binary-state consecutive-k-out-of-n:F system.