Fast Algorithm for Optimal Arrangement Problems of Multi-state Consecutive-k-out-of-n:F System(Theory and Methodology)

Abstract

In many practical situations, the states of the systems and their components are assumed to take more than two different levels, ranging from working perfectly to complete failre. In a multi-state system, both the system and the components are allowed to be in M+1 possible states, where M is a positive integer that represents the system or components in a state working perfectly. while zero is a state of complete failure. Therefore, the multi-state system reliability model provides more flexibility for the modeling of equipment conditions. In this study, we discuss the multi-state consecutive-k-out-of-n:F system. This system is applicable to the quality control problem for batch products, preventive maintenance problem for oil pipeline systems, and similar items. For the consecutive-kout-of-n:F system, the optimal arrangement problem, where the solution is obtained by the arrangement of components with maximum system reliability, is one of the most important problems in this system. So, we consider the optimal component arrangement for a multi-state consecutive-k-out-of-n:F system that has the maximum expectation values for the system state distribution when these components are arranged in positions in the system. The multi-state consecutive-k-out-of-n:F system consists of ii components arranged along a linear path. As the number of components n increases, the number of calculations to obtain the exact solution to the optimal component arrangement problems becomes large. Therefore, in this study, first, we propose an algorithm for obtaining the exact solution for optimal arrangement problems in multi-state consecutive-k-out-of-n:F systems. It is possible to solve the problems if the expectations for all arrangements are calculated. However, we have to calculate the expected values for many arrangements. We propose an algorithm, which is based on the branch-and-bound method, to obtain optimal solutions for such problems and remove operations that are not useful via certain properties of the arrangements. Next, we evaluate our proposed algorithm in terms of the computing time. The results of the numerical experiments show that the proposed algorithm is more efficient for systems where the number of components a is large.