Evaluation Methods for the Reliability of a Linear Connected-(1, 2)-or-(2, 1)-Out-of-(m, n):F Lattice System

This study focuses on system reliability evaluation methods for the linear connected-(1, 2)-or-(2, 1)-out-of-(m, n):F lattice systems. To compute system reliability, previous studies have proposed the recursive equation and finite Markov chain imbedding approaches. However, no study directly compared the efficiency of both approaches. Hence, for the first time in the literature, this paper comprehensively compares the efficiency of both approaches. Accordingly, infer that their efficiency depends on the situation. This comparison will provide a guideline to help decide the approach that should be adopted. Furthermore, upper and lower bounds are also employed, provided it is unnecessary to obtain the exact system reliability. Several useful and simple bounds were reported; however, tighter bounds that require the computational burden have not been sufficiently discussed. Therefore, we derive the upper and lower bounds for the system reliability. The results of the numerical experiment indicate that we obtained the tighter bounds at the expense of computational effort, compared with existing bounds. These tighter bounds can sufficiently evaluate the reliability of large systems. The theoretical results in this paper would provide useful insights into industrial manufacturing, contribute to the stable operation of practical systems, and promote Industry 4.0.