MBNPy's system catalogue
20 Jul 2024Tags: system-type functionality
There is no free lunch and efficiency of MBNPy is no exception. While simulation-based methods like MCS are applicable to any general systems, MBNPy requires system-specific algorithms to quantify a system's probability distribution.
We note that for all systems below, conventional approach has complexity of $O(M^N)$. Usually, with a 16GB RAM, many software will raise a warning for exceeding $2^{33}$; this means 33 binary-state components.
Table 1: MBNPy's system catalogue.
| System type1 | Complexity2 | Application examples | Ref. |
|---|---|---|---|
| Series/parallel system (B) | $O(N)$ | Structural systems | [1] |
| Series-parallel system (B/M) | Worst case: $O(NM)$ | Mechanical systems | [2] |
| $k$-out-of-$N$ sysem (B/M) | To be computed. | Oil distribution system | [2] |
| Coherent system (B/M)3 | $O(\mathcal{R})$ | Maximum flow, shortest path | [3] |
1. B and M denote binary- and multi-state respectively.
2. $N$ refers to the number of components, which is the primary bottleneck. $M$ is the number of states. $\mathcal{R}$ denotes the number of failure and survival mechanisms.
3. This definition is very broad, covering all systems above.
References:
[1] Byun, J. E., Zwirglmaier, K., Straub, D. & Song, J. (2019). Matrix-based Bayesian Network for efficient memory storage and flexible inference. Reliability Engineering & System Safety, 185, 533-545.
[2] Byun, J. E. & Song, J. (2021). Generalized matrix-based Bayesian network for multi-state systems. Reliability Engineering & System Safety, 211, 107468.
[3] Byun, J. E., Ryu, H. & Straub, D. (in preparation). Branch and bound algorithm for efficient reliability analysis of general coherent systems.