Optimal Stopping Rules for Preventing Overloading of Multicomponent Systems
Andrzej Z Grzybowski1, Zbigniew Domański1, Tomasz Derda1
1Department of Mathematics, Czestochowa University of Technology, PL-42201 Czestochowa, Poland.
Materials (Basel, Switzerland)
|April 13, 2023
Summary
This study models failure spreading in parallel systems under increasing loads. An optimal stopping rule is developed to maximize load capacity while minimizing failure probability, depending on load-step distribution.
Area of Science:
- Engineering
- Physics
- Applied Mathematics
Background:
- Multicomponent systems with random strengths face cascading failures under increasing workloads.
- Component failures redistribute loads, potentially triggering further failures and system degradation.
Purpose of the Study:
- To introduce and analyze a minimal model of failure spreading in progressively loaded parallel systems.
- To develop an optimal stopping rule for decision-makers managing system load.
Main Methods:
- Analysis of a minimal model simulating failure spreading in an array of progressively loaded pillars.
- Construction and evaluation of an optimal stopping rule for load management.
Main Results:
- The optimal stopping rule is shown to be of a threshold type.
- The rule's effectiveness significantly depends on the load-step probability distribution.
Conclusions:
- An optimal strategy exists for managing load in systems prone to cascading failures.
- The decision to stop loading should be based on a threshold determined by failure probability distributions.
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