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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.