Reliability%20Analysis%20of%20Multi-state%20Systems%20with%20Heterogeneous%20Multi-state%20Elements

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Reliability Analysis of Multi-state Systems with
Heterogeneous Multi-state Elements

• Dmitrij Birjukov
• National Taras Shevchenko University of Kyiv
• Faculty of Cybernetics
• birjukov_at_unicyb.kiev.ua

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Multi-state system example and definition

• Example. Lets consider communication network
  that provide message passing. The information
  security achieved via information encoding.
• In the case of encoding unit(subsystem) failure,
  the network will still perform message passing,
  but with the lower level of security. So this
  system has at least 3 states.
• Definition. Systems that characterized by
  different levels of performance are known as
  multi-state systems (MSS).
• Another examples of MSS are power systems and
  computer systems, where the elements performance
  is characterized by generating capacity and data
  processing speed respectively.
• Most of reliability analysis and optimization
  models assume that system consists of
  binary-state components, where the states are
  functioning and failure. Binary-state reliability
  models don't allow to describe adequately MSS
  operation processes, remaining resources, system
  state evolution, reasons of system failures and
  mechanisms of their prevention.

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Report overview

• The aim of this work is to provide decision
  making framework for reliable MSS design.
• This report represents the following results
• reliability model of multi-state system with
  heterogeneous multi-state elements
• redundancy optimization problem for multi-state
  elements (where redundant elements are identical
  or non-identical).

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Multi-state systems reliability models overview

• MSS reliability assessment based on (1) extension
  of the Boolean models to the multi-valued case,
  (2) stochastic processes (mainly Markov and
  semi-Markov) approach, (3) universal generating
  function approach.
• The main difficulty in the MSS reliability
  analysis is the dimension damnation since each
  system element can have many different states
  (not only two states as the binary-state system).
  
• This makes the known approaches overworked and
  time consuming, because the number of system
  states increases dramatically with the increase
  in the number of system elements.
• However, mentioned method were applied to simple
  models, such as the series, parallel systems (so
  called simple-structured systems models). In
  practice, technical systems are more complex,
  they include huge number of elements, that
  perform different tasks.

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Multi-state systems reliability models overview

• Main restrictions of known multi-state
  reliability models are the following
• state sets of elements consist states with same
  meaning (therefore each element have same number
  of identical states)
• state sets of elements are ordered
  (partially-ordered)
• system consists of elements with same
  functionality.
• The reliability evaluation is strongly required
  on the stage of system engineering design. To
  evaluate MSS reliability in the case of complex
  technical systems special mathematical approach
  and software are needed.

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Multi-state system with heterogeneous elements (1)
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Multi-state system with heterogeneous elements (2)
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Multi-state system with heterogeneous elements (3)
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Multi-state system with heterogeneous elements (4)
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Multi-state system with heterogeneous elements (5)
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Multi-state system with heterogeneous elements (6)
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Multi-state system reliability and efficiency
indexes (1)
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Multi-state system reliability and efficiency
indexes (2)
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Multi-state System reliability and efficiency
indexes (3)
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Redundancy allocation of multi-state elements
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Redundancy allocation of multi-state elements
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Redundancy allocation of multi-state elements
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MSSHE redundancy optimization problem
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Conclusions
When considering the system composed from
heterogeneous elements (of different intending)
known multi-state system reliability models can't
be implemented. This paper presents a novel
approach to multi-state complex-structured system
reliability analysis. It provides decision
making framework for reliable MSS design.