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Method for solving steady-state probabilities of polymorphic systems with general distribution

A system state equation and steady state probability technology, applied in complex mathematical operations and other directions, to achieve broad application prospects, improve solution efficiency and accuracy, and strong universality.

Active Publication Date: 2018-12-21
BEIHANG UNIV
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Problems solved by technology

[0005] A new steady-state availability solution method is given for multi-state systems under general distribution, which provides solutions for practical problems such as multi-state system analysis and maintenance strategy optimization

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  • Method for solving steady-state probabilities of polymorphic systems with general distribution
  • Method for solving steady-state probabilities of polymorphic systems with general distribution
  • Method for solving steady-state probabilities of polymorphic systems with general distribution

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Embodiment

[0055] The invention provides a method for solving the steady-state probability of a multi-state system under general distribution, which can be applied to the problem of solving the steady-state availability of a repairable system subject to general time distribution in reliability engineering. Taking the repairable electromechanical system with five degraded states as an example, the state transition diagram of the system is shown in the attached figure 2 , when the failure rate, maintenance turnover rate, and repair rate all obey the general time distribution, the traditional steady-state availability calculation method cannot be applied, and the calculation method proposed by the present invention can complete the calculation of the steady-state availability.

[0056] In this embodiment, each rate function of the system obeys the Weibull distribution, λ i (0≤i≤4), μ i (1≤i≤5), w i (1≤i≤5) respectively correspond to the scaling parameters of failure rate function, mainte...

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Abstract

The invention provides a method for solving the steady state probability of a polymorphic system under a general distribution, which can establish a system state equation for a system of arbitrary distribution and give a method for obtaining the steady state probability of the system. The transition of system state is described as a generalized Markov process by using the supplementary variable method, and the state equation of the system is transformed into an ordinary differential equation according to the characteristic that the system state does not change according to the absolute time inthe steady state. Combined with the boundary conditions and initial conditions of the system, the equations are solved preliminarily, the important parameters of the system state equation are extracted by using the generalized integral mean value theorem, and the system state equation is transformed by means of the equivalence relations among the parameters. The generalized probability equation is obtained by using the total probability formula and solved by using the least square method. This method can significantly reduce the difficulty of obtaining the steady-state solutions of state probabilities of multi-state systems and has certain universality. It is suitable for solving the problems of system state analysis and maintenance strategy optimization in the fields of reliability engineering and mechanical engineering.

Description

technical field [0001] The invention provides a method for solving the steady-state probability of a multi-state system under general distribution. The method can establish a system state equation for a system with any distribution, and provides a method for obtaining the system steady-state probability. This method is suitable for solving problems such as system state analysis, system steady-state availability solution, and maintenance strategy optimization in fields such as reliability engineering and mechanical engineering. Background technique [0002] For the system state transition process described by the Markov process, the state equation of the system can be transformed by using the Laplace transform method, and then the steady-state probability of the system state can be obtained by calculating the limit of the transformed equation. The Markov process requires that the state time of the system such as work, failure and maintenance all obey the exponential distribut...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/18
CPCG06F17/18
Inventor 王乃超李明远马麟
Owner BEIHANG UNIV
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