SYSTEM AND METHOD FOR CALCULATING A PRODUCTIVITY OF AN INDUSTRIAL INSTALLATION
First Claim
1. A method for calculating a productivity of an industrial installation including installation modules:
- storing a Markov model for each installation module, said Markov model indicating, for operating states of the relevant installation module with a different productivity, probabilities of the relevant installation module being in the different operating states and transition rates of state changes between the operating states of the relevant installation module,calculating a Cartesian product from a first Markov model of a first installation module and from a second Markov model of a second installation module linked with the first installation module within the industrial installation or of a sub-installation linked with the first installation module within the industrial installation, said Cartesian product indicating, for operating states of a combined sub-installation including the two linked installation modules or of the sub-installation linked with the first installation module, probabilities of the combined sub-installation being in different operating states and transition rates of state changes between the operating states of the combined sub-installation, wherein the calculated Cartesian product is subsequently reduced to a Markov model of the combined sub-installation by those operating states of the calculated Cartesian product which have the same productivity being combined to form one operating state,carrying out progressively, the calculation of the Cartesian product and the subsequent reduction thereof, until the combined sub-installation forms the entire industrial installation.
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Abstract
A method and a system for calculating a productivity of an industrial system consisting of system modules is provided. A Markov model is stored for each system module, the Markov model indicating the probabilities that a system module is in different operating states and indicating transition rates of state changes between the operating states of the respective system module for each operating state of the respective system module with a different productivity. A Cartesian product is calculated from a first Markov model of a first system module and from a second Markov model of a second system module linked to the first system module. The calculated Cartesian product is then reduced to a Markov model of the combined sub-system. The calculation of the Cartesian product and the subsequent reduction are carried out successively until the combined sub-system forms the entire industrial system.
3 Citations
16 Claims
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1. A method for calculating a productivity of an industrial installation including installation modules:
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storing a Markov model for each installation module, said Markov model indicating, for operating states of the relevant installation module with a different productivity, probabilities of the relevant installation module being in the different operating states and transition rates of state changes between the operating states of the relevant installation module, calculating a Cartesian product from a first Markov model of a first installation module and from a second Markov model of a second installation module linked with the first installation module within the industrial installation or of a sub-installation linked with the first installation module within the industrial installation, said Cartesian product indicating, for operating states of a combined sub-installation including the two linked installation modules or of the sub-installation linked with the first installation module, probabilities of the combined sub-installation being in different operating states and transition rates of state changes between the operating states of the combined sub-installation, wherein the calculated Cartesian product is subsequently reduced to a Markov model of the combined sub-installation by those operating states of the calculated Cartesian product which have the same productivity being combined to form one operating state, carrying out progressively, the calculation of the Cartesian product and the subsequent reduction thereof, until the combined sub-installation forms the entire industrial installation. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
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15. A system for calculating a productivity of an industrial installation including installation modules, comprising
a database, in which a Markov model is stored for each installation module, said Markov model indicating, for operating states of the relevant installation module with a different productivity, probabilities of the relevant installation module being in the different operating states and transition rates of state changes between the operating states of the relevant installation module; - and comprising a calculation unit, which calculates a Cartesian product from a first Markov model of a first installation module and from a second Markov model of a second installation module linked with the first installation module within the industrial installation or of a sub-installation linked with the first installation module within the industrial installation, said Cartesian product indicating, for operating states of a combined sub-installation including the two linked installation modules or of the sub-installation linked with the first installation module, probabilities of the combined sub-installation being in different operating states and transition rates of state changes between the operating states of the combined sub-installation, wherein the calculated Cartesian product is subsequently reduced to a Markov model of the combined sub-installation by those operating states of the calculated Cartesian product which have the same productivity being combined to form one operating state, wherein the calculation of the Cartesian product and the subsequent reduction thereof are carried out progressively until the combined sub-installation forms the entire industrial installations.
- View Dependent Claims (16)
Specification