THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES
System reliability/availability is a complex concept that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures in reliability analysis. Some of the most used indices are important measures. These measures allow us to evalu...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
National Aerospace University «Kharkiv Aviation Institute»
2019-12-01
|
| Series: | Радіоелектронні і комп'ютерні системи |
| Subjects: | |
| Online Access: | http://nti.khai.edu/ojs/index.php/reks/article/view/1006 |
| _version_ | 1797714014953799680 |
|---|---|
| author | Elena Zaitseva Peter Sedlacek Andrej Forgac |
| author_facet | Elena Zaitseva Peter Sedlacek Andrej Forgac |
| author_sort | Elena Zaitseva |
| collection | DOAJ |
| description | System reliability/availability is a complex concept that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures in reliability analysis. Some of the most used indices are important measures. These measures allow us to evaluate the influence of fixed system components or set of components to the system reliability/availability. Importance measures are used today to allow for various aspects of the impact of system elements on its failure or operability. Analysis of element importance is used in the system design, diagnosis, and optimization. In this paper new algorithms for the calculation, some of the important measures are developed based on the matrix procedures. This paper's goal is the development of a new algorithm to calculate importance measures of the system based on the matrix procedures that can be transformed in the parallel procedures/algorithms. These algorithms are developed based on the application of Logical Differential Calculus of Boolean logic for the important analysis of the system. The application of parallel algorithms in importance analysis allows the evaluation of the system of large dimensions. Importance specific of the proposed matrix procedures for calculation of importance measures is the application of structure-function for the mathematical representation of the investigated system. This function defined the correlation of the system components states and system reliability/ availability. The structure-function, in this case, is defined as a truth vector to be used in the matrix transformation. The truth vector of a Boolean function is a column of the truth table of function if the values of the variables are lexicographically ordered. Therefore, the structure-function of any system can be represented by the truth vector of 2n elements un-ambiguously. |
| first_indexed | 2024-03-12T07:45:44Z |
| format | Article |
| id | doaj.art-5d692655e05c44869c91ae16aa592070 |
| institution | Directory Open Access Journal |
| issn | 1814-4225 2663-2012 |
| language | English |
| last_indexed | 2024-03-12T07:45:44Z |
| publishDate | 2019-12-01 |
| publisher | National Aerospace University «Kharkiv Aviation Institute» |
| record_format | Article |
| series | Радіоелектронні і комп'ютерні системи |
| spelling | doaj.art-5d692655e05c44869c91ae16aa5920702023-09-02T20:58:01ZengNational Aerospace University «Kharkiv Aviation Institute»Радіоелектронні і комп'ютерні системи1814-42252663-20122019-12-0104717810.32620/reks.2019.4.081047THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURESElena Zaitseva0Peter Sedlacek1Andrej Forgac2University of Zilina, ZilinaUniversity of Zilina, ZilinaUniversity of Zilina, ZilinaSystem reliability/availability is a complex concept that is evaluated based on numerous indices and measures. There are different methods for the calculation of these indices and measures in reliability analysis. Some of the most used indices are important measures. These measures allow us to evaluate the influence of fixed system components or set of components to the system reliability/availability. Importance measures are used today to allow for various aspects of the impact of system elements on its failure or operability. Analysis of element importance is used in the system design, diagnosis, and optimization. In this paper new algorithms for the calculation, some of the important measures are developed based on the matrix procedures. This paper's goal is the development of a new algorithm to calculate importance measures of the system based on the matrix procedures that can be transformed in the parallel procedures/algorithms. These algorithms are developed based on the application of Logical Differential Calculus of Boolean logic for the important analysis of the system. The application of parallel algorithms in importance analysis allows the evaluation of the system of large dimensions. Importance specific of the proposed matrix procedures for calculation of importance measures is the application of structure-function for the mathematical representation of the investigated system. This function defined the correlation of the system components states and system reliability/ availability. The structure-function, in this case, is defined as a truth vector to be used in the matrix transformation. The truth vector of a Boolean function is a column of the truth table of function if the values of the variables are lexicographically ordered. Therefore, the structure-function of any system can be represented by the truth vector of 2n elements un-ambiguously.http://nti.khai.edu/ojs/index.php/reks/article/view/1006importance measuresstructure-functionlogical differential calculusdirect partial boolean derivatives |
| spellingShingle | Elena Zaitseva Peter Sedlacek Andrej Forgac THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES Радіоелектронні і комп'ютерні системи importance measures structure-function logical differential calculus direct partial boolean derivatives |
| title | THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES |
| title_full | THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES |
| title_fullStr | THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES |
| title_full_unstemmed | THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES |
| title_short | THE MATRIX PROCEDURES FOR CALCULATION OF IMPORTANCE MEASURES |
| title_sort | matrix procedures for calculation of importance measures |
| topic | importance measures structure-function logical differential calculus direct partial boolean derivatives |
| url | http://nti.khai.edu/ojs/index.php/reks/article/view/1006 |
| work_keys_str_mv | AT elenazaitseva thematrixproceduresforcalculationofimportancemeasures AT petersedlacek thematrixproceduresforcalculationofimportancemeasures AT andrejforgac thematrixproceduresforcalculationofimportancemeasures AT elenazaitseva matrixproceduresforcalculationofimportancemeasures AT petersedlacek matrixproceduresforcalculationofimportancemeasures AT andrejforgac matrixproceduresforcalculationofimportancemeasures |