There are so many existing methods to obtain system reliability like re-generating point function technique, supplementary variables technique etc., but all these techniques are full of complicated calculations. Keepi...There are so many existing methods to obtain system reliability like re-generating point function technique, supplementary variables technique etc., but all these techniques are full of complicated calculations. Keeping above these facts in mind, the authors in this paper have evaluated some reliability parameters for tele-communication system by using Boolean functions technique and algebraic method. Reliability of considered tele-communication system has been evaluated by considering the fact that failures follow arbitrary time distribution. In particular, the reliability expression has also been calculated for Exponential and Weibull distributions. Further, an important reliability parameter namely M.T.T.F. (mean time to failure) has also been calculated. A numerical example with graphical illustrations has been appended at the end to highlight the important results and practical utility of the model.展开更多
To simplify the process for identifying 12 types of symmetric variables in Boolean functions, we propose a new symmetry detection algorithm based on minterm expansion or the truth table. First, the order eigenvalue ma...To simplify the process for identifying 12 types of symmetric variables in Boolean functions, we propose a new symmetry detection algorithm based on minterm expansion or the truth table. First, the order eigenvalue matrix based on a truth table is defined according to the symmetry definition of a logic variable. By analyzing the constraint conditions of the order eigenvalue matrix for 12 types of symmetric variables, an algorithm is proposed for identifying symmetric variables of the Boolean function. This algorithm can be applied to identify the symmetric variables of Boolean functions with or without don't-care terms. The proposed method avoids the restriction by the number of logic variables of the graphical method, spectral coefficient methods, and AND-XOR expansion coefficient methods, and solves the problem of completeness in the fast computation method. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. The application results show that, compared with the traditional methods, the new algorithm is an optimal detection method in terms of the applicability of the number of logic variables, the Boolean function including don't-care terms, detection type, and complexity of the identification process.展开更多
文摘There are so many existing methods to obtain system reliability like re-generating point function technique, supplementary variables technique etc., but all these techniques are full of complicated calculations. Keeping above these facts in mind, the authors in this paper have evaluated some reliability parameters for tele-communication system by using Boolean functions technique and algebraic method. Reliability of considered tele-communication system has been evaluated by considering the fact that failures follow arbitrary time distribution. In particular, the reliability expression has also been calculated for Exponential and Weibull distributions. Further, an important reliability parameter namely M.T.T.F. (mean time to failure) has also been calculated. A numerical example with graphical illustrations has been appended at the end to highlight the important results and practical utility of the model.
基金supported by the National Natural Science Foundation of China(Nos.61471314 and 61271124)the Zhejiang Provincial Natural Science Foundation(No.LY13F010001)the National Key Technology R&D Program of China(Nos.2013BAH27F01,2013BAH27F02,and 2013BAH27F03)
文摘To simplify the process for identifying 12 types of symmetric variables in Boolean functions, we propose a new symmetry detection algorithm based on minterm expansion or the truth table. First, the order eigenvalue matrix based on a truth table is defined according to the symmetry definition of a logic variable. By analyzing the constraint conditions of the order eigenvalue matrix for 12 types of symmetric variables, an algorithm is proposed for identifying symmetric variables of the Boolean function. This algorithm can be applied to identify the symmetric variables of Boolean functions with or without don't-care terms. The proposed method avoids the restriction by the number of logic variables of the graphical method, spectral coefficient methods, and AND-XOR expansion coefficient methods, and solves the problem of completeness in the fast computation method. The algorithm has been implemented in C language and tested on MCNC91 benchmarks. The application results show that, compared with the traditional methods, the new algorithm is an optimal detection method in terms of the applicability of the number of logic variables, the Boolean function including don't-care terms, detection type, and complexity of the identification process.
