Open AccessDispersion of the number of failures in restoration processes
Author(s) -
В. И. Вайнштейн
Publication year - 2019
Publication title -
nadëžnostʹ
Language(s) - English
Resource type - Journals
eISSN - 2500-3909
pISSN - 1729-2646
DOI - 10.21683/1729-2646-2019-19-4-12-16
Subject(s) - dependability , variance (accounting) , process (computing) , exponential function , dispersion (optics) , simple (philosophy) , computer science , mathematical optimization , reliability engineering , mathematics , algorithm , engineering , mathematical analysis , philosophy , business , physics , accounting , optics , epistemology , operating system
Optimal organization of the restoration process is of significant importance in the operation of technical, information and computer systems, since failures occurring during their operation lead to substantial negative consequences. In this paper, a formula for the variance of the number of failures is obtained for the general restoration process, which depends on the restoration functions (average number of failures) of the simple and general restoration processes. Also obtained are the formulas for the variances of the number of failures and restorations during the alternating restoration process, when along with the element’s time to failure, for example, the restoration time is taken into account. For an exponential distribution with a simple and general restoration process, formulas are written for the variance of the number of failures, as well as the Chebyshev inequality and the formula for the coefficient of variation of the number of failures for a simple restoration process. The paper presents an algorithm for obtaining dispersion in the form of series for the operation time distribution laws common to the dependability theory. The developed mathematics are intended for the definition and solution of various optimization problems of information and computer security, as well as in the operation of technical and information systems, software and formware information protection facilities affected by random failures, threats of attacks and security threats.