Mathematical Models and Applicable Technologies to ... Development for Information&Communication...
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Mathematical Models and Applicable Technologies to Forecast, Analyze and Optimize Quality and Risks for Complex Systems
Andrey KOSTOGRYZOV 1, Vladimir KRYLOV 2, Andrey NISTRATOV 3
George NISTRATOV ,
4, Vladimir POPOV 5, Pavel STEPANOV 6
1 Dr., Professor, General Director of the Center of Standardization, Design and Development for Information&Communication Technologies and Systems, 15-135 Vinnitskaja Str., Moscow, Russia, 119192, e-mail: firstname.lastname@example.org 2 Ph.D, General Designer of the Scientific&Technical Center “NAOPRO”, Moscow, Russia, e-mail: email@example.com 3 Candidate for researcher's career of the Russian Academy of Sciences, 44 – bld.2 Vavilova Str., Moscow, Russia, 119333, e-mail: firstname.lastname@example.org 4 Ph.D, Chief of the Software Department of the Research Institute of Applied Mathematics and Certification, 2-bld.2, Krasnobogatyrskaja Str., Moscow, Russia, 107564, E-mail: email@example.com 5 Deputy of the General Director of the Center of Standardization, Design and Development for Information&Communication Technologies and Systems, Moscow, Russia, E-mail: firstname.lastname@example.org 6
Deputy Director of the Institute of Informatics Problems of the Russian Academy of Sciences, 44 – bld.2 Vavilova Str., Moscow, Russia, 119333, e-mail: email@example.com
Mathematical models, supporting software tools and applicable technologies that are accessible to wide use, are offered. The criteria and mathematical statements of problems to forecast analyze and optimize quality and risks are formulated. It can be used in system life cycle to form system requirements, compare different processes, substantiate technical decisions, adjust technological parameters, and improve system operation, increase efficiency. The users can prove answers on system engineering questions: «Is expected quality achievable? », «How much safe are these or others scenarios? », «What about the real risks, profits and possible damages? », «What choice is rational? », «What measures are more effective? » etc. On the base of the offered models and technologies the best decisions may be found before critical events. Preventive effective measures may be used in time. Some examples demonstrate practical possibilities.
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Today processes of systems design, development and operation (including transportation systems) in different conditions of threats are the main objects for forecasting, analysis and optimization. As a result of analyzing practices approaches to safety (to industrial, fire, radiating, nuclear, chemical, biological, transport, ecological systems, safety of buildings and constructions, information security) were made in the next conclusion - see Figure 1. (Kostogryzov and Stepanov, 2008; Kostogryzov and Nistratov, 2005).
For the spheres of industrial, fire, radiating, nuclear, aviation safety in which already there were numerous facts of tragedies - requirements to admissible risks are expressed quantitatively at probability level and qualitatively at level of necessary requirements to the initial materials, used resources, protective technologies and operation conditions. Usually risk estimations from one sphere are not used in others spheres because of methods and metrics for risk analysis are different, interpretations are not identical in spite of processes are logically similar ;for the spheres of chemical, biological, transport, ecological safety, safety of buildings and constructions, information security, including the conditions of terrorist threats – requirements to admissible risks are set mainly at qualitative level in the form of requirements to performance. The methods for quantitatively risk analysis are not created. The term “Admissible risk” can not be defined because of one depend on methods. Experience from other spheres is missing.
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. Figure 1 Comparison results to risk estimations
To improve essentially this situation the offered way includes mathematical
models and applicable technologies to forecast, analyze and optimize quality and risks for complex systems.
2. THE OFFERED MATHEMATICAL MODELS
Mathematical modeling – the high technology process accompanied by creation and operation of the complex systems, allows estimating probabilities of success, risks, profits and damages. The offered mathematical models should be used actively for rational management.
Rational management means wide use of existing models and software tools for decision-making in life cycle of systems. The criteria used for rational management are maximization of a prize (profit, a degree of quality or safety, etc.) at limits on expenses or minimization of expenses at limits on a comprehensible degree of quality and-or safety or their combination. The offered models support an analysis and substantiation of requirements according to system engineering standards. As a result of adequate modeling more deep and extend knowledge of system allows the customer to formulate well-reasoned system requirements. And it is rational to developer to execute them without excessive expenses of resources, and to the user – as much as possible effectively to implement in practice the incorporated potential of system (see Figure 2).
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Figure 2 the offered way is the use of created mathematical models according to
standard system processes
The offered models are founded on use of theory for random processes. The main models are: “The model of functions performance by a system in conditions of unreliability of its components”, “The models complex of calls processing”, “The model of items gathering (information, elements etc.)”, “The model of items analysis (information, patterns, events etc.)”, “The models complex of dangerous influences on a protected system”, “The models complex of an authorized access to system resources” and their combination and development (total more than 100 models) (Kostogryzov and Stepanov, 2008; Kostogryzov and Nistratov, 2005) Universality of the models is caused by focusing to meet system standards requirements and use of models of random processes physically peculiar to various systems irrespective of their functional applications.
3. THE OFFERED TECHNOLOGIES
The offered applicable technology includes technology off-line and on-line to forecast, analyze and optimize quality and risks. Modeling shouldn’t be carried out only for modeling itself. If as a result of modeling we get only one value it is not quite clear
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how we should appreciate it. That is why the offered technologies uses only analytical models (Kostogryzov and Stepanov, 2008; Kostogryzov et al., 2003) is developed in such a way to carry out computations fast, catch tendencies, reveal stability of processes in case of input data changes in the range –50% +200% and in a few minutes (!) to find admissible solutions of complex inverse synthesis problems. As a result of the offered models use a system analyst gets an ability to sense the whole quality field, which may be appropriate at different scenarios of system operation.
By using technology on-line an analyst should perform modeling by the Internet versions of the some offered models (see Figure 3). He prepares input and receives analytical report in Word or pdf-file about 50-100 sheets as a result of on-line interaction. This report will be formed automatically and include a formalization of analyst’s problem, input, results of mathematical modeling in pictures, analysis of system processes for different conditions, choice of the most rational variant and recommendations. The offered models and technologies have been presented at conferences and other forums since 1981 in Russia, Australia, the USA, Canada, Finland, France, Germany, Kuwait, and Serbia etc. Complexes were awarded by the Golden Medal of the International Innovation and Investment Salon, the International Exhibition “Intellectual Robots”, the on-line technology awarded in Russia as the best innovative project of 2007.
Figure 3. The essence of the offered on-line Internet technology
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4. EXAMPLES 4.1. Estimation of data gathering and processing in control station.
The control station use SCADA information for decision making. Wrong interpretation may be caused by errors of dispatcher personnel, which can miss important information or turn harmless information into dangerous one, fails of SCADA system. The information flow is measured in some conventional units and the information flow is of 100 units per hour. The total information contains not more then 1% of data related to potentially dangerous events. Taking into account automatic data analysis system we suppose the speed of event interpretation to be near 30 sec per information unit. In this case 100 information units will be processed during 50 min. At that the frequency of errors for the whole dispatcher shift on duty, including fails of the SCADA system itself is about 1 error per year according to statistical data. The task is to estimate the risk of inadequate interpretation of events by the dispatcher on the control station for a time period of 1 hour, during one dispatcher shift turn of 8 hours, 1 month, 1 year, and 10 years. Results of modeling characterize an acceptable risk rate for control stations.
This means that th