1. Introduction

All next years and decades form an epoch of using smart systems. What about the usefulness of smart systems for prediction and rationale of preventive measures against possible threats? To answer this question, we address to some definitions.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

According to ISO Guide 73, in general, case risk is defined as the effect of uncertainty on objectives. An effect is a deviation from the expected—positive and/or negative. Objectives can have different aspects (such as financial, health and safety, and environmental goals) and can be applied at different levels (such as strategic, organization-wide, project, product, and process). Risk is often characterized by reference to potential events and consequences or a combination of these. Risk may be estimated by a probability of potential events, leading to effects considering consequences. The chapter, including examples, is focused on events leading to losses of system integrity (often with negative consequences). But it does not limit a generality of proposed approaches.

general case, "smart" is a mnemonic acronym, giving criteria to guide in the setting of objectives, and "smart systems" are defined as miniaturized devices that incorporate functions of

Probabilistic Methods and Technologies of Risk Prediction and Rationale of Preventive Measures by Using…

http://dx.doi.org/10.5772/intechopen.75109

25

Developing existing researches [1–17], this manuscript includes correct probabilistic interpretation of risk prediction effectively using "smart" systems, some original basic probabilistic models for risk prediction, the improvement of existing risk control concept, and approaches

Because "smart" possibilities allow to forecast a future, we should view probabilistic vision of event prediction, its scientific interpretation, and, unfortunately, some existing illusory vision. Here, from the scientific point of view for anticipating dangerous development of events, it is difficult to construct an adequate probability distribution function (PDF) [1–4] of time between losses of system integrity. Damage may be to some extent estimated on practice (we will consider that the deviations in estimations can reach 100%). Therefore, leaving an estimation of a possible damage out of the work, we will stop on researches of a probabilistic component of risk. What deviations in risk predictions are possible here? To answer this question, it is necessary to understand typical metrics and engineering methods of risk predictions, in defi-

In practice probabilistic estimations of system integrity losses are quite often carried out by the frequency of emergencies or any adverse events. For example, with reference to safety, it can be frequencies of different danger threats influences, leading to a damage. That is, frequency replaces estimations of probability (risk to lose integrity of system during prognostic period). It is correct? From probability theory it is known that for defined PDF one of its characteristics is the mathematical expectation (Texp.). In turn, for PDF of time between losses of system integrity, the mathematical expectation is the mean time between neighboring losses of system integrity Texp., and moreover the frequency λ of system integrity losses is equal to 1/Texp. If to be guided only by frequency λ (with ignoring PDF) in practice, a large deviation may take place. Indeed, a probability that event has occurred till moment Texp. can be equal to 0.00 for approximation by deterministic (discrete) PDF and 0.36 for exponential approximation (see Figure 2). That is, as a result of erroneous choice of PDF, characterized by identical λ, the enormous difference may take place! On the one hand, it means ambiguity of a probabilistic estimation of events, being guided only on frequency λ, and on the other hand, a necessity of search (or creations) of more

Often today, engineers prefer exponential PDF: R(t, λ)=1 – exp. (λ∙t). If, for example, for 1 year of prognostic period to put λ about 10<sup>3</sup> times in a year or less, then under Taylor's

practically coincides with the value of probability. But if value λ∙t increases, it is capable to exceed 1 and by definition generally cannot be perceived as probability. Resume: focusing on

). And, if t = 1 year, the absolute value of frequency

∙t 2

sensing, actuation, and control (www.wikipedia.org, www.thefullwiki.org).

2. Probabilistic interpretation of risk prediction for effective using

nition and concept to use "admissible risk," and then to compare various variants.

adequate PDF of time between losses of system integrity is very high.

expansion R(t, λ) ≈ λ∙t with accuracy o(λ<sup>2</sup>

for solving some problems of industrial safety for coal branch.

"smart" systems

According to ISO/IEC/IEEE 15288 "Systems and software engineering—System life cycle processes," a system is a combination of interacting elements organized to achieve one or more stated purposes. An enabling system is a system that supports a system of interest during its life cycle stages but does not necessarily contribute directly to its function during operation. A system of systems (SoS) is a system of interest whose elements are themselves systems. A SoS brings together a set of systems for a task that none of the systems can accomplish on its own. Each constituent system keeps its own management, goals, and resources while coordinating within the SoS and adapting to meet SoS goals. The research covers systems defined in itself as "smart" system or using "smart" systems (see Figure 1).

For modern or perspective system or for a system of systems from the point of view of prediction and rationale of preventive measures against possible threats, the "smart" systems are and will be used as the systems in itself or as system elements or enabling systems. In a

Figure 1. To the definition of "smart system" in a system.

general case, "smart" is a mnemonic acronym, giving criteria to guide in the setting of objectives, and "smart systems" are defined as miniaturized devices that incorporate functions of sensing, actuation, and control (www.wikipedia.org, www.thefullwiki.org).

According to ISO Guide 73, in general, case risk is defined as the effect of uncertainty on objectives. An effect is a deviation from the expected—positive and/or negative. Objectives can have different aspects (such as financial, health and safety, and environmental goals) and can be applied at different levels (such as strategic, organization-wide, project, product, and process). Risk is often characterized by reference to potential events and consequences or a combination of these. Risk may be estimated by a probability of potential events, leading to effects considering consequences. The chapter, including examples, is focused on events leading to losses of system integrity (often with negative consequences). But it does not limit a

According to ISO/IEC/IEEE 15288 "Systems and software engineering—System life cycle processes," a system is a combination of interacting elements organized to achieve one or more stated purposes. An enabling system is a system that supports a system of interest during its life cycle stages but does not necessarily contribute directly to its function during operation. A system of systems (SoS) is a system of interest whose elements are themselves systems. A SoS brings together a set of systems for a task that none of the systems can accomplish on its own. Each constituent system keeps its own management, goals, and resources while coordinating within the SoS and adapting to meet SoS goals. The research covers systems defined in itself as

For modern or perspective system or for a system of systems from the point of view of prediction and rationale of preventive measures against possible threats, the "smart" systems are and will be used as the systems in itself or as system elements or enabling systems. In a

generality of proposed approaches.

24 Probabilistic Modeling in System Engineering

"smart" system or using "smart" systems (see Figure 1).

Figure 1. To the definition of "smart system" in a system.

Developing existing researches [1–17], this manuscript includes correct probabilistic interpretation of risk prediction effectively using "smart" systems, some original basic probabilistic models for risk prediction, the improvement of existing risk control concept, and approaches for solving some problems of industrial safety for coal branch.
