5.3. About some effects from adequate probabilistic methods and technology applications

Some effects from the proposed adequate probabilistic methods and technologies of RMS are estimated on the level of predicting risks to lose object safety (integrity) by PDF [16].

Example 5.3.1. According to statistics from multifunctional safety system (MFSS), a frequency of occurrence of the latent or obvious threats is equal to once a month, and an average time of development of threats (from occurrence of the first signs of a critical situation up to failure) is about 1 day. A work shift is equal to 8 hours. The system control is used once for work shift, and a mean duration of the system control is about 10 minutes (it is supposed that recovery of object integrity is expected also for 10 minutes). The workers (they may be mechanics, technologists, engineers, etc.) of medium-level and skilled workers are capable to revealing signs of a critical situation after their occurrence, and workers of the initial level of proficiency are incapable. Medium-level workers can commit errors on the average not more often once a month, and skilled workers are not more often once a year. How consideration of the qualification level influences on predicted risks to lose object safety for a year and for 10 years?

The results of modeling. For workers of the initial level of proficiency, risks to lose object safety are near 1 (losses of integrity are inevitable). For workers of medium-level of proficiency, risk to lose object safety for a year is about 0.007 and for 10 years is about 0.067, and for skilled workers, risk equals to 0.0006 for a year and 0.0058 for 10 years because of effective monitoring using RMS possibilities.

Example 5.3.3. This allowed to estimate operation of object as "black box," described by characteristics of skilled workers. On dangerous manufacture critical operations are carried out by skilled workers in interaction with RMS (including reservation and supports of another). Formally, they operate as parallel elements with hot reservation. Thereby, the consideration of such interaction allows to increase adequacy of modeling. Let's estimate risk to lose object safety for this variant (all input data for each from two parallel elements are the same

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Calculated PDF fragment shows (see Figure 17) that risk to lose object safety increases from 0.0000003 (for a year) to 0.00014 (for 20 years). Thus, the mean time between neighboring losses of object safety Tmean, calculated from known PDF, equals to 663 years. That is, the frequency λ of system safety losses is about 0.0015 times a year. It is 8000 times less (!) in comparison with a primary frequency of occurrence of the latent or obvious threats (once a month). And, at the expense of reservation estimated, Tmean is 34.5% longer in comparison

If to compare with exponential approximation of PDF with the same frequency λ, the risk to lose object safety will grow from level 0.0015 (for a year) to 0.03 (for 20 years). Difference is in 200–5000 times more against adequate PDF. The border of admissible risk 0.0015 will be reached for 195 years, not for 1.3 year as for exponential PDF. That is, the real duration of effective object operation (i.e., without losses of safety) is 150 times more! Such effect can be reached at the expense of mutual aid (reservation and supports) of skilled workers using RMS.

Example 5.3.4. Come back to the SUEK value chain (see Figure 10). According to system engineering principles (see ISO/IEC/IEEE 15288 and Figure 1), we decompose logically this chain into nine serial components. Components from 1 to 6 are united by MFSS of mine, component 7 is associated with washing factory, component 8 is associated with transport, component 9 is associated with port (see Figure 18). For every element of this chain, a specific

that in Example 5.3.2).

with Tmean from Example 5.3.2.

Figure 17. Calculated PDF fragment for Example 5.3.3.

Example 5.3.2. We will concentrate on the analysis of errors of skilled workers from the point of object safety. Raising adequacy of modeling, in addition to initial data of Example 5.3.1, we will consider that mean recovery time of the lost integrity of object equals to 1 day instead of 10 minutes [10]. What effect may be from risk prediction?

Calculated PDF fragment shows (see Figure 16) that risk to lose object safety increases from 0.0006 (for a year) to 0.0119 (for 20 years). Thus, the calculation from PDF mean time between neighboring losses of object safety Tmean equals to 493 years. That is, the frequency λ = 1/ Tmean of system safety losses is about 0.002 times a year. It is 6000 times less (!) in comparison with a primary frequency of occurrence of the latent or obvious threats (once a month). And, estimated Tmean is almost 500 times more in comparison with a primary mean time between errors of skilled workers (once a year). And, such effect can be reached at the expense of undertaken control measures, monitoring, and system recovering in case of revealing in time the signs of threat development. To the point, the frequency λ of system safety losses is extracted latent knowledge from PDF, built in a calculated form.

If to compare with exponential approximation of PDF with the same frequency λ, the risk to lose object safety will grow from level 0.002 (for a year) to 0.04 (for 20 years). These are also extracted latent knowledge considering Taylor's expansion R(t, λ) ≈ λ∙t (see Section 2). Difference is in 3.3–3.4 times more against adequate PDF. To feel, it is enough to ascertain that for created PDF the border of admissible risk 0.002 will be reached for 3 years, not for 1 year as for exponential PDF. That is, the real duration of effective object operation (i.e., without losses of safety) is three times more!

Figure 16. Calculated PDF fragment for Example 5.3.2.

Example 5.3.3. This allowed to estimate operation of object as "black box," described by characteristics of skilled workers. On dangerous manufacture critical operations are carried out by skilled workers in interaction with RMS (including reservation and supports of another). Formally, they operate as parallel elements with hot reservation. Thereby, the consideration of such interaction allows to increase adequacy of modeling. Let's estimate risk to lose object safety for this variant (all input data for each from two parallel elements are the same that in Example 5.3.2).

Calculated PDF fragment shows (see Figure 17) that risk to lose object safety increases from 0.0000003 (for a year) to 0.00014 (for 20 years). Thus, the mean time between neighboring losses of object safety Tmean, calculated from known PDF, equals to 663 years. That is, the frequency λ of system safety losses is about 0.0015 times a year. It is 8000 times less (!) in comparison with a primary frequency of occurrence of the latent or obvious threats (once a month). And, at the expense of reservation estimated, Tmean is 34.5% longer in comparison with Tmean from Example 5.3.2.

If to compare with exponential approximation of PDF with the same frequency λ, the risk to lose object safety will grow from level 0.0015 (for a year) to 0.03 (for 20 years). Difference is in 200–5000 times more against adequate PDF. The border of admissible risk 0.0015 will be reached for 195 years, not for 1.3 year as for exponential PDF. That is, the real duration of effective object operation (i.e., without losses of safety) is 150 times more! Such effect can be reached at the expense of mutual aid (reservation and supports) of skilled workers using RMS.

Example 5.3.4. Come back to the SUEK value chain (see Figure 10). According to system engineering principles (see ISO/IEC/IEEE 15288 and Figure 1), we decompose logically this chain into nine serial components. Components from 1 to 6 are united by MFSS of mine, component 7 is associated with washing factory, component 8 is associated with transport, component 9 is associated with port (see Figure 18). For every element of this chain, a specific

Figure 17. Calculated PDF fragment for Example 5.3.3.

workers, risk equals to 0.0006 for a year and 0.0058 for 10 years because of effective monitoring

Example 5.3.2. We will concentrate on the analysis of errors of skilled workers from the point of object safety. Raising adequacy of modeling, in addition to initial data of Example 5.3.1, we will consider that mean recovery time of the lost integrity of object equals to 1 day instead of

Calculated PDF fragment shows (see Figure 16) that risk to lose object safety increases from 0.0006 (for a year) to 0.0119 (for 20 years). Thus, the calculation from PDF mean time between neighboring losses of object safety Tmean equals to 493 years. That is, the frequency λ = 1/ Tmean of system safety losses is about 0.002 times a year. It is 6000 times less (!) in comparison with a primary frequency of occurrence of the latent or obvious threats (once a month). And, estimated Tmean is almost 500 times more in comparison with a primary mean time between errors of skilled workers (once a year). And, such effect can be reached at the expense of undertaken control measures, monitoring, and system recovering in case of revealing in time the signs of threat development. To the point, the frequency λ of system safety losses is extracted latent

If to compare with exponential approximation of PDF with the same frequency λ, the risk to lose object safety will grow from level 0.002 (for a year) to 0.04 (for 20 years). These are also extracted latent knowledge considering Taylor's expansion R(t, λ) ≈ λ∙t (see Section 2). Difference is in 3.3–3.4 times more against adequate PDF. To feel, it is enough to ascertain that for created PDF the border of admissible risk 0.002 will be reached for 3 years, not for 1 year as for exponential PDF. That is, the real duration of effective object operation (i.e., without losses of

using RMS possibilities.

44 Probabilistic Modeling in System Engineering

10 minutes [10]. What effect may be from risk prediction?

knowledge from PDF, built in a calculated form.

Figure 16. Calculated PDF fragment for Example 5.3.2.

safety) is three times more!

implements corresponding typical functions of Systems 1–9. Safety of whole value chain system is provided, if "AND" the first subsystem, "AND" the second, …, and "AND" the ninth subsystem safety are provided (see Figure 18). Reservation of elements for every subsystem is explained by RMS possibilities. Those input data for every element are the same as in Example

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Calculated PDF fragment shows (see Figure 19) that risk to lose safety increases from 0.000003 (for a year) to 0.0013 (for 20 years). Thus, the mean time between neighboring losses of safety Tmean equals to 283 years. That is, the frequency λ of system safety losses is about 0.0035 times a year. It is 2.3 times more often against the results of Example 5.3.3. In comparison with a primary frequency of occurrence of the latent or obvious threats (once a month), the frequency

For exponential approximation of PDF with the same frequency λ, the risk to lose safety will grow from level 0.0035 (for a year) to 0.07 (for 20 years). Difference is in 54–1167 times more

The border of admissible risk 0.002 will be reached for 24 years, not for 7 months as for exponential PDF (see Section 2). That is, the real duration of effective operation (i.e., without

Example 5.3.5. How much risks will increase, if in a system of value chain from Example 5.3.4

Calculated PDF fragment shows (see Figure 20) that risk to lose safety increases from 0.0009 (for a year) to 0.25 (for 20 years). Thus, the mean time between neighboring losses of safety Tmean equals to 24 years. That is, the frequency λ of system safety losses is about 0.04 times a year. It is 11.4 times less often against the results of Example 4 for skilled workers. In

5.3.3.

λ is 3430 times lower!

against adequate PDF.

losses of safety) is 41 times more!

only medium-level workers are used?

Figure 19. Calculated PDF fragment for Example 5.3.4.

Figure 18. Illustration of system, combined from parallel and series subsystems.

set of threats exists. Let us analyze a system of such value chain. The typical systems of this value chain, including MFSS, are:


What about the safety for analyzed value chain for existing threats considering possibilities of remote monitoring systems (RMS), covering all components of chain?

Let's put that the workers, interacted with RMS, participate in each chain process. Their activity is modeled by the models of Section 3, considering examples above. The high adequacy is reached by decomposition of chain system to nine logical subsystems, each of which implements corresponding typical functions of Systems 1–9. Safety of whole value chain system is provided, if "AND" the first subsystem, "AND" the second, …, and "AND" the ninth subsystem safety are provided (see Figure 18). Reservation of elements for every subsystem is explained by RMS possibilities. Those input data for every element are the same as in Example 5.3.3.

Calculated PDF fragment shows (see Figure 19) that risk to lose safety increases from 0.000003 (for a year) to 0.0013 (for 20 years). Thus, the mean time between neighboring losses of safety Tmean equals to 283 years. That is, the frequency λ of system safety losses is about 0.0035 times a year. It is 2.3 times more often against the results of Example 5.3.3. In comparison with a primary frequency of occurrence of the latent or obvious threats (once a month), the frequency λ is 3430 times lower!

For exponential approximation of PDF with the same frequency λ, the risk to lose safety will grow from level 0.0035 (for a year) to 0.07 (for 20 years). Difference is in 54–1167 times more against adequate PDF.

The border of admissible risk 0.002 will be reached for 24 years, not for 7 months as for exponential PDF (see Section 2). That is, the real duration of effective operation (i.e., without losses of safety) is 41 times more!

Example 5.3.5. How much risks will increase, if in a system of value chain from Example 5.3.4 only medium-level workers are used?

Calculated PDF fragment shows (see Figure 20) that risk to lose safety increases from 0.0009 (for a year) to 0.25 (for 20 years). Thus, the mean time between neighboring losses of safety Tmean equals to 24 years. That is, the frequency λ of system safety losses is about 0.04 times a year. It is 11.4 times less often against the results of Example 4 for skilled workers. In

Figure 19. Calculated PDF fragment for Example 5.3.4.

set of threats exists. Let us analyze a system of such value chain. The typical systems of this

What about the safety for analyzed value chain for existing threats considering possibilities of

Let's put that the workers, interacted with RMS, participate in each chain process. Their activity is modeled by the models of Section 3, considering examples above. The high adequacy is reached by decomposition of chain system to nine logical subsystems, each of which

2. The system of modular decontamination equipment and compressed air control.

1. The control system of ventilation and local airing equipment.

Figure 18. Illustration of system, combined from parallel and series subsystems.

5. The system of dynamic phenomena control and forecasting.

remote monitoring systems (RMS), covering all components of chain?

value chain, including MFSS, are:

46 Probabilistic Modeling in System Engineering

3. The system of air and gas control.

4. The system of air dust content control.

6. The system of fire prevention protection.

7. The safety system of washing factory.

8. The safety system for transport.

9. The safety system of port.

The application of the methods and technologies by the joint-stock company "Siberian Coal Energy Company," implemented on the level of the remote monitoring systems, allowed to rethink system possibilities for increasing reliability and industrial safety, improve multifunctional safety systems, decrease risks, and provide predictive maintenance and oper-

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

\*

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49

, Jury Rudenko<sup>1</sup> and George Nistratov<sup>2</sup>

2 Scientific Research Institute of Applied Mathematics and Certification, Moscow, Russia

[1] Feller W. An Introduction to Probability Theory and its Applications. Vol. II. Willy; 1971

[2] Kostogryzov A, Nistratov G. Standardization, mathematical modeling, rational management and certification in the field of system and software engineering, Moscow. Arma-

[3] Kostogryzov AI, Stepanov PV. Innovative management of quality and risks in systems life

[4] Zio E. An introduction to the basics of reliability and risk analysis. World Scientific. 2006.

[5] Kostogryzov A, Nistratov A, Nistratov G. Applicable technologies to forecast, analyze and optimize reliability and risks for complex systems. Proceedings of the 6st Interna-

[6] Kostogryzov A, Nistratov G, Nistratov A. Some Applicable Methods to Analyze and Optimize System Processes in Quality Management. Total Quality Management and Six Sigma: InTech. 2012. pp. 127-196. Available from: http://www.intechopen.com/books/total-quality- management-and-six-sigma/some-applicable-methods-to-analyze-and-optimize-system-pro-

[7] Kostogryzov A, Grigoriev L, Nistratov G, Nistratov A, Krylov V. Prediction and optimization of system quality and risks on the base of modeling processes. American Journal of

tional Summer Safety and Reliability Seminar, Poland. September 2012;3(1):1-14

cycle, Moscow. Armament Policy Conversion. 2008. 404p. (in Russian)

ation efficiency in company value chain.

\*Address all correspondence to: george.icie@gmail.com

ment Policy Conversion. 2004. 395 p

cesses-in-quality-management

Operations Research, Special Issue;3(1A):217-244

[8] January 2013, Available from: http://www.scirp.org/journal/ajor/

Author details

Vladimir Artemyev1

References

222 p

1 JSC "SUEK", Moscow, Russia

Figure 20. Calculated PDF fragment for Example 5.3.5.

comparison with a primary frequency of occurrence of the latent or obvious threats (once a month), the frequency λ is 21 times lower!

For exponential approximation of PDF with the same frequency λ, the risk to lose safety will grow from level 0.04 (for a year) to 0.55 (for 20 years). Difference is 2.2–44.4 times more against adequate PDF. The border of admissible risk 0.002 will be reached for 2 years, not for one month as for exponential PDF. That is, the real duration of effective operation (i.e., without losses of safety) is 24 times more!
