Mathematics Idea of Sustainable Safety System Development-Approach by Survival Theory

Safety is one of important feature each real system. Safety of system can be quantitatively described by "resource of system safety", in other words "safety potential" P. = (P+, P-), which at any time system has to purpose realization, here: potential of system safety is determined by two-dimensional vector positive potential P+ and negative potential P- analyzed real system. Known in literature analogue of safety potential is resource (exploitation potential), that is experimentally and theoretically fixed measure of useful ability of machine, which is expressed in proper units. It is presupposed that in that time safety and exploitation ability is warranted. We are interested in safety system changes in time. There are many possible variants of such changes, but the most often is that, when safety potential getting down, what makes increase system destruction or cooperated systems or surroundings. Very interesting variant is when safety system potential is consumed but at the same time is recreating totally or partly. This variant of safety system potential change can be described as rule of sustainable safety development: sustainable development is such process which realizes presupposed purposes, using resources to leave them in sufficient amount to realize the same aim for next generations. Rule of sustainable safety development (sustainable safety principle) implies many research problems. One of the most important is "mathematics model of decreasing safety system potential". The basic thesis of research conception presented in this lecture is that to model the process of decreasing safety system potential can be used, known in many related theories (survival analysis; event history analysis; duration analysis; transition analysis; reliability analysis) so called cumulated risk function Lambda(t) which is interpreter as a measure of using the possibility of making by object the task in time interval [0, t]. In the paper are presented theories abort mathematics conception of recording rule of sustainable safety development. There are also possible use, i.e. mathematics modeling the process of sustainable traffic road safety (sustainable road safety).