B.P. Harlamov - head of the laboratory

M.S. Ermakov - professor, Doctor of Sc (mathematics and physics) - probability theory and mathematical statistics

V.V. Koulaguin - Ph.D (mathematics and physics) - mathematical cybernetics

V.A. Proursin - Ph.D (mathematics and physics) - mathematical cybernetics

S.A. Baiguzina - mathematical reliability

N.V. Zaborova - mathematical cybernetics

199178, Saint Petersburg, V.O., Bolshoi ave. 61, aud. 44,

telephon : (812) 3214783

fax: (812) 3214771

The laboratory investigates mathematical models of operating processes for technical systems, machines, parts of machines and their materials in case of uncerteinty and irregularity. This main task of the laboratory subordinates two theoretical directions:

1 - development and investigation of probabilistic models of reliability of these processes attracting newest achievments of the theory of random processes and mathematical statistics (we call this direction reliability theory of systems with rare failures),

2 - development and investigation of deterministic models of these processes attracting newest achievments of the operation research and optimal control theory.

In frames of the first direction three work series are distinguished:

1a - work series on the classical mathematical reliability theory developing results of russian and foreign specialists (in spite of abundance of works on that there are lots of unsolved problems relating to the rare failure problem such as remainder resource, prophylaxis, and reserving in case of partial observation of the system state, etc.),

1b - work series on statistical problems in the reliability theory (rare failures are connected with well-known problems of the mathematical statistics relating to small samples, large deviations, nonparametric hypotheses, robust estimation, etc.),

1c - work series on development of the random processes theory relative to the reliability theory mainly such its divisions which are connected with the first exit times from prescribed regions; we deal with an actual problem to elaborate models of random processes reflecting specific character of the system quality evolution and at the same time being simple enough to be analitically treatable (in this respect the class of continuous semi-Markov processes, in particular monotone and diffusion type ones, seems to be perspective).

In frames of the second direction two work series are distinguished:

2a - work series on mathematical modelling of systems with a maximal generalized resource (i.e. the system which does not fail under maximal destroing actions on it),

2b - work series on optimal control for a demage accumulation process with minimax quality criterion.

## 5. Ready elaborations:

At the laboratory some works were elaborated on numerical and imitative modelling and also on specific engineering applications; we should note the following:

3a - works on dampering and demage diagnosis for constructions under vibrational and shock perturbation,

3b - works on approximation of multifactorial dependence.

3c - works on increasing reliability by analyzing trees of damages.

## 6. Proposals for cooperation:

The laboratory seeks for contacts with relative divisions of Russian and foreign scientific centers with a view to interchange with ordinary and electronic mail information and with personal visits.

The laboratory is ready to apply its theoretical elaborations for optimisation of enterprises of its potential clients with respect to reliability and safety under condition that all needed data base or possibility to form it will be submitted to us.

Publications and Conferences: Harlamov, Ermakov, Koulaguin, Proursin, Baiguzina, Zaborova