Kuznetsov . Analytical and statistical investigations of the reliability of complex systems

The thesis is devoted to the developing of new efficient asymptotic methods and fast simulation methods which contribute into systems probability analysis when the system structure is too complicated to use existing analytical methods and the use of direct simulation of rare events by Monte Carlo method leads to excessive time losses and doesn't permit to obtain estimates of required accuracy. An asymptotical analysis of two Markovian queueing systems was conducted. Necessary and sufficient conditions for the probability of failure during a busy period to be equivalent to the probability of monotone failure were obtained. A fast simulation method for the evaluation of the probability of nonmonotone failure in a busy period of the system is proposed. The unbiasedness of the estimate for the nonmonotone failure was proved. Conditions ensuring the boundedness of coefficient of variation were established. These conditions guarantee the stability of calculations when the rate of input flow is vanishing. An analytical-statistical method enabling to construct upper and lower estimates for the number of -measurable subspaces of the weight over a finite field is proposed. Conditions ensuring the boundedness of coefficient of variation of analytical-statistical estimates with the increasing of the number of components of a finite field are established. An analytical-statistical method making it possible to construct upper and lower estimates for the number of -measurable subspaces for arbitrary values of and was developed. Key words: queueing system, monotone failure, asymptotic method, analytical-statistical method, unbiased estimate, coefficient of variation, finite field, vector space, weight of subspace.