Prediction of Service Life for Machines and Structures

analogous analysis approximation assume characteristic coefficient coefficient of variation components compute consider coordinate correlation function corresponding crack growth crack tip curves damage accumulation damage measure delamination denote dependent distribution function earthquakes equation equilibrium estimate example expected value exponent failure failure-free operation fatigue crack formula fracture mechanics given ground motion indexes instant integral interval limit load level loading process machines and structures macroscopic crack material matrix method nominal stresses number of cycles object obtain parameters plastic posteriori probabilistic probability density probability of failure-free problem process q(t properties random process random variable region relation reliability theory residual service respect right-hand side risk risk function safety scatter seismic sensor specified specimen stability statistical stress intensity factor structural elements subequilibrium sufficiently t₁ taking into account tests tion total probability theorem variation vector process Weibull distribution