The model and algorithm for RUL estimation of the rotating machinery is constructed. RUL estimates are presented analytically. Random walk model of finite segments of the wavelet coefficients of observed signal is considered as the original model. We consider all possible cases in the problems of multi-dimensional random walk vectors free walk, walk with limitations of walk in a multiply connected space. In this case, the problem of RUL estimate is reduced to the assessment of the achievement by the wandering vector the preassigned critical values or areas of critical values. For this the probability of transition from the initial value to some preassigned values is determined using the representation of this probability by the Feynman path integral. During the monitoring of the operation of mechanical block is determined the type of random walk of observable process. After that there is an automatic choice of model for RUL estimates. In some cases it is possible to calculate the Feynman path integral and result analytical formula for RUL estimates. In other cases, after select the type random walk for RUL estimates the solutions of evolution equations for the transition probabilities are studied numerically. It is shown that for the RUL estimates is needed mode of continuous or periodic monitoring, because the state of the mechanical system can change and therefore the conditions of applicability of the random walk model are changed. In this case, the correction of the calculated estimates is needed. Therefore, the paper discusses the issue about prognosis of changing the conditions of applicability of random walk models. The described algorithm is implemented in PHM computing cluster. For full analysis of life time estimates the cloud computing service is used. The experimental data are shown.
