Li-Chao Wang

Discretization model of instantaneous availability for continuous-time systems

In this paper, the instantaneous availability models in continuous and discrete time are proposed for the one-unit repairable systems with delay under exponential distributions. Prior to this, error analyses of sampling discrete distributions are given. Then, the numerical solutions for the continuous- time model and the discrete-time model are presented. The comparison of the solutions reveals that with the step length and sampling interval decreasing, the accuracy of the numerical model is much better. Also, in the same accuracy level, less computation time is needed to solve the discrete-time model. Hence, the discrete-time model is more feasible to analyze instantaneous availability. Finally an example is given to describe the application of the results.

Construction and Simulation Analysis for Stability Speed Parameter of Instantaneous Availability for One-Unit Repairable Systems

According to the stability theory, the mathematical model of the stability parameter of linear systems is established for analysis of instantaneous availability of one-unit repairable systems, and the concept of stability parameter is presented. The conditions of determining the parameter stability are derived, and the measure of parameter stability speed is put forward. On the above basis, the stability speed parameter K is given for one-unit repairable systems in instantaneous availability fluctuation, and the typical fluctuation problems are analyzed by use of simulations. The obtained results confirm the rationality and applicability of the stability speed parameter K.

Approximate instantaneous availability and its error analysis

The one-unit repairable system is studied in this paper, whose lifetime, repair time and repair-delayed time are all supposed to be random variables with general distributions. The instantaneous availability satisfying a second type Volterra integral equation which is solved by a successive approximation approach in this paper, and then the approximate instantaneous availability is obtained. Furthermore, the physical meaning of the approximate instantaneous availability and its error function are both analyzed. Then we get the conclusion that the approximate instantaneous availability can be used to substitute the real one to some extent, whose validity is verified by some numerical examples finally.