A realistic modeling of fault-tolerant systems requires to take into account phenomena such as the dependence of component failure rates and coverage parameters o n the operational configuration of the system, which cannot be properly captured using combinatoric techniques. Such dependencies can be modeled with detail using continuous-time Markov chains (CTMC’s). However, the use of C T M C mod...

This investigation deals with the transient analysis of the machine repair system consisting of M-operating units operating under the care of single repairman. To improve the system reliability/availability, Y warm standby and S cold standby units are provided to replace the failed units. In case when all spares are being used, the failure of units occurs in degraded fashion. In such situation ...

The quantitative analyses of Nuclear Power Plant (NPP)’s repairable systems are conventionally Markov-based methods. The thing is, systems’ state space grows exponentially with the increase of basic events, which makes the problem hard or even impossible to solve. In addition, the maintenance /test activities are frequently imposed on some safety-critical components, which make the Markov based...

Markov models are commonly used to asses the dependability/performability of fault-tolerant systems. Computation of many dependability/performability measures for repairable fault-tolerant systems requires the transient analysis of irreducible Markov models. Examples of such measures are the unavailability at time and the -expected interval unavailability at time . Randomization (also called un...

A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the resu...

Interval availability is a dependability measure defined by the fraction of time during which a system is in operation over a finite observation period. The system is assumed to be modeled by a finite Markov process. Because the computation of the distribution of this random variable is very expensive, it is common to compute only its expectation. In this paper, we propose a new algorithm to co...

Interval availability is a dependability measure defined by the fraction of time during which a system is operational over a finite observation period. The computation of its distribution allows the user to ensure that the probability that its system will achieve a given availability level is high enough. The system is assumed to be modeled as a Markov process with countable state space. We pro...

The fundamental mathematical definitions of the controlled feedback Markov dynamics of quantum-mechanical systems are introduced with regard to the dynamical reduction and filtering of quantum states in the course of quantum measurement in either discrete or continuous real time. The concept of sufficient coordinates for the description of a posteriori quantum states in a given class is introdu...

The multiple repairable systems may present system-to-system variability owing to the factors such as operation environments and working intensities of individual systems. It may be more reasonable to assume a heterogeneity among all the systems. In this paper, we propose a nonlinear mixed-effects model (NLMM), called power law process-nonlinear mixed-effects model (PLP-NLMM) and log linear pro...

We consider a single stock point for a repairable item. The repairable item is a critical component that is used in a fleet of technical systems such as trains, planes or manufacturing equipment. A number of spare repairables is purchased at the same time as the technical systems they support. Demand for those items is a Markov modulated Poisson process of which the underlying Markov process ca...