Many algorithms for computing the reliability of linear or circular consecutive-k-out-of-n:F systems appeared in this Transactions. The best complexity estimate obtained for solving this problem is O(k log(n/k)) operations in the case of i.i.d. components. Using fast algorithms for computing a selected term of a linear recurrence with constant coefficients, we provide an algorithm having arithm...

A k-out-of-n system configuration requires that, for the overall system to be functional, at least k out of the total of n components be working. We consider the problem of sequentially testing the components of a k-out-of-n system in order to learn the state of the system, when the tests are costly and when the individual component tests are imperfect, which means that a test can identify a co...

Availability/reliability is a main feature of design and operation of all engineering systems. Recently, availability evaluation of multi-state systems with different structures is at the center of attention due to the wide applications in engineering. In this paper, a dynamic model is developed for the availability assessment of multi-state weighted k-out-of-n systems. Then, in a design optimi...

Many fielded systems use cold standby redundancy as an effective system design strategy. However, methods for analyzing the reliability of k-out-of-n cold standby systems, particularly with components having age-dependent hazard rates, are limited. In this paper, using the concepts of counting processes, we propose an efficient method to evaluate the reliability of k-out-of-n cold standby syste...

By considering k-out-of-n systems with independent and nonidentically distributed components, we discuss stochastic monotone properties of the residual life and the inactivity time. We then present some stochastic comparisons of two systems based on the residual life and inactivity time.

Many practical systems are phased-mission systems (PMS) where the mission consists of multiple, consecutive, and non-overlapping phases. An accurate reliability analysis of a PMS must consider the statistical dependencies of component states across phases as well as dynamics in system configuration, success criteria and component behavior. In this paper, we propose an efficient method for exact...

Multi-state weighted k-out-of-n systems are widely applied in various scenarios, such as multiple line (power/oil transmission line) transmission systems where the capability of fault tolerance is desirable. However, the complex operating environment and the dynamic features of load demands influence the evaluation of system reliability. In this paper, a stochastic multiple-valued (SMV) approac...

In this paper, a K-out-of-N:G system with N categories of components is studied. Each component category is characterized by its own failure and repair rates. There are R repair facilities, and repair priorities are specified between the N non-identical components. An algorithm for automatic construction of the system state transition diagram is presented. The stationary availability of each co...

A system with n independent components which has a k-out-of-n: G structure operates if at least k components operate. Parallel systems are 1-out-of-n: G systems, that is, the system goes out of service when all of its components fail. This paper investigates the mean residual life function of systems with independent and nonidentically distributed components. Some examples related to some lifet...