Reliability evaluation of consecutive k-out-of-m: F balanced systems with a symmetry line

Based on some real backgrounds, a new balanced system structure, a consecutive k-out-of- m: F system with a symmetry line, is proposed in this paper. Considering different state numbers of a subsector, the new balanced system is analyzed under two situations respectively: the subsector with binary-state and the subsector with multi-state, while the multi-state balanced systems have not been studied in the previous research. Besides, two models are developed in terms of assumptions for the two situations, respectively. For this system, several methods, such as the finite Markov chain imbedding approach, the order statistics technique and the phase-type distributions, are used on the models. In addition to system reliability formulas, the means and variances of the system lifetimes under two models for different situations are given. Finally, numerical examples are presented to illustrate the results obtained in this paper.

Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism

Failures of safety-critical systems may result in irretrievable economic losses and significant safety hazards, thus enhancing the reliability of safety-critical system is crucial. As applied widely in engineering fields, protective devices are commonly equipped for the systems operating in shock environment to reduce external damage, which has not been taken into consideration in existing literatures. This paper investigates the reliability of multi-state systems with competing failure patterns supported by a protective device. According to the system failure modes, state-based and shock number-based triggering mechanism of the protective device are developed. That is, the protective device is triggered once the system state or cumulative number of shocks exceeds corresponding critical thresholds respectively. After being triggered, the protective device can reduce the probability of damaging shocks for the system. The protective device fails when the number of consecutive valid shocks reaches a threshold. Based on the constructed model, a finite Markov chain imbedding approach is employed to derive reliability indices including distribution functions of system lifetime and residual lifetime, together with expected operating time of the protective device. Moreover, two age-based replacement policies together with a condition-based replacement policy are developed to accommodate different maintenance scenarios and corresponding optimal solutions are acquired. Numerical illustrations based on the application of cooling systems in engines are presented to validate the results.

An approximation method for evaluating the reliability of a dynamic k-out-of-n:F system subjected to cyclic alternating operation conditions

This article extends the finite Markov chain imbedding approach to evaluate the system reliability of a dynamic k-out-of- n:F system operating under two cyclic alternating conditions, and this article presents a method to obtain the optimal replacement interval of the system according to age-based replacement policy. In terms of the “dynamic k-out-of- n:F” model, we regard the system as two distinct k-out-of- n:F systems with different values of k while the system is operating under each condition. We apply the proposed model to analyze the reliability of a wireless sensor network, whose sensors switching into sleep state to save energy and shifting into listen state to detect the information alternatively. We also obtain the optimal replacement interval to redeploy the wireless sensor networks.

Boundary crossing probabilities for high-dimensional Brownian motion

The two-sided nonlinear boundary crossing probabilities for one-dimensional Brownian motion and related processes have been studied in Fu and Wu (2010) based on the finite Markov chain imbedding technique. It provides an efficient numerical method to computing the boundary crossing probabilities. In this paper we extend the above results for high-dimensional Brownian motion. In particular, we obtain the rate of convergence for high-dimensional boundary crossing probabilities. Numerical results are also provided to illustrate our results.

Discrete, Continuous and Conditional Multiple Window Scan Statistics

The distributions of discrete, continuous and conditional multiple window scan statistics are studied. The finite Markov chain imbedding technique has been applied to obtain the distributions of fixed window scan statistics defined from a sequence of Bernoulli trials. In this manuscript the technique is extended to compute the distributions of multiple window scan statistics and the exact powers for multiple pulse and Markov dependent alternatives. An application in blood component quality monitoring is provided. Numerical results are also given to illustrate our theoretical results.

Discrete, Continuous and Conditional Multiple Window Scan Statistics

The distributions of discrete, continuous and conditional multiple window scan statistics are studied. The finite Markov chain imbedding technique has been applied to obtain the distributions of fixed window scan statistics defined from a sequence of Bernoulli trials. In this manuscript the technique is extended to compute the distributions of multiple window scan statistics and the exact powers for multiple pulse and Markov dependent alternatives. An application in blood component quality monitoring is provided. Numerical results are also given to illustrate our theoretical results.