Consecutive k-out-of-n systems with maintenance

A consective k-out-of-n system consists of n linearly or cycliccally ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system's components we prove a limit theorem for the time to first failure of both linear and circular systems.     

Minimax design of two-state k-out-of-n systems

The optimal size of k is specified for two-state k-out-of-n systems that may be functioning or fail in either state. It is assumed that the steady-state, success and failure probabilities are not known exactly. The problem is reduced to finding the saddle-point solution to a minimax optimization problem. An example shows that the minimax design is robust with regard to uncertainty.     

Joint reliability importance of k-out-of-n systems

Joint Reliability Importance (JRI) is investigated to provide information on the type and the degree of interactions between two components by identifying the sign and the size of it. In specific, JRI is analyzed for k-out-of-n systems with (i) independently identically distributed (IID) components, (ii) non-identical and independent components and (iii) pair-wise dependent components. The closed form solution of JRI is derived for IID components. By using the solution, the variations of JRI are investigated with respect to the level of redundancy (n/k). In non-identical and independent case, the point of sign change of JRI is obtained. It is also shown that the sign of JRI can be determined by the relationships between the Schur-convexity (concavity) and the JRI. For dependent case, only the pair-wise dependence is considered. As a result, the error caused by assuming statistical independence between pair-wise dependent components is shown to be measured by their covariance and JRI.     

On reliability analysis of consecutive k-out-of-n systems with arbitrarily dependent components

In this paper, we consider the linear and circular consecutive k-out-of-n systems consisting of arbitrarily dependent components. Under the condition that at least n?r+1 components (r ≤ n) of the system are working at time t, we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive k-out-of-n systems. In the following, we investigate the inactivity time of the component with lifetime T_r:n at the system level for the consecutive k-out-of-n systems under the condition that the system is not working at time t > 0, and obtain some stochastic properties of this conditional random variable.     

Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates

k-out-of-n systems frequently appear in applications. They consist of n components of the same kind with independent and identically distributed life-lengths. The life-length of such a system is described by the (n–k+1)-th order statistic in a sample of size n when assuming that remaining components are not affected by failures. Sequential order statistics are introduced as a more flexible model to describe sequential k-out-of-n systems in which the failure of any component possibly influences the other components such that their underlying failure rate is parametrically adjusted with respect to the number of preceding failures. Useful properties of the maximum likelihood estimators of the model parameters are shown, and several tests are proposed to decide whether the new model is the more appropriate one in a given situation. Moreover, for specific distributions, e.g. Weibull distributions, simultaneous maximum likelihood estimation of the model parameters and distribution parameters is considered.     

Reliability analysis of k-out-of-n: F balanced systems with multiple functional sectors

In this paper, new concepts of balanced systems are proposed based on real engineering problems. The system under study consists of l groups and each group has n functional sectors. The conception of balance difference is proposed for the first time. It is assumed that unbalanced systems are rebalanced by either forcing down some working units into standby or resuming some standby units into operation. In addition, a case that the forced-down units are subject to failure during standby is studied in this paper. Based on different balanced cases and system failure criteria, two reliability models for balanced systems are developed. The proposed systems have widespread applications in aerospace and military industries, such as wing systems of airplane and unmanned aerial vehicles with balanced engine systems. Markov process imbedding method is used to analyze the number of working units in each sector for each model. Finite Markov chain imbedding approach and universal generating function technique are used to obtain the system reliability for different models. Several case studies are finally presented to demonstrate the new models.     

考虑负载共享的线性连续k-out-of-n:F系统检测策略优化

针对线性连续k-out-of-n:F系统提出定期检测策略,每隔固定周期对系统中各部件状态进行检查并以新部件更换故障部件,若系统发生故障则立即停机并更换故障部件.由于受到负载共享的影响,各工作部件故障率不仅与系统中发生故障的部件数量相关,还与其相邻部件状态有关;为此,引入损伤故障率模型描述部件故障率.基于故障序列图和更新报酬理论建立定期检测策略优化模型以最小化单位时间内的期望成本,确定最优检测周期.最后,通过算例分析验证模型的有效性.     

Some issues of utilities in time-sharing systems

Translated from Issledovaniya po Prikladnoi Matematike, No. 3, pp. 9–13, 1975.     

Optimization of solutions in expert systems

The problem of construction of expert systems that are able to compute the optimal (with the greatest value) solution using the information accumulated in BK. The formalization of the problem is given and its mathematical model is constructed in the conditionally-extremal and game-theoretic form. The necessity of application of the methods of solution of partially defined problems of the Boolean programming and two-person zero-sum games with Boolean strategies is justified.Translated from Dinamicheskie Sistemy, No. 9, pp. 107–111, 1990.     

Optimization of periodic systems

The problem of designing a regulator, optimal by a quadratic performance criterion, on an infinite time interval is examined for a linear periodic system. It is assumed that the control plant's motion is described by a system of linear periodic finite-difference equations. Controllable plants whose motion is described by differential and by finite-difference equations on different parts of the period are analyzed as well. The optimal regulator design problem is reduced to the determination of a periodic solution of an appropriate Riccati equation. An algorithm for constructing such a solution is derived. It is noted that this result can be used in periodic optimization problems /1/ and in the design of a stabilization system for a pacing apparatus.     

Optimization of functional differential systems

A method of determining optimal control for functional differential systems is presented. This is a generalization of Krasovskii's results on the optimal control of time delay systems, which include several of the results published recently. A technique for the numerical solution of the resulting Riccati equations is developed, and an example is worked to illustrate the presented results.The research reported herein was partly supported by JSEP Contract No. F44620-71-C-0091 and AF Grant No. AFOSR-72-2371.     

Reliability-Based Optimization of structural systems

A method to carry out a Reliability-Based Optimization (RBO) of especially nonlinear structural systems is introduced. Statistical uncertainties involving both structural and loading properties are considered. The concept is based on the separation of structural reliability analyses and the optimization procedures. Two approaches are discussed, depending on the interaction of reliability analysis and mathematical programming and the way of representation of the limit state functions (LSF) of the structure. As, for cases of practical significance, the LSF is known only pointwise it is approximated by Response Surfaces (RS). For the response calculations Finite Element (FE) procedures are utilized. Failure probabilities are determined by applying variance reducing Monte Carlo simulation (MCS) techniques such as Importance Sampling (IS). Following the reliability analysis, the optimization procedure is controlled by the NLPQL algorithm. A numerical example in terms of a template ocean platform exemplifies the procedures.Formerly Institute of Engineering Mechanics, Leopold-Franzens-University, Innsbruck, Austria     

Optimization for discretized switched systems

Switching time optimization is a crucial topic in the optimal control of hybrid systems. Since it is rare that such problems can be solved analytically, the use of numerical discretization schemes for the integration of state and adjoint systems is indispensable. Thus, in this contribution, the switching time optimization problem is studied in a discretized formulation directly from the beginning. An analysis of the discretized problem reveals that smoothness of the original (continuous time) problem is lost, i.e. the problem will in general become nondifferentiable in discrete time. This has to be taken into account when deriving an adjoint-based formula for the optimization of the discretized problem. A hybrid double pendulum example is used for illustration of the results. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)