Exact reliability formula and bounds for general k-out-of-n systems

The paper deals with reliability of general k-out-of-n systems whose component failures need not be independent and identically distributed. The result is an exact closed form reliability formula which is based on Feller's result. The formula is efficient and easy to use for manual and computer computations. The approximations for the system reliability are given and are useful when dealing with large systems. Two examples illustrate the use of the results.     

New bounds on the reliability of the consecutive k-out-of-r-from-n:F system

The main goal of this article is to show that the lower and upper bounds on the failing probability resp. reliability of consecutive k-out-of-r-from-n:F reliability systems developed by Sfakianakis, Kounias and Hillaris [M. Sfakianakis, S. Kounias, A. Hillaris, IEEE Trans. Reliability 1992;R-41:442–447] can be improved by applying fourth order Boole–Bonferroni bounds. Further we propose the application of the Hunter–Worsley bound in the framework of reliability system analysis, too. Numerical results of the formerly published test examples and harder problems are given. The computer code was written in and is available on request from the authors.     

Optimal design of multi-state weighted k-out-of-n systems based on component design

This paper presents a study on design optimization of multi-state weighted k-out-of-n systems. The studied system reliability model is more general than the traditional k-out-of-n system model. The system and its components are capable of assuming a whole range of performance levels, varying from perfect functioning to complete failure. A utility value corresponding to each state is used to indicate the corresponding performance level. A widely studied reliability optimization problem is the “component selection problem”, which involves selection of components with known reliability and cost characteristics. Less adequately addressed has been the problem of determining system cost and utility based on the relationships between component reliability, cost and utility. This paper addresses this topic. All the optimization problems dealt with in this paper can be categorized as either minimizing the expected total system cost subject to system reliability requirements, or maximizing system reliability subject to total system cost limitation. The resulting optimization problems are too complicated to be solved by traditional optimization approaches; therefore, genetic algorithm (GA) is used to solve them. Our results show that GA is a powerful tool for solving these kinds of problems.     

On the availability of a k-out-of-N system given limited spares and repair capacity under a condition based maintenance strategy

This paper considers a k-out-of-N system with identical, repairable components. Maintenance is initiated when the number of failed components exceeds some critical level. After a possible set-up time, all failed components are replaced by spares. A multi-server repair shop repairs the failed components. The system availability depends on the spare part stock level, the maintenance policy and the repair capacity. We present a mathematical model supporting the trade-off between these three parameters. We present both an exact and an approximate approach to analyse our model. In some numerical experiments, we provide insight on the impact of repair capacity, number of spares and preventive maintenance policy on the availability.     

New insights into the assessment of k-out-of-n and related systems

k-out-of-n and related systems have received much attention in the recent past years. Hundreds of articles were devoted to various methods to assess them. In this article, we show that there exist very efficient algorithms to compute the reliability of k-out-of-n, l-to-h-out-of-n and consecutive k-out-of-n systems. k-within-r-out-of-n systems are intrinsically much harder. We study the performance of binary decision diagrams (BDDs) on these systems. Then, we propose a new approximation scheme. This algorithm is much more efficient in practice than already proposed methods.     

System-level load–strength interference based reliability modeling of k-out-of-n system

The issue of information loss in the process of system reliability modeling through conventional load–strength interference analysis is discussed first, and the reason why it is impossible to construct dependent system reliability model simply by means of component reliability index is demonstrated. Then, an approach to modeling the reliability of dependent system with common cause failure (CCF) is presented. The approach is based on system-level load–strength interference analysis and a concept of ‘conditional failure probability of component’ as well. With the opinion that load randomness is the direct cause of failure dependence, a discrete type system reliability model is developed via the conditional component failure probability concept. At last, the model's capabilities to estimate system reliability with CCF effect and to predict high multiplicity failure probability based on low multiplicity failure event data are proved.     

A consecutive k-out-of-n:G system with dependent elements—a matrix formulation and solution

The reliability of a consecutive k-out-of-n:G system is studied. The system may involve dependent trials, so that the probability of success of a certain test is increased after carrying out corrective actions. The problem is solved via a matrix formulation, using state space methods. Results are shown to correlate for the case of independent trials with those in the literature.     

Exact equation and an algorithm for reliability evaluation of K-out-of-N:G system

An expression for reliability of K-out-of-N:G system is proposed. An algorithm for computing reliability of K-out-of-N system is given. It is an easy to implement, fast and memory efficient algorithm and helps to improve the computational efficiency considerably.     

Availability of K-out-of-N:G systems with non-identical components subject to repair priorities

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 component and that of the system are evaluated by using a multi-dimensional Markov model. We show how this model can be represented as a network of stochastic automata with state-dependent transitions that can be implemented via generalized tensor (or Kronecker) algebra. For the efficiency assessment, an analog Monte Carlo simulation model is developed. Experiments are then conducted and simulation results are compared to those obtained by the proposed approach.     

Synthesis and characterization of a novel poly(N-vinyl)-3-[p-nitrophenylazo]carbazolyl-CdS nanocomposites through chemical hybridization

A novel bi-functional photorefractive (PR) poly(N-vinyl)-3-[p-nitrophenylazo]carbazolyl with carbazolyl fragments and chromophoric azophenyl was synthesized by a post azo coupling reaction and characterized by ¹H NMR, elemental analysis, UV–Vis absorption and FTIR spectroscopy. Then chemical hybridized poly(N-vinyl)-3-[p-nitrophenylazo]carbazolyl-CdS nanocomposites with different molar ratio of CdS to poly(N-vinyl)-3-[p-nitrophenylazo]carbazolyl were prepared. It was confirmed that the CdS particles had a nanoscale size and quantum confinement effect adopting transmission electron microscopy and UV–Vis absorption spectroscopy. The generation of photocurrent on illumination and photoconductive properties of the nanocomposites were studied. Significant enhancement in photoconductivity induced by the chemical doping of CdS in poly(N-vinyl)-3-[p-nitrophenylazo]carbazolyl has also been demonstrated.     

Availability of a general k-out-of-n:G system with non-identical components considering shut-off rules using quasi-birth-death process

A general repairable k-out-of-n:G system with non-identical components, which is a common form of redundancy, is considered in this paper. The number of repairmen is assumed to be r (1≤r≤n−k+1) while components can have similar or different repair priorities. The objective of this work is to address the problem of efficient evaluation of the system's availability in a way that steady state solutions can be obtained systematically in a reasonable computational time. This problem is modeled as a finite state-dependent non-homogeneous quasi-birth-death (QBD) process. An algorithm is introduced to systematically generate the system state vectors and transition rate matrix and then an iterative method based on the Block Gauss-Seidel method is employed to determine the steady state probabilities. These are the novel contributions made in this paper. An analog Monte Carlo simulation is presented to demonstrate the correctness and the efficiency of the proposed method.     

Economic design of a circular consecutive--out-of-:F system with -step Markov dependence

A circular consecutive-k-out-of-n:F system consists of n components arranged along a circular path. The system fails if and only if at least k consecutive components in the system fail. The system reliability, the expected system life, and the expected number of failures are obtained under the assumption that the failure rate of a component depends on the number of consecutive failed components that follow it. A procedure to find the optimal k and a simulation procedure to search the near-optimal k are proposed with illustrative numerical examples. An expected cost per unit time is considered as the objective function to be minimized.     

Preparation of composite nanofibers containing gold nanoparticles by using poly(N-vinylpyrrolidone) and β- cyclodextrin

We report a new method for preparing β-cyclodextrin/poly(N-vinylpyrrolidone) composite nanofibers containing gold nanoparticles by electrospinning. β-Cyclodextrin is mixed into fibers as a new material, and it acts as stabilized reagent and reducing reagent in the synthesis of gold nanoparticles. TEM observation confirms that the gold nanoparticles are completely encapsulated within the composite nanofibers.     

Superconducting transition temperatures in the Ru-1232 system, RuSr2(Gd1? x Ln x Ce1.8Sr0.2)Cu2O z (Ln = Sm, Dy, and Ho)

We have investigated effects of the lanthanide element Ln and the composition changes on the superconducting transition temperatureT _c in the Ru-1232 system, RuSr₂(Gd_1−x Ln _x Ce_1.8Sr_0.2)Cu₂O _z (Ln = Sm, Dy, and Ho). At first, in the case of the samples with Ln = Sm among almost the single 1232 phase samples, the values of the superconducting onset temperatureT _co are almost the same forx=0.00−0.15, and each of the lattice parametersa andc is almost constant. While, in each of the cases of the samples with Ln = Dy and Ho, the sample withx=0.05 shows the maximum values for both the superconducting onset temperatureT _co and the zero resistivity temperatureT _cz. Especially for the sample with Ln = Dy, the values ofT _co andT _cz are 18.5 and 6.5 K, respectively. These are higher than those of the mother sample of RuSr₂(GdCe_1.8Sr_0.2)Cu₂O _z . Moreover, from variations ofT _co, lattice parameters ofa andc in the RuSr₂(Gd_1−x Dy _x Ce_1.8Sr_0.2)Cu₂O _z system as a function of Dy contentx, the relationship between the superconducting transition temperature and the lattice parameters in the present system are investigated.     

Superconductivity and Ferromagnetism of the Ru-1232 Compounds in the (Ru1?xNbx)Sr2(GdCe1.8Sr0.2)Cu2Oz System

The Ru-1232 compounds have been synthesized in the (Ru_1–xNb _x )Sr₂(GdCe_1.8Sr_0.2)Cu₂O _z system, and effects of Nb substitution for Ru on superconductivity and ferromagnetism of the Ru-1232 compounds have been investigated. First, X-ray powder diffraction study shows that nearly the single 1232 phase samples can be obtained in the x composition range from 0.0 to 0.3. Then, from the electrical resistivity study, it is found that each of the samples shows resistivity dropping phenomenon at two temperatures of T _c ^l and T _c ^h, which originates from superconductivity of the Ru-1232 phase and the Ru-1222 one, respectively. Both of the starting temperatures are lowering with increasing Nb content x. Lastly, from the magnetic susceptibility study, it is found that superconducting transition temperature T _c is 20 K for the Ru-1232 sample with x = 0.0 and the ferromagnetic transition temperature T _m is about 90 K. This study also shows that both of the values of T _c and T _m become low with increasing x from 0.0 to 0.3.     

Structure and Superconducting Properties of Cd0.8Ba2(Y0.7Ca0.4)Cu3.5Oy

A new Cd-containing superconductor with nominal composition ofCd_0.8Ba₂(Y_0.7Ca_0.4)Cu_3.5O _y was synthesized and investigated. The obtained Cd and Ca-doped 123 phase exhibits an orthorhombic (T _c=80 K) or tetragonal (T _c=65 K) modification depending on the reaction atmosphere. It was shown that the combined Cd and Ca substitution facilitates the 123 phase formation. The results of the EDX analysis, as well as the comparison of the obtained lattice parameters with those of undoped, Cd-doped, and Ca-doped 123 have shown that both Cd and Ca enter the 123 phase and form a new Cd–Ba–Y–Ca–Cu–O superconducting compound.     

Growth and spectral properties of Cr:KAl(MoO4)2 crystal

The Cr³⁺:KAl(MoO₄)₂ single crystal was grown by top seeding solution growth method (TSSG). Based on the absorption and emission spectra, the crystal field strength Dq, the Racah parameters B and C, the effective phonon energy ?ω and the Huang-Rhys factor S were calculated: Dq = 1494.8 cm^− 1, B = 585.5 cm^− 1 and C = 3049 cm^− 1, ?ω = 373.8 cm^− 1 and the Huang-Rhys factor S = 3.74, respectively. The value Dq/B = 2.55 indicates that Cr³⁺ ion occupies the strong crystal field site in KAl(MoO₄)₂ crystal. A comparison of crystal field parameters for Cr³⁺:KAl(MoO₄)₂ with other Cr³⁺-doped crystals was presented. The results of spectral measurement show that Cr³⁺:KAl(MoO₄)₂ may be a potential candidate for broadband laser applications.     

Growth and spectral properties of Er:NaGd(WO4)2 crystal

A high optical quality Er³⁺-doped NaGd(WO₄)₂ single crystal with dimensions of ∅18 × 50 mm³ has been grown using the Czochralski method. The structure of the grown crystal was proved by X-ray powder diffraction. The accurate concentration of Er³⁺ ion in the crystal was measured. The absorption spectra, fluorescence spectra and fluorescence lifetime of the crystal were measured at room temperature. Green up-conversion luminescence has been observed when the crystal is excited at 965 nm.     

Intrinsic surface depression of the order parameter under mixed (s+id)-wave pair symmetry and its effect on the critical current of high-Tc SIS Josephson junctions

An intrinsic gap depression at the superconductor-insulator interface due to the very short value of the coherence length in high-T _c superconductors [HTS] is considered in the framework of a mixed (s+id)-wave pair symmetry for the order parameter ranging from pures to pured-wave. This gap depression acts as the main physical agent causing the relevant reduction ofI _c (T)R _n (T) values with respect to BCS expectations in HTS SIS Josephson junctions. Good agreement with various experimental data is obtained with both pures-wave and pured-wave symmetries of the order parameter, but with amounts of gap depression depending on the pair symmetry adopted. Regardless of the apir symmetry considered, these results prove the importance of the surface order-parameter depression in the correct interpretation of theI _c (T)R _n (T) data in HTS SIS junctions. In the case of a planar YBCO-based junction the use of the de Gennes condition allowed us to tentatively obtain an upper limit for the amount ofd-wave present in the gap of YBCO.     

独角仙鞘翅微结构及其纳米力学性能

利用SEM对独角仙鞘翅的微结构进行了观测, 并借助纳米压痕仪测试分析了鞘翅的纳米力学性能。SEM试验表明独角仙鞘翅是一种具有拱形空腔的中空轻质生物复合材料, 其断面占空比为26.36%。鞘翅由外表皮和内表皮构成, 而内表皮又通过11~12层纤维层采用45°角正交叠加铺设, 层间辅以许多微纤维丝交叉连接方式编织在一起, 形成层合板结构。试验测得鞘翅外表皮纳米力学性能分别为: 硬度(0.28±0.13) GPa, 弹性模量(5.62±1.21) GPa, 接触刚度 (1.67±0.14)×10⁴ N/m。其纳米力学性能呈现拓扑分布规律, 由头部至尾部区域有增大趋势。试验测试结果为后续研究中设计一种基于独角仙鞘翅的新型轻质仿生结构提供了仿生学模型和理论参考。