Reliability Of Parallel Systems Research Articles

Reliability Analysis of a System Designed to Withstand a Specified Shock Magnitude Range

The system under consideration has 𝑛 independent components, and its operation relies on the functioning of at least 𝑘 components, 1 ≤ 𝑘 ≤ 𝑛. The system experiences (𝑛 + 1) distinct shocks. Shock 𝑗 impacts the 𝑗!" component, 𝑗 = 1, 2, . . . , 𝑛, while shock (𝑛 + 1) simultaneously impacts all components. Any shock is lethal if its magnitude is below or above the component-designed thresholds 𝑑# or 𝑑$, respectively. A shock is characterized by its magnitude and arrival time, forming a bivariate random vector. The bivariate random vectors specifying the magnitudes and the arrival times of the shocks are assumed to be independent and follow non-identical bivariate distributions. The reliability of a 𝑘-out-of-𝑛: 𝐺 system under the influence of this type of shocks is derived. The reliability of parallel and series systems is obtained as special situations. The bivariate Pareto type I distribution is applied as an example of the bivariate distribution of the magnitude and arrival time of the shocks. Furthermore, numerical illustrations are conducted to highlight the theoretical results obtained.

Comparing the Stress–Strength Reliability of Multicomponent Parallel Systems with Heterogeneous Exponentiated Half Logistic-F Components

In this paper, the stress–strength reliability of two multicomponent parallel systems with heterogeneous exponentiated half logistic-[Formula: see text] components under the same and the different baseline distribution functions are compared. The comparisons are carried out concerning the usual stochastic order and reversed hazard rate order with majorized shape parameters of the distributions. Also, the maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) of the stress–strength reliability of the aforementioned multicomponent parallel system are obtained and then compared via Monte Carlo simulations.

Stochastic Comparisons of Lifetimes of Series and Parallel Systems with Dependent Heterogeneous MOTL-G Components under Random Shocks

To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods.

A Holistic Solution for Reliability of 3D Parallel Systems

Monolithic 3D technology is emerging as a promising solution that can bring massive opportunities, but the gains can be hindered due to the reliability issues exaggerated by high temperature. Conventional reliability solutions focus on one specific feature and assume that the other required features would be provided by different solutions. Hence, this assumption has resulted in solutions that are proposed in isolation of each other and fail to consider the overall compatibility and the implied overheads of multiple isolated solutions for one system. This article proposes a holistic reliability management engine, R2D3, for post-Moore’s M3D parallel systems that have low yield and high failure rate. The proposed engine, comprising a controller, reconfigurable crossbars, and detection circuitry, provides concurrent single-replay detection and diagnosis, fault-mitigating repair, and aging-aware lifetime management at runtime. This holistic view enables us to create a solution that is highly effective while achieving a low overhead. Our solution achieves 96% coverage of defect; reduces V th degradation by 53%, leading to a 78% performance improvement on average over 8 years for an eight-core system; and ultimately yields a 2.16× longer mean-time-to-failure (MTTF) while incurring an overhead of 7.4% in area, 6.5% in power, and an 8.2% decrease in frequency.

A Unified Model for System Reliability Evaluation Under Dynamic Operating Conditions

The working conditions of multicomponent systems are usually dynamic and stochastic. Reliability evaluation of such systems is challenging, since the components are generally positively correlated. Based on the cumulative exposure principle, we model the effects of the dynamic environments on the component lifetimes by a common stochastic time scale, and exponential dispersion process is utilized to describe the stochastic time scale. Then, the component lifetimes are shown to be positively quadrant dependent, and the joint survival function of the component lifetimes is derived, which includes the results of [1] as special cases. In this article, we show that neglecting either the effects of dynamic environments or the correlation among component lifetimes would underestimate the reliability of series systems and overestimate the reliability of parallel systems. We also investigate the problem of parameter redundancy of the model, and give some suggestions for data analysis. Simulation studies show that the unified model is flexible and useful for suggesting an optimal model given observed data.

Mathematical model and heuristics for maximizing reliability of parallel systems with alternatives and budget constraints

Reliability is defined as the ability to perform a given function over a period of time in a particular environment. Designing problem of the system structure appears in many industries, and various reliability optimization issues arise. Especially in military defence area, it is very important to achieve maximum reliability under a given budget. In this study, maximum reliability optimization problem in parallel system, each component has several alternatives, and limited budget reliability optimization problem is considered. Objective function of the problem is expressed as a nonlinear function because it is a reliability of a parallel system. Therefore, it is generally known as difficult to obtain a global optimal solution. In this paper, we propose a heuristic methodology that solves the problem by using Combinatorial Bender's Cut. The results of experiments proved that the proposed algorithm showed good performance in terms of value of the obtained reliability and consumed CPU time. Keywords : parallel system, reliability, nonlinear programming, heuristic DOI: 10.7176/IEL/10-2-07 Publication date: April 30 th 2020

A Holistic Solution for Reliability of 3D Parallel Systems

A Holistic Solution for Reliability of 3D Parallel Systems

Оцінка надійності паралельних обчислювальних систем при виконанні заданого комплексу взаємопов'язаних робіт

Оцінка надійності паралельних обчислювальних систем при виконанні заданого комплексу взаємопов'язаних робіт

Considerations concerning the calculation of the reliability of deck systems

As is well known, the calculation of the reliability of series and parallel systems is solved in the literature. To calculate the reliability of deck systems, methods based on the formula of Bayes are currently being used. In this paper we present a method of calculating the reliability of triangle-star systems and of transforming a triangle system into a star-type system that then leads to the calculation of the reliability of the deck systems.

Fuzzy reliability estimation using the new operations of transmission average on Rational-linear patchy fuzzy numbers

This paper presents a new practical method for fuzzy system reliability analysis based on the fuzzy arithmetic operations of transmission average (TA) (Abbasi et al. in J Intell Fuzzy Syst 29:851–861, 2015) on Rational-linear patchy fuzzy numbers. The concept of fuzzy numbers is extended by idea of Rational-linear patchy fuzzy numbers. Then, we have introduced fuzzy arithmetic operations of TA between two Rational-linear patchy fuzzy numbers. Finally, a new method has been developed for analyzing the fuzzy system reliability of series and parallel systems based on the fuzzy arithmetic operations of TA, where the reliability of each component is represented by a Rational-linear patchy fuzzy number. A technical example is given to illustrate applying the method and comparing the results of the new method with the previous methods. The proposed method can model and analyze the fuzzy system reliability in a more flexible and intelligent manner in comparison with the other methods.

On Gaussian approximation of the strength of Daniels' bundle with brittle Weibull fibers

AbstractThe paper deals with the classical fiber bundle model with brittle Weibull fibers and equal load sharing. This model is significant for the strength of fibrous materials and composites, and the generally random strength of quasi‐brittle structures. The model is also relevant for the analysis of the reliability of various parallel systems (computer components, infrastructure etc.). An improved closed‐form Gaussian approximation of the standard deviation of bundle strength is presented and compared with accurate solution calculated by recursive formula proposed by Daniels. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A novel approach for analyzing the reliability of series-parallel system using credibility theory and different types of intuitionistic fuzzy numbers

The main objective of this paper is to present an alternative method for computing the membership function of the system under intuitionistic fuzzy set environment. Conventionally, it is not always easy to obtain the system reliability for components with different individual failure probability density function due to necessary but complicated combination and integration of various probability density functions. Also, in the literature, it is assumed that failure rates of all the components of a system follow the same type of fuzzy set which is rarely occurring in the practical situations. Thus, this paper addresses the fuzzy system reliability analysis to construct the membership and non-membership functions by considering the different types of intuitionistic fuzzy failure rates. Functions of intuitionistic fuzzy numbers are calculated using credibility theory. The effectiveness of the proposed approach is illustrated with analyze of the fuzzy reliability of series, parallel and series-parallel systems using different types of intuitionistic fuzzy failure rates. The computed results from the analysis have a less range of uncertainty as the comparability of existing results.

Dynamic reliability models of mechanical load-sharing parallel systems considering strength degradation of components

Conventional reliability analysis of load-sharing parallel systems is mainly based on failure rate of components, in which failure dependence of components and load redistribution are also characterized by specified failure rates. However, the failure rate of mechanical components always varies with time, which is difficult to measure. Therefore, in this paper, quantitative dynamic reliability models of mechanical load-sharing parallel systems are developed in terms of stress parameters and strength parameters rather than failure rate of components, which consider the degradation mechanism of mechanical components. The proposed models take into account the strength degradation path dependence (SDPD) of a component, the strength degradation process dependence between different components in a system, and the random load redistribution. In addition, Monte Carlo simulation is carried out to verify the proposed models. The results show that SDPD and the load-sharing effect have considerable influences on dynamic reliability of mechanical load-sharing parallel systems.

MINT: A Reliability Modeling Frameworkfor Energy-Efficient Parallel Disk Systems

The Popular Disk Concentration (PDC) technique and the Massive Array of Idle Disks (MAID) technique are two effective energy conservation schemes for parallel disk systems. The goal of PDC and MAID is to skew I/O load toward a few disks so that other disks can be transitioned to low power states to conserve energy. I/O load skewing techniques like PDC and MAID inherently affect reliability of parallel disks, because disks storing popular data tend to have high failure rates than disks storing cold data. To study reliability impacts of energy-saving techniques on parallel disk systems, we develop a mathematical modeling framework called MINT. We first model the behaviors of parallel disks coupled with power management optimization policies. We make use of data access patterns as input parameters to estimate each disk's utilization and power-state transitions. Then, we derive each disk's reliability in terms of annual failure rate from the disk's utilization, age, operating temperature, and power-state transition frequency. Next, we calculate the reliability of PDC and MAID parallel disk systems in accordance with the annual failure rate of each disk in the systems. Finally, we use real-world trace to validate out MINT model. Validation result shows that the behaviors of PDC and MAID which are modeled by MINT have a similar trend as that in the real-world.

Investigation of the reliability and longevity of parallel systems with defects using Daniels’ sequences

The Reliability and longevity of parallel systems is studied using the example of a fibrous composite material using Daniels sequences’ and the Markov chain theory. The connection between the strength distribution function of the separate longitudinal elements forming the parallel system and the longevity distribution function of this system under cyclic loads is analyzed. The obtained models do not give direct coincidence with the experimental data but can be used for their nonlinear regressive analysis. Numerical experimental data processing examples are given.

Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set

In general, fuzzy sets are used to analyse the system reliability. In this article, the concept of fuzzy set is extended by the idea of intuitionistic fuzzy set (IFS) and a new general procedure is proposed to construct the membership and non-membership functions of the fuzzy reliability using time-dependent IFS. Here, failure rate function of the system is represented by a triangular intuitionistic fuzzy number (IFN). Also, using proposed approach, membership and non-membership functions of fuzzy reliability of series and parallel systems are constructed, where the failure rate of each component is taken as a time-dependent triangular IFN. The major advantage of using IFS over fuzzy sets is that IFS separate the positive and negative evidences for membership of an element in the set. Numerical examples are given to illustrate the proposed approach.

Reliability Model of Series and Parallel Systems under Imperfect Information

In the situation that unit failure probability is imprecise when calculation the failure probability of system, classical probability method is not applicable, and the analysis result of interval method is coarse. To calculate the reliability of series and parallel systems in above situation, D-S evidence theory was used to represent the unit failure probability. Multi-sources information was fused, and belief and plausibility function were used to calculate the reliability of series and parallel systems by evidential reasoning. By this mean, lower and upper bounds of probability distribution of system failure probability were obtained. Simulation result shows that the proposed method is preferable to deal with the imprecise probability in reliability calculation, and can get additional information when compare with interval analysis method.

Calculation of Failure Probability of Series and Parallel Systems for Imprecise Probability

In the situation that unit failure probability is imprecise when calculation the failure probability of system, classical probability method is not applicable, and the analysis result of interval method is coarse. To calculate the reliability of series and parallel systems in above situation, D-S evidence theory was used to represent the unit failure probability. Multi-sources information was fused, and belief and plausibility function were used to calculate the reliability of series and parallel systems by evidential reasoning. By this mean, lower and upper bounds of probability distribution of system failure probability were obtained. Simulation result shows that the proposed method is preferable to deal with the imprecise probability in reliability calculation, and can get additional information when compare with interval analysis method.

A new approach for analysing the fuzzy system reliability using intuitionistic fuzzy number

In general, fuzzy sets are used to analyse the fuzzy system reliability. In this paper, a new approach is developed for analysing the fuzzy system reliability of series and parallel systems using intuitionistic fuzzy set theory. For analysing the fuzzy system reliability, the definition of trapezoidal intuitionistic fuzzy number is introduced and arithmetic operations between two trapezoidal intuitionistic fuzzy numbers are also introduced. Also by considering several cases, it is shown that definitions of triangular intuitionistic fuzzy number, trapezoidal fuzzy number and triangular fuzzy number are the particular cases of the definition of trapezoidal intuitionistic fuzzy number introduced in this paper. For evaluating the fuzzy reliability of a series system and a parallel system, formulae are derived. For numerical verification of proposed approach, the fuzzy reliability of the basement flooding has been analysed using the proposed approach.

A reliability model of energy-efficient parallel disk systems with data mirroring

In the last decade, parallel disk systems have increasingly become popular for data-intensive applications running on high performance computing platforms. Conservation of energy in parallel disk systems has a strong impact on the cost of cooling equipment and backup power-generation. This is because a significant amount of energy is consumed by parallel disks in high performance computing centres. Although a wide range of energy conservation techniques have been developed for disk systems, most energy saving schemes have adverse impacts on the reliability of parallel disk systems. To address this deficiency, we must focus on reliability analysis for energy-efficient parallel disk systems. In this paper, we make use of a Markov process to develop a quantitative reliability model for energy-efficient parallel disk systems using data mirroring. With the new model in place, a reliability analysis tool is developed to efficiently evaluate reliability of fault-tolerant parallel disk systems with two power modes. More importantly, the reliability model makes it possible to provide good trade-offs between energy efficiency and reliability in energy-efficient and fault-tolerant parallel disk systems.