Load-sharing System Research Articles

Reliability Estimation in Load-Sharing System Model with Application to Real Data

This study deals with the reliability analysis of a multi-component load sharing system where failure of any component within the system induces higher failure rate on the remaining surviving components. It is assumed that each component failure time follows Chen distribution. In classical set up, the maximum likelihood estimates of the load sharing parameters, system reliability and hazard rate along with their standard errors are computed. Since maximum likelihood estimates are not in closed form, so asymptotic confidence intervals and two bootstrap confidence intervals for the unknown parameters have also been constructed. Further, by assuming both informative and non-informative prior for the unknown parameters, Bayes estimates along with their posterior standard errors and HPD intervals of the parameters are obtained. Thereafter, a simulation study elicitates the theoretical developments. A real data analysis, at the end, eshtablishes the applicability of the proposed theory.

Maintenance analysis of a two-component load-sharing system

This paper presents a two-component load-sharing system. The failure rates of the two components are time dependent and load dependent. Whenever one fails, it is imperfectly repaired with a time delay during which the failure rate of the survival component increases because of the resulting overload. Three maintenance policies are proposed considering imperfect preventive maintenance and system replacement. The optimal average costs in the long run under different maintenance policies are derived from the theoretical propositions. Sensitivity analyses through numerical examples are carried out.

Reliability Analysis of Load-Sharing Systems Subject to Dependent Degradation Processes and Random Shocks

Many systems often experience multiple failures resulting from simultaneous exposure to degradation processes and random shocks. For a load-sharing system, the dependencies among the degradation processes, random shocks and component failures potentially cause the system to fail more easily, which poses new challenging issues to evaluate the reliability. A novel reliability model for load-sharing systems subject to dependent degradation processes and random shocks is proposed. The new model extends previous models for simple parallel systems by considering the characteristics and specific dependencies of load-sharing systems. In a load-sharing system, the workload and shock load shared by each surviving component will increase after a component failure, leading to the higher degradation rate, the more serious sudden degradation damage caused by random shocks, and the greater probability of hard failure. In the model, the analytical expression is utilized to calculate the complex reliability. The complexity of this calculation is caused by the stochastic failure time of surviving components, the stochastic arriving time of shocks, and their interaction. A case of the load-sharing redundant micro-engines in micro-electro-mechanical system is presented to demonstrate the proposed model, and the result shows that the reliability of load-sharing system is lower than that of a simple parallel system.

Longitudinal arch load-sharing system of the foot

The longitudinal arch of the human foot is a complex mechanical structure that must be compliant on uneven surfaces and also have sufficient stiffness to allow the foot to be an efficient propulsive organ during walking and running gait. To serve these functions, the longitudinal arch has a unique four-layer load-sharing system consisting of the plantar fascia, plantar intrinsic muscles, plantar arch extrinsic muscles and plantar ligaments. These four layers of tension load-bearing elements, working together with the osseous elements which serve as the framework of the longitudinal arch, work synergistically to increase longitudinal arch stiffness during weightbearing activities. The passive tension load-bearing elements of this load-sharing system, the plantar fascia and plantar ligaments, are not under direct central nervous system control and thus serve to stiffen the longitudinal arch with an automatic stiffening mechanism that is based on Achilles tendon tension and plantar forefoot loading. The active tension load-bearing elements, the plantar intrinsic and plantar extrinsic muscles, are under direct central nervous system control and serve to increase or decrease the stiffness of the medial and lateral longitudinal arches depending on the type and intensity of the prevailing weightbearing activity of the individual. Together, the elements of the longitudinal arch load-sharing system ensure that proper weightbearing function of the longitudinal arch, and the foot and lower extremity, can still occur even when a failure of one of these tension load-bearing elements occurs due to injury.

Sistema de reparto de cargas del arco longitudinal del pie

The longitudinal arch of the human foot is a complex mechanical structure that must be compliant on uneven surfaces and also have sufficient stiffness to allow the foot to be an efficient propulsive organ during walking and running gait. To serve these functions, the longitudinal arch has a unique four-layer load-sharing system consisting of the plantar fascia, plantar intrinsic muscles, plantar arch extrinsic muscles and plantar ligaments. These four layers of tension load-bearing elements, working together with the osseous elements which serve as the framework of the longitudinal arch, work synergistically to increase longitudinal arch stiffness during weightbearing activities. The passive tension load-bearing elements of this load-sharing system, the plantar fascia and plantar ligaments, are not under direct central nervous system control and thus serve to stiffen the longitudinal arch with an automatic stiffening mechanism that is based on Achilles tendon tension and plantar forefoot loading. The active tension load-bearing elements, the plantar intrinsic and plantar extrinsic muscles, are under direct central nervous system control and serve to increase or decrease the stiffness of the medial and lateral longitudinal arches depending on the type and intensity of the prevailing weightbearing activity of the individual. Together, the elements of the longitudinal arch load-sharing system ensure that proper weightbearing function of the longitudinal arch, and the foot and lower extremity, can still occur even when a failure of one of these tension load-bearing elements occurs due to injury.

Interval estimation for k-out-of-n load-sharing systems

ABSTRACTLoad-sharing systems are commonly seen in industry; e.g., water pumps in a cooling system. In a load-sharing system, the stress level on each surviving component increases as components fail. The load-sharing nature of the component failure process creates difficulties in statistical inference for the system. This article develops two interval procedures for failure data from load-sharing systems. We assume that the component lifetime under each stress level follows an exponential distribution, a common distribution in reliability engineering. A log-linear link function is used to model the relationship between the stress levels and component lifetimes. In the two proposed interval procedures, we construct confidence intervals for the model parameters by using pivotal quantities and generalized pivotal quantities. Interval estimation for important reliability characteristics including the mean lifetime and the reliability of the load-sharing system is also discussed. A simulation study shows that the confidence intervals produced from the proposed procedures are more accurate compared with traditional approximate interval procedures, such as the large sample normal approximation and the bootstrap. A numerical example is used to demonstrate the performance of the proposed procedures.

A Cumulative-Exposure-Based Algorithm for Failure Data From a Load-Sharing System

In a load-sharing system, total workloads are shared by all components and failure of one component increases stress of the surviving ones. The time interval between two consecutive component failures reflects component reliability under different stress and is of interest to us. This study develops an iterative algorithm for analysis of such data from load-sharing systems. In each iteration, we first obtain the equivalent operating time of each component under a given stress by capitalizing on the cumulative exposure principle. Then the equivalent operating times, which are simply right-censored, are fitted to update the parameter estimates. The conversion has closed forms for most common distributions such as the log-location-scale family and the gamma distribution, and the subsequent fitting of right-censored data is straightforward. Therefore, the algorithm is easy to implement compared with existing methods such as the maximum likelihood estimation. Convergence properties of the algorithm are investigated theoretically and through extensive simulations. Three examples representing different types of real problems are used to demonstrate the proposed algorithm.

An Extension of the Freund's Bivariate Distribution to Model Load-Sharing Systems

SYNOPTIC ABSTRACTSeveral authors have considered the analysis of load-sharing parallel systems. The main characteoristics of such a two-component system is that after the failure of one component, the surviving component has to shoulder extra load, and hence, it is more likely to fail earlier than would be expected under the original model. In other cases, the failure of one component may release extra resources to the other component, thus delaying the system failure. Freund introduced a bivariate extension of the exponential distribution, which is applicable to two-component load-sharing systems. It is based on the assumption that the lifetime distributions of the components are exponential random variables before and after the change. In this article, we introduce a new class of bivariate distribution using the proportional hazard model. It is observed that the bivariate model proposed by Freund is a particular case of our model. We study different properties of the proposed model. Different statistical inferences have also been developed. We have considered four different special cases: when the base distributions are exponential, Weibull, linear failure rate, and Pareto III distributions. One data analysis has been performed for illustrative purposes. Finally, we propose some generalizations.

Stochastic properties and parameter estimation for a general load-sharing system

ABSTRACTWe study here a general load-sharing parallel system in which the lifetimes of the components of the system are arbitrary continuous random variables. The system functions if at least one component in the system functions and the surviving unit shares the whole load. Some sufficient conditions are obtained for the usual stochastic order between two different load-sharing systems. We then consider the optimal allocation problem of one load standby in a series system with two independent components. Finally, the maximum likelihood estimation of the parameters for some specific systems is discussed.

A model for k-out-of-m load-sharing systems

ABSTRACTIn a load-sharing system, the failure of a component affects the residual lifetime of the surviving components. We propose a model for the load-sharing phenomenon in k-out-of-m systems. The model is based on exponentiated conditional distributions of the order statistics formed by the failure times of the components. For an illustration, we consider two component parallel systems with the initial lifetimes of the components having Weibull and linear failure rate distributions. We analyze one data set to show that the proposed model may be a better fit than the model based on sequential order statistics.

Maintenance of a two dependent component system: a case study

This paper considers a two component load-sharing system. The load and components failure rate are time dependent. It proposes a maintenance policy considering minimal repairs, imperfect maintenance and replacements. The existence of the optimal cost rate in the long run is proved. The optimal maintenance results are derived from the theoretical propositions and the sensitivity of the system parameters to the maintenance policy optimization criteria is pointed out.

An efficient chaotic based PSO for earliness/tardiness optimization in a batch processing flow shop scheduling problem

The flow shop is a well-known class of manufacturing system for production process planning. The need for scheduling approaches arises from the requirement of most systems to implement more than one process at a moment. Batch processing is usually carried out to load balance and share system resources effectively and gain a desired quality of service level. A flow shop manufacturing problem with batch processors (BP) is discussed in current paper so as to minimize total penalty of earliness and tardiness. To address the problem, two improved discrete particle swarm optimization (PSO) algorithms are designed where most important properties of basic PSO on velocity of particles are enhanced. We also employ the attractive properties of logistic chaotic map within PSO so as to investigate the influence of chaos on search performance of BP flow shop problem. In order to investigate the suggested algorithms, a comprehensive computational study is carried out and performance of algorithms is compared with (1) a commercial optimization solver, (2) a well-known algorithm from PSO’s literature and (3) three algorithms from BP’s literature. The experimental results demonstrate the superiority of our algorithm against others.

Periodic Inspection Optimization of a k-Out-of-n Load-Sharing System

In this paper, we consider a k-out-of-n load-sharing system with $n$ identical components sharing a certain amount of load. Each time a component fails, its load is distributed to the remaining components; we assume an increase in load increases the hazard rates of the remaining components. The system is periodically inspected to detect failed components. Two cases may occur in an inspection interval: if the number of failed components is less than $n-k+1$ , then the failed components are only rectified at periodic inspections; if the number of failures reaches $n-k+1$ , then the system fails, and at this time, all the failed components are inspected and rectified. A failed component is replaced or minimally repaired according to a probability which depends on its age at the failure time. The components' failures follow a Non-Homogenous Poisson Process (NHPP), and their intensity functions depend on their ages and the loads to which they are exposed at any moment. In this paper, we develop a model to find the optimal inspection interval for such a system, which minimizes the total expected cost incurred over the system lifecycle. We derive the analytical solution for the special case of a 1-out-of-2 system, and discuss its computational difficulties. We then present a simulation algorithm to find the required expected values in the objective function. Several numerical examples are presented to illustrate the proposed model.

Reliability Analysis of Load-SharingK-out-of-NSystem Considering Component Degradation

TheK-out-of-Nconfiguration is a typical form of redundancy techniques to improve system reliability, where at leastK-out-of-Ncomponents must work for successful operation of system. When the components are degraded, more components are needed to meet the system requirement, which means that the value ofKhas to increase. The current reliability analysis methods overestimate the reliability, because using constantKignores the degradation effect. In a load-sharing system with degrading components, the workload shared on each surviving component will increase after a random component failure, resulting in higher failure rate and increased performance degradation rate. This paper proposes a method combining a tampered failure rate model with a performance degradation model to analyze the reliability of load-sharingK-out-of-Nsystem with degrading components. The proposed method considers the value ofKas a variable which is derived by the performance degradation model. Also, the load-sharing effect is evaluated by the tampered failure rate model. Monte-Carlo simulation procedure is used to estimate the discrete probability distribution ofK. The case of a solar panel is studied in this paper, and the result shows that the reliability considering component degradation is less than that ignoring component degradation.

Reliability Evaluation of a Load-sharing Parallel System with Failure Dependence

In a parallel structure load-sharing system, the failure rate of the operating components will usually increase, due to the additional loading induced by the other components' failure. Hence failure dependency exists among components. To quantify the failure dependency, a dependence function is introduced. Under the assumptions that the repair time distributions of components are arbitrary and life times are exponential distributions whose failure rates vary with the number of operating components, a new load-sharing parallel system with failure dependency is proposed. To model the stochastic behavior of the system, the Semi-Markov process induced by it is given. The Semi-Markov kernel associated with the process is also presented. The availability and the time to the first system failure are obtained by employing Markov renewal theory. A numerical example is presented to illustrate the results obtained in the paper. The impact of the failure dependence on the system is also considered.

A Load Sharing System Reliability Model With Managed Component Degradation

Motivated by an industrial problem affecting a water utility, we develop a model for a load sharing system where an operator dispatches work load to components in a manner that manages their degradation. We assume degradation is the dominant failure type, and that the system will not be subject to sudden failure due to a shock. By deriving the time to degradation failure of the system, estimates of system probability of failure are generated, and optimal designs can be obtained to minimize the long run average cost of a future system. The model can be used to support asset maintenance and design decisions. Our model is developed under a common set of core assumptions. That is, the operator allocates work to balance the level of the degradation condition of all components to achieve system performance. A system is assumed to be replaced when the cumulative work load reaches some random threshold. We adopt cumulative work load as the measure of total usage because it represents the primary cause of component degradation. We model the cumulative work load of the system as a monotone increasing and stationary stochastic process. The cumulative work load to degradation failure of a component is assumed to be inverse Gaussian distributed. An example, informed by an industry problem, is presented to illustrate the application of the model under different operating scenarios.

An inverse problem of the load-sharing system reliability analysis: Constructing the load function

The reliability analysis of the load-sharing systems under different behaviors of the load has been provided in this article. An inverse problem of determining the load function by having requirements concerning the system survivor function is solved. Simple and explicit expressions for computing the load function are provided under the assumption that the Weibull probability distributions of time to failure are derived. A standby system consisting of two units under the changeable load is studied. The various numerical examples illustrate the proposed models.

Partition-Based Priors and Multiple Event Censoring: An Analysis of Rosen’s Fibrous Composite Experiment

Multiple event censoring occurs when the censoring mechanism depends on preceding observations. This arises naturally in load-sharing systems when component failure under increased load can initiate a series of component failures due to load transfer from the failed components, causing the subsequent component strengths to be interval censored. Here the intervals are determined by the breaking stress that initiates the series of failures. The partition-based nonparametric priors developed in 2009 by Sethuraman and Hollander are a class of natural conjugate priors for this situation. Load-sharing systems are used to model fibrous composite materials. The modeling approach is based on some remarkable experiments conducted in 1964 and 1965 by Rosen, who discovered that load could not be supported through the composite matrix material around a fiber break beyond a distance referred to as the ineffective length. The ineffective length is used to discretize the composite into a system of components for which the load-sharing is determined by mechanical considerations. A Bayesian analysis of the components’ strength distribution of the data from Rosen’s experiment is given based on a partition-based prior. This article has supplementary material.

Surgical Outcome in Thoracolumbar Fractures Managed by Short-segment Pedicle Instrumentation

This study aims to evaluate the efficiency of short-segment instrumentation in treating thoracolumbar fractures in our institute. Twenty-two patients underwent posterior short-segment instrumentation for thoracolumbar fractures in our institute from 2007 to 2010 were included in this retrospective study. Radiological evaluations were carried out by measuring regional kyphosis angle (RA), anterior vertebral body compression percentage (AVC), and sagittal index (SI) during preoperative, postoperative and final follow-up, with the aim to investigate the rate of correction loss and implantation failure in relation to the Arbeitsgemeinschaft für Osteosythese(AO) classification of fracture system and the Load Sharing score system. CT scans were also used to determine the preoperative to postoperative canal compromise ratio. During the final follow-up, clinical outcomes were analysed based on scores from the Denis' Pain's and Work scales and neurological function was scored according to the Frankel classification. At the final follow-up (average duration of 15 months), 21 patients (95%) who partially or fully recovered from thoracolumbar fractures were able to resume daily activities with no complaints of pain, or only slight pain. No deterioration in neurological function were recorded. Upon evaluation at each point of time, (preoperative, postoperative and final follow-up), the average RA improved from 21º to 3.5º to 5.6º, average AVC improved from 40.8% to 90.2% to 88.2%, and average SI changed from 19.1º to 3.1º to 4.1º, respectively. Average canal compromise ratio decreased from 45% to 6.7% after surgery. No correlation was found between loss of correction and AO classification of fracture system, and loss of correction and Load Sharing system scores. Also, no correlation was found between clinical outcomes and the correction loss limited to 10º. Posterior short-segment fixation in thoracolumbar fractures showed a satisfactory outcome in 95% of the patients based on a 15-month follow-up in our institute, even among patients with comminuted fractures injuries.

Bayesian reliability estimation of a 1-out-of-k load-sharing system model

The study deals with the reliability analysis of a 1-out-of-k load-sharing system model under the assumption that each component’s failure time follows generalized exponential distribution. With the assumption of load-sharing inclination among the system’s components, the system reliability and hazard rate functions have been derived. In classical set up, we derive maximum likelihood estimates of the load-sharing parameters with their standard errors. Classical confidence intervals and two bootstrap confidence intervals for the parameters, system reliability and hazard rate functions have also been proposed. For Bayesian estimation, we adopt sampling-based posterior inference procedure based on Markov Chain Monte Carlo techniques such as Gibbs and Metropolis–Hastings sampling algorithms. We assume both non-informative and informative priors representing the variations in the model parameters. A simulation study is carried out for highlighting the theoretical developments.