Standby redundancies at component level versus system level in series system

Abstract

It is known that the redundancy at the component level is better than the system level for the case of active redundancy. However, few results are available for standby redundancy due to the complexity of convolution. This note stochastically compares allocations of standby redundancies in series systems with exponential components at the component level versus the system level in sense of the likelihood ratio ordering. The established results strengthen and extend some known ones in the literature.     

On Redundancy Allocation to Series and Parallel Systems of Two Components

Abstract

For two components and one standby redundancy, we develop a characterization on the hazard rate order and the reversed hazard rate order of the redundant system lifetime in the context of mutually independent components lifetimes. Also, the likelihood ratio order is derived on the lifetime of the series system with two components lifetimes and two matched active redundancies lifetimes both following the proportional hazard model.     

An alternative approach to reliability analysis of cold standby systems

ABSTRACT

An alternative approach is applied for reliability analysis of standby systems on the basis of matrix renewal function. In this regard, a single-server, two identical unit cold standby systems with an imperfect switch is considered as a three-state semi-Markov process. Several important reliability measures such as availability, mean time to failure, expected number of failures, etc., are obtained for general lifetime distributions. Also, the main results have been treated to the case of exponential lifetimes and explicit formulas obtained for this case in addition of some numerical illustrations. This approach can easily be extended to more general standby systems with different configurations.     

An improved algorithm for reliability bounds of multistate networks

Abstract

Indirect approaches based on minimal path vectors (d-MPs) and/or minimal cut vectors (d-MCs) are reported to be efficient for the reliability evaluation of multistate networks. Given the need to find more efficient evaluation methods for exact reliability, such techniques may still be cumbersome when the size of the network and the states of component are relatively large. Alternatively, computing reliability bounds can provide approximated reliability with less computational effort. Based on Bai’s exact and indirect reliability evaluation algorithm, an improved algorithm is proposed in this study, which provides sequences of upper and lower reliability bounds of multistate networks. Novel heuristic rules with a pre-specified value to filter less important sets of unspecified states are then developed and incorporated into the algorithm. Computational experiments comparing the proposed methods with an existing direct bounding algorithm show that the new algorithms can provide tight reliability bounds with less computational effort, especially for the proposed algorithm with heuristic L1.     

Reliability design for a MANET with cluster-head gateway routing protocol

ABSTRACT

A MANET is a self-configuring network connected by wireless links. In order to facilitate communication within the network, a routing protocol is used to control the traffic. One of the prominent routing protocols for MANET is CGSR. Network reliability related problems have resulted in the construction of many algorithms. The UGFT has an enterprise approach to analyze the reliability of the MANET. The emphasis in this paper has been on executing the MANET reliability using UGFT. An efficient algorithm has been proposed to guarantee the reliability of MANET using UGFT with CGSR and is validated with a case study in a military test bed.     

Benchmark profile and inferences for joint-exposure quantal data in quantitative risk assessment

Abstract

In risk assessment, it is often desired to make inferences on the minimum dose levels (benchmark doses or BMDs) at which a specific benchmark risk (BMR) is attained. The estimation and inferences of BMDs are well understood in the case of an adverse response to a single-exposure agent. However, the theory of finding BMDs and making inferences on the BMDs is much less developed for cases where the adverse effect of two hazardous agents is studied simultaneously. Deutsch and Piegorsch [2012. Benchmark dose profiles for joint-action quantal data in quantitative risk assessment. Biometrics 68(4):1313–22] proposed a benchmark modeling paradigm in dual exposure setting—adapted from the single-exposure setting—and developed a strategy for conducting full benchmark analysis with joint-action quantal data, and they further extended the proposed benchmark paradigm to continuous response outcomes [Deutsch, R. C., and W. W. Piegorsch. 2013. Benchmark dose profiles for joint-action continuous data in quantitative risk assessment. Biometrical Journal 55(5):741–54]. In their 2012 article, Deutsch and Piegorsch worked exclusively with the complementary log link for modeling the risk with quantal data. The focus of the current paper is on the logit link; particularly, we consider an Abbott-adjusted [A method of computing the effectiveness of an insecticide. Journal of Economic Entomology 18(2):265–7] log-logistic model for the analysis of quantal data with nonzero background response. We discuss the estimation of the benchmark profile (BMP)—a collection of benchmark points which induce the prespecified BMR—and propose different methods for building benchmark inferences in studies involving two hazardous agents. We perform Monte Carlo simulation studies to evaluate the characteristics of the confidence limits. An example is given to illustrate the use of the proposed methods.     

Copula-based reliability analysis for a parallel system with a cold standby

The traditional reliability models cannot well reflect the effect of performance dependence of subsystems on the reliability of system, and neglect the problems of initial reliability and standby redundancy. In this paper, the reliability of a parallel system with active multicomponents and a single cold-standby unit has been investigated. The simultaneously working components are dependent and the dependence is expressed by a copula function. Based on the theories of conditional probability, the explicit expressions for the reliability and the MTTF of the system, in terms of the copula function and marginal lifetime distributions, are obtained. Let the copula function be the FGM copula and the marginal lifetime distribution be exponential distribution, a system with two parallel dependent units and a single cold-standby unit is taken as an example. The effect of different degrees of dependence among components on system reliability is analyzed, and the system reliability can be expressed as the linear combination of exponential reliability functions with different failure rates. For investigating how the degree of dependence affects the mean lifetime, furthermore, the parallel system with a single cold standby, comprising different number of active components, is also presented. The effectiveness of the modeling method is verified, and the method presented provides a theoretical basis for reliability design of engineering systems and physics of failure.     

A Study on Reliability for A Two-Item Cold Standby Markov Repairable System with Neglected Failures

This article studies reliability for a Markov repairable two-item cold standby system with neglected failures. In the system, if a failed time of the system is too short (less than a given critical value) to cause the system to fail, then the failed time may be omitted from the downtime record, i.e., the failure effect could be neglected. In ion-channel modeling, this situation is called the time interval omission problem. The availability indices and the mean downtime are presented as two measures of reliability for this repairable system. Some numerical examples are shown to illustrate the results obtained in this article.     

Unsupervised learning of regression mixture models with unknown number of components

ABSTRACT

We propose a new unsupervised learning algorithm to fit regression mixture models with unknown number of components. The developed approach consists in a penalized maximum likelihood estimation carried out by a robust expectation–maximization (EM)-like algorithm. We derive it for polynomial, spline, and B-spline regression mixtures. The proposed learning approach is unsupervised: (i) it simultaneously infers the model parameters and the optimal number of the regression mixture components from the data as the learning proceeds, rather than in a two-fold scheme as in standard model-based clustering using afterward model selection criteria, and (ii) it does not require accurate initialization unlike the standard EM for regression mixtures. The developed approach is applied to curve clustering problems. Numerical experiments on simulated and real data show that the proposed algorithm performs well and provides accurate clustering results, and confirm its benefit for practical applications.     

Weighted total least-squares joint adjustment with weight correction factors

Abstract

A joint adjustment involves integrating different types of geodetic datasets, or multiple datasets of the same data type, into a single adjustment. This paper applies the weighted total least-squares (WTLS) principle to joint adjustment problems and proposes an iterative algorithm for WTLS joint (WTLS-J) adjustment with weight correction factors. Weight correction factors are used to rescale the weight matrix of each dataset while using the Helmert variance component estimation (VCE) method to estimate the variance components, since the variance components in the stochastic model are unknown. An affine transformation example is illustrated to verify the practical benefit and the relative computational efficiency of the proposed algorithm. It is shown that the proposed algorithm obtains the same parameter estimates as the Amiri-Simkooei algorithm in our example; however, the proposed algorithm has its own computational advantages, especially when the number of data points is large.     

On stochastic behaviors of load-sharing parallel systems

Abstract

This paper mainly investigates a general load-sharing parallel system having two units. First, we construct some comparisons among a load standby system, a warm standby system, a hot standby system and a cold standby system. Moreover, some stochastic comparisons between the load-sharing parallel system and one of its two components are obtained in the sense of the usual stochastic order. Finally, the residual life of this system and its properties are examined.     

Subgroup identification by recursive segmentation

A new modeling approach called ‘recursive segmentation’ is proposed to support the supervised exploration and identification of subgroups or clusters. It is based on the frameworks of recursive partitioning and the Patient Rule Induction Method (PRIM). Through combining these methods, recursive segmentation aims to exploit their respective strengths while reducing their weaknesses. Consequently, recursive segmentation can be applied in a very general way, that is in any (multivariate) regression, classification or survival (time-to-event) problem, using conditional inference, evolutionary learning or the CART algorithm, with predictor variables of any scale and with missing values. Furthermore, results of a synthetic example and a benchmark application study that comprises 26 data sets suggest that recursive segmentation achieves a competitive prediction accuracy and provides more accurate definitions of subgroups by models of less complexity as compared to recursive partitioning and PRIM. An application to the German Breast Cancer Study Group data demonstrates the improved interpretability and reliability of results produced by the new approach. The method is made publicly available through the R-package rseg (http://rseg.r-forge.r-project.org/).     

Equivariant estimation for the parameters of location-scale multivariate exponential models and its application in reliability analysis

ABSTRACT

By considering an absolutely continuous location-scale multivariate exponential model (Weier and Basu, 1980), we obtain minimum risk equivariant estimator(s) of the parameter(s). Given a location-scale multivariate exponential random vector, it is shown that the normalized spacings associated with the random vector are independent standard exponential. The distribution of the complete sufficient statistic is derived. We derive the performance measures of standby, parallel, and series systems and also obtain the minimum risk equivariant estimator of the mean time before failure of the three systems. Some of the results of this article are extensions of those of Chandrasekar and Sajesh (2010).     

A stochastic approximation algorithm for maximum-likelihood estimation with incomplete data

We propose a new stochastic approximation (SA) algorithm for maximum-likelihood estimation (MLE) in the incomplete-data setting. This algorithm is most useful for problems when the EM algorithm is not possible due to an intractable E-step or M-step. Compared to other algorithm that have been proposed for intractable EM problems, such as the MCEM algorithm of Wei and Tanner (1990), our proposed algorithm appears more generally applicable and efficient. The approach we adopt is inspired by the Robbins-Monro (1951) stochastic approximation procedure, and we show that the proposed algorithm can be used to solve some of the long-standing problems in computing an MLE with incomplete data. We prove that in general O(n) simulation steps are required in computing the MLE with the SA algorithm and O(n log n) simulation steps are required in computing the MLE using the MCEM and/or the MCNR algorithm, where n is the sample size of the observations. Examples include computing the MLE in the nonlinear error-in-variable model and nonlinear regression model with random effects.     

Reliability of weighted k-out-of-n: G systems consisting of two types of components and a cold standby component

In this article, the influence of a cold standby component to the reliability of weighted k-out-of-n: G systems consisting of two different types of components is studied. Weighted k-out-of-n: G systems are generalization of k-out-of-n systems that has attracted substantial interest in reliability theory because of their various applications in engineering. A method based on residual lifetimes of mixed components is presented for computing reliability of weighted k-out-of-n: G systems with two types of components and a cold standby component. Reliability and mean time to failure of different structured systems have been computed. Moreover, obtained results are used for defining optimal system configurations that can minimize the overall system costs.     

An em algorithm for a semiparametric finite mixture model

We propose a semiparametric version of the EM algorithm under the semiparametric mixture model introduced by Anderson (1979, Biometrika , 66 , 17-26). It is shown that the sequence of proposed EM iterates, irrespective of the starting value, converges to the maximum semiparametric likelihood estimator of the vector of parameters in the semiparametric mixture model. The proposed EM algorithm preserves the appealing monotone convergence property of the standard EM algorithm and can be implemented by employing the standard logistic regression program. We present one example to demonstrate the performance of the proposed EM algorithm.     

Stochastic comparisons of two-unit repairable systems

Abstract

We consider two models of two-unit repairable systems: cold standby system and warm standby system. We suppose that the lifetimes and repair times of the units are all independent exponentially distributed random variables. Using stochastic orders we compare the lifetimes of systems under different assumptions on the parameters of exponential distributions. We also consider a cold standby system where the lifetimes and repair times of its units are not necessarily exponentially distributed.     

On estimating the reliability in a multicomponent stress-strength model based on Chen distribution

Abstract

In this article, we obtain point and interval estimates of multicomponent stress-strength reliability model of an s-out-of-j system using classical and Bayesian approaches by assuming both stress and strength variables follow a Chen distribution with a common shape parameter which may be known or unknown. The uniformly minimum variance unbiased estimator of reliability is obtained analytically when the common parameter is known. The behavior of proposed reliability estimates is studied using the estimated risks through Monte Carlo simulations and comments are obtained. Finally, a data set is analyzed for illustrative purposes.     

Maximum entropy in the mean methods in propensity score matching for interval and noisy data

Abstract

In this paper, we propose maximum entropy in the mean methods for propensity score matching classification problems. We provide a new methodological approach and estimation algorithms to handle explicitly cases when data is available: (i) in interval form; (ii) with bounded measurement or observational errors; or (iii) both as intervals and with bounded errors. We show that entropy in the mean methods for these three cases generally outperform benchmark error-free approaches.     

Parallelizing multiple linear regression for speed and redundancy: an empirical study ∗

The purpose of this paper is to present a parallel implementation of multiple linear regression. We discuss the multiple linear regression model. Traditionally parallelism has been used for either speed up or redundancy (hence reliability). With stochastic data, by clever parsing and algorithm development, it is possible to achieve both speed and reliability enhancement. We demonstrate this with multiple linear regression.