Constant Stress Accelerated Life Test on a Multiple-Component Series System under Weibull Lifetime Distributions

We will discuss the reliability analysis of the constant stress accelerated life test on a series system connected with multiple components under independent Weibull lifetime distributions whose scale parameters are log-linear in the level of the stress variable. The system lifetimes are collected under Type I censoring but the components that cause the systems to fail may or may not be observed. The data are so called masked for the latter case. Maximum likelihood approach and the Bayesian method are considered when the data are masked. Statistical inference on the estimation of the underlying model parameters as well as the mean time to failure and the reliability function will be addressed. Simulation study for a three-component case shows that Bayesian analysis outperforms the maximum likelihood approach especially when the data are highly masked.     

Failure Data Analysis with Extended Weibull Distribution

A consecutive k-out-of-n: G system consists of n linearly ordered components functions if and only if at least k consecutive components function. In this article we investigate the consecutive k-out-of-n: G system in a setup of multicomponent stress-strength model. Under this setup, a system consists of n components functions if and only if there are at least k consecutive components survive a common random stress. We consider reliability and its estimation of such a system whenever there is a change and no change in strength. We provide minimum variance unbiased estimation of system reliability when the stress and strength distributions are exponential with unknown scale parameters. A nonparametric minimum variance unbiased estimator is also provided.     

A dynamic system for Gompertz model

Two-parameter Gompertz distribution has been introduced as a lifetime model for reliability inference recently. In this paper, the Gompertz distribution is proposed for the baseline lifetimes of components in a composite system. In this composite system, failure of a component induces increased load on the surviving components and thus increases component hazard rate via a power-trend process. Point estimates of the composite system parameters are obtained by the method of maximum likelihood. Interval estimates of the baseline survival function are obtained by using the maximum-likelihood estimator via a bootstrap percentile method. Two parametric bootstrap procedures are proposed to test whether the hazard rate function changes with the number of failed components. Intensive simulations are carried out to evaluate the performance of the proposed estimation procedure.     

Estimation of reliability in multicomponent stress–strength based on two parameter exponentiated Weibull Distribution

In this research article, we estimate the multicomponent stress–strength reliability of a system when strength and stress variates are drawn from an exponentiated Weibull distribution with different shape parameters α?and?β, and common shape and scale parameters γ and λ, respectively. We estimate the parameters by using maximum likelihood estimation (MLE) and hence the estimate of reliability obtained applying the MLE method of estimation when samples are drawn from stress and strength distributions. The small sample comparison of the reliability estimates is made through Monte Carlo simulation.     

Point estimation of the stress–strength reliability parameter for parallel system with independent and non-identical components

In this article, the estimation problem of the multicomponent stress–strength reliability parameter is considered where the stress and the strength systems have arbitrary fixed numbers of independent and non-identical parallel components. It is assumed that the distribution functions of the stress and the strength components satisfy the proportional reversed hazard rate model. The study is done in more details when the baseline distributions are exponential. Maximum likelihood and uniformly minimum variance unbiased estimators are obtained and compared. Also, Bayes and empirical Bayes estimators are discussed and Monte Carlo simulations are carried out to compare their performances.     

Robust Bayesian analysis for parallel system with masked data under inverse Weibull lifetime distribution

Abstract

This paper considers the statistical analysis of masked data in a parallel system with inverse Weibull distributed components under type II censoring. Based on Gamma conjugate prior, the Bayesian estimation as well as the hierarchical Bayesian estimation for the parameters and the reliability function of system are obtained by using the Bayesian theory and the hierarchical Bayesian method. Finally, Monte Carlo simulations are provided to compare the performances of the estimates under different masking probabilities and effective sample sizes.     

A Jackknife Method for Estimation of Variance Components

This paper concerns a method of estimation of variance components in a random effect linear model. It is mainly a resampling method and relies on the Jackknife principle. The derived estimators are presented as least squares estimators in an appropriate linear model, and one of them appears as a MINQUE (Minimum Norm Quadratic Unbiased Estimation) estimator. Our resampling method is illustrated by an example given by C. R. Rao [7] and some optimal properties of our estimator are derived for this example. In the last part, this method is used to derive an estimation of variance components in a random effect linear model when one of the components is assumed to be known.     

Some Uniform Limit Results in Additive Regression Model

In the setting of additive regression model components estimation, we establish some uniform limit results in probability. Our results allow to give an asymptotic simultaneous 100% confidence band for these components. These results are stated in the framework of i.i.d random vectors when the marginal integration estimation method is used.     

Estimation of reliability with cumulative stress and strength degradation

In many real-life scenarios, system reliability depends on dynamic stress–strength interference where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of estimating reliability of a system under deterministic strength degradation and cumulative damage due to shocks arriving according to a point process. Maximum likelihood estimation under two different sampling plans has been considered. Large sample properties in general are discussed. The method is illustrated through simulation and real-life data analysis.     

Estimation and comparison of the stress-strength models with more than two states under Weibull distribution and type II censoring scheme

This paper presents the extension of the inferences on the stress-strength reliability in more than two states to the system depending on the ratio of the strength and stress values when the stress and strength follow independent exponential distributions. The main objective of present paper is to consider different method of estimation, under Type II censoring, for the stress-strength models and to compare them, in more than two states, to the system depending on the ratio of the strength and stress values, when the stress and strength follow independent Weibull distributions, sharing the common shape parameter α.     

Quality and Reliability in Top-event Estimation: Quantitative Fault Tree Analysis in Case of Dependent Events

This article deals with the quantitative Fault Tree Analysis (FTA) and the estimation method of the top-event in case of dependent events. It aims at addressing two main issues: (1) the decomposition of variability for the top-event according to several error components linked to the estimation of the top-event and sources of internal and external variations for a complex system; and (2) the definition of a Performance Measure Independent of Adjustment in order to set the quality of the top-event as a complex measure of the system failure. A simulated study applied to the health system is also carried out.     

Bayesian Analysis of Masked Data in Step-stress Accelerated Life Testing

This article considers a k level step-stress accelerated life testing (ALT) on series system products, where independent Weibull-distributed lifetimes are assumed for the components. Due to cost considerations or environmental restrictions, causes of system failures are masked and type-I censored observations might occur in the collected data. Bayesian approach combined with auxiliary variables is developed for estimating the parameters of the model. Further, the reliability and hazard rate functions of the system and components are estimated at a specified time at use stress level. The proposed method is illustrated through a numerical example based on two priors and various masking probabilities.     

Efficiency Measure from Dynamic Stochastic Production Frontier: Application to Tunisian Textile, Clothing, and Leather Industries

This paper adresses the measurement of technical efficiency of textile, clothing, and leather (TCL) industries in Tunisia through a panel data estimation of a dynamic translog production frontier. It provides a perspective on productivity and efficiency that should be instructive to a developing economy which will face substantial competitive pressure along the gradual economic liberalisation process. The importance of TCL industries in Tunisian manufacturing sector is a reason for obtaining more knowledge of productivity and efficiency for this key industry. Dynamic is introduced to reflect the production consequences of the adjustment costs, which are associated with changes in factor inputs. Estimation of a dynamic error components model is considered using the system generalized method of moments (GMM) estimator suggested by Arellano and Bover (1995), Another look at the instrumental-variable estimation of error-components models, J. Econometrics68:29-51) and Blundell and Bond (Blundell, R., Bond, S. (1998a), Initial conditions and moment restrictions in dynamic panel data models. J. Econometrics87:115-143; Blundell, R., Bond, S. (1998b), GMM estimation with persistent panel data: an application to production functions, Paper presented at the Eighth International Conference on Panel Data, Goteborg University). Our study evaluates the sensitivity of the results, particularly of the efficiency measures, to different specifications. Firm-specific time-invariant technical efficiency is obtained using the Schmidt and Sickles (Schmidt, P., Sickles, R. C. (1984). Production frontiers and panel data. J. Bus. Econ. Stat.2:367-374) approach after estimating the dynamic frontier. We stress the importance of allowing for lags in adjustment of output to inputs and of controlling for time-invariant variables when estimating firm-specific efficiency. The results suggest that the system GMM estimation of the dynamic specification produces the most accurate parameter estimates and technical efficiency measure. Mean efficiency scores is of 68%. Policy implications of the results are outlined.     

Reliability estimation in a multicomponent stress–strength model under generalized half-normal distribution based on progressive type-II censoring

In this paper, based on progressively Type-II censored samples, the problem of estimation of multicomponent stress–strength reliability under generalized half-normal (GHN) distribution is considered. The reliability of a k-component stress-strength system is estimated when both stress and strength variates are assumed to have a GHN distribution with various cases of same and different shape and scale parameters. Different methods such as the maximum likelihood estimates (MLEs) and Bayes estimation are discussed. The expectation maximization algorithm and approximate maximum likelihood methods are proposed to compute the MLE of reliability. The Lindley's approximation method, as well as Metropolis–Hastings algorithm, are applied to compute Bayes estimates. The performance of the proposed procedures is also demonstrated via a Monte Carlo simulation study and an illustrative example.     

Robust estimation of variance components

New robust estimates for variance components are introduced. Two simple models are considered: the balanced one-way classification model with a random factor and the balanced mixed model with one random factor and one fixed factor. However, the method of estimation proposed can be extended to more complex models. The new method of estimation we propose is based on the relationship between the variance components and the coefficients of the least-mean-squared-error predictor between two observations of the same group. This relationship enables us to transform the problem of estimating the variance components into the problem of estimating the coefficients of a simple linear regression model. The variance-component estimators derived from the least-squares regression estimates are shown to coincide with the maximum-likelihood estimates. Robust estimates of the variance components can be obtained by replacing the least-squares estimates by robust regression estimates. In particular, a Monte Carlo study shows that for outlier-contaminated normal samples, the estimates of variance components derived from GM regression estimates and the derived test outperform other robust procedures.     

Assessing direct and indirect seasonal decomposition in state space

The problem of whether seasonal decomposition should be used prior to or after aggregation of time series is quite old. We tackle the problem by using a state-space representation and the variance/covariance structure of a simplified one-component model. The variances of the estimated components in a two-series system are compared for direct and indirect approaches and also to a multivariate method. The covariance structure between the two time series is important for the relative efficiency. Indirect estimation is always best when the series are independent, but when the series or the measurement errors are negatively correlated, direct estimation may be much better in the above sense. Some covariance structures indicate that direct estimation should be used while others indicate that an indirect approach is more efficient. Signal-to-noise ratios and relative variances are used for inference.     

Estimation and variable selection for partially functional linear models

In this paper, a new estimation procedure based on composite quantile regression and functional principal component analysis (PCA) method is proposed for the partially functional linear regression models (PFLRMs). The proposed estimation method can simultaneously estimate both the parametric regression coefficients and functional coefficient components without specification of the error distributions. The proposed estimation method is shown to be more efficient empirically for non-normal random error, especially for Cauchy error, and almost as efficient for normal random errors. Furthermore, based on the proposed estimation procedure, we use the penalized composite quantile regression method to study variable selection for parametric part in the PFLRMs. Under certain regularity conditions, consistency, asymptotic normality, and Oracle property of the resulting estimators are derived. Simulation studies and a real data analysis are conducted to assess the finite sample performance of the proposed methods.     

Stress–strength reliability of a non-identical-component-strengths system based on upper record values from the family of Kumaraswamy generalized distributions

In an attempt to produce more realistic stress–strength models, this article considers the estimation of stress–strength reliability in a multi-component system with non-identical component strengths based on upper record values from the family of Kumaraswamy generalized distributions. The maximum likelihood estimator of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Bayes estimates under symmetric squared error loss function using conjugate prior distributions are computed and corresponding highest probability density credible intervals are also constructed. In Bayesian estimation, Lindley approximation and the Markov Chain Monte Carlo method are employed due to lack of explicit forms. For the first time using records, the uniformly minimum variance unbiased estimator and the closed form of Bayes estimator using conjugate and non-informative priors are derived for a common and known shape parameter of the stress and strength variates distributions. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error, bias and coverage probabilities. Finally, a demonstration is presented on how the proposed model may be utilized in materials science and engineering with the analysis of high-strength steel fatigue life data.     

A new orthogonality-based estimation for varying-coefficient partially linear models

Varying coefficient partially linear models are usually used for longitudinal data analysis, and an interest is mainly to improve efficiency of regression coefficients. By the orthogonality estimation technology and the quadratic inference function method, we propose a new orthogonality-based estimation method to estimate parameter and nonparametric components in varying coefficient partially linear models with longitudinal data. The proposed procedure can separately estimate the parametric and nonparametric components, and the resulting estimators do not affect each other. Under some mild conditions, we establish some asymptotic properties of the resulting estimators. Furthermore, the finite sample performance of the proposed procedure is assessed by some simulation experiments.     

主成分回归能消除多重共线性吗?

主成分回归方法已得到广泛应用,但该方法是否能减小参数估计的误差,理论上并没有明确的结论。以3个假设模型为例,运用模拟计算的方法对主成分回归方法进行了研究,发现主成分回归估计的误差可能比普通最小二乘估计更小,也可能更大,依赖于实际的模型。