Pooling reliability functions

In this article large sample pooling procedures for reliability functions of an exponential life testing model is considered. Asymptotic properties of shrinkage estimation procedure subsequent to preliminary tests are developed. It is shown that the proposed estimator possesses substantially snakker asymptotic mean squared error than the usual estimator in a region of the lparameter space. Relative efficiencies of the purposed estimators to the usual estimators are obtained and recommendations of the level of the preliminary tests are provided. Relative dominance picture of the estimators is presented. It is shown that the proposed estimator provides a wider dominance range over usual estimator than the usual preliminary test estimator. More importantly, the size of the preliminary test is meaningful. Simulation studies is also carried out to appraise the performance of the estimators when samples are small.     

员工工作满意度调查问卷的有效性及民营企业员工工作满意度影响因素研究

本研究选取我国浙江杭州和广州深圳市各一中型民营企业员工共780人作为被试,采用自编的民营企业员工满意度调查问卷(问卷由8个分量表构成,共61个项目)探查我国民营企业员工的工作满意度情况及其影响因素.结果表明:(1)民营企业员工满意度调查问卷的信度系数r为0.9555,内容效度和结构效度的相关系数均达到了可接受水平,是一个可接受的满意度调查问卷;(2)民营企业员工满意度调查问卷的维度"培训与发展"、"高层管理"、"所在部门"和"客户服务"对员工的满意度具有较大的影响,而"直接主管"、"薪资与福利"和"工作目标与绩效"等对员工满意度几乎没有什么影响;(3)民营企业B(深圳)的员工在所有八个分量表上的工作满意度均显著地满意于民营企业A(杭州)的员工的工作满意度;(4)无论是在总体水平上还是在各个分量表上,男员工的工作满意度均显著地高于女员工的工作满意度;(5)在总体水平上,在企业服务两年以上的员工(下简称为"老员工")的工作满意度显著地高于在企业工作2年以下的员工(下简称为"新员工")的工作满意度.具体地说,老员工在"所在部门"和"高层管理"两个维度上的工作满意度显著地高于新员工,而在"工作目标与绩效"、"直接主管"、"培训与发展"、"薪资与福利"以及"客户服务"等维度上,两者没有显著的差异.     

Modeling systems with two dependent components under bivariate shock models

Series and parallel systems consisting of two dependent components are studied under bivariate shock models. The random variables N₁ and N₂ that represent respectively the number of shocks until failure of component 1 and component 2 are assumed to be dependent and phase-type. The times between successive shocks are assumed to follow a continuous phase-type distribution, and survival functions and mean time to failure values of series and parallel systems are obtained in matrix forms. An upper bound for the joint survival function of the components is also provided under the particular case when the times between shocks follow exponential distribution.     

Estimating the turning point of a bathtub-shaped failure distribution

The turning point of a hazard rate function is useful in assessing the hazard in the useful life phase and helps to determine and plan appropriate burn-in, maintenance, and repair policies and strategies. For many bathtub-shaped distributions, the turning point is unique, and the hazard varies little in the useful life phase. We investigate the performance of an empirical estimator for the turning point in the case of the modified Weibull distribution, a bathtub-shaped generalization of the Weibull distribution, that has been found to be useful in reliability engineering and other areas concerned with life-time data. We illustrate the theory by means of an example, and also conduct a simulation study to assess the performance of the estimator in practice.     

Robust Bayesian analysis of generalized inverted family of distributions

ABSTRACT

In the current study we develop the robust Bayesian inference for the generalized inverted family of distributions (GIFD) under an ε-contamination class of prior distributions for the shape parameter α, with different possibilities of known and unknown scale parameter. We used Type II censoring and Bartholomew sampling scheme (1963) for the following derivations under the squared-error loss function (SELF) and linear exponential (LINEX) loss function : ML-II Bayes estimators of the i) parameters; ii) Reliability function and; iii) Hazard function. We also present simulation study and analysis of a real data set.     

ASYMPTOTIC PROPERTIES FOR MAXIMUM LIKELIHOOD ESTIMATORS FOR RELIABILITY AND FAILURE RATES OF MARKOV CHAINS

ABSTRACT

In this paper, we shall study a homogeneous ergodic, finite state, Markov chain with unknown transition probability matrix. Starting from the well known maximum likelihood estimator of transition probability matrix, we define estimators of reliability and its measurements. Our aim is to show that these estimators are uniformly strongly consistent and converge in distribution to normal random variables. The construction of the confidence intervals for availability, reliability, and failure rates are also given. Finally we shall give a numerical example for illustration and comparing our results with the usual empirical estimator results.     

Data-transformation approach to lifetimes data analysis: An overview

This article consists of a review and some remarks on the scope, common models, methods, their limitations and implications for the analysis of lifetime data. Also a new approach based upon data-transformations analogous to that of Box and Cox (1964) is introduced. The basic methods and theory of the subject are most familiarly and commonly encountered by the statistical community in the context of problems in reliability studies and survival analysis. However, they are also useful in areas of statistical applications such as goodness-of-fit and approximations for sampling distributions and are applicable in such diverse fields of applied research as economics, finance, sociology, meteorology and hydrology. The discussion includes examples from the mainstream statistical, social sciences and business literature.     

The analysis of mixed interval-censored and complete data

The article focuses mainly on a conditional imputation algorithm of quantile-filling to analyze a new kind of censored data, mixed interval-censored and complete data related to interval-censored sample. With the algorithm, the imputed failure times, which are the conditional quantiles, are obtained within the censoring intervals in which some exact failure times are. The algorithm is viable and feasible for the parameter estimation with general distributions, for instance, a case of Weibull distribution that has a moment estimation of closed form by log-transformation. Furthermore, interval-censored sample is a special case of the new censored sample, and the conditional imputation algorithm can also be used to deal with the failure data of interval censored. By comparing the interval-censored data and the new censored data, using the imputation algorithm, in the view of the bias of estimation, we find that the performance of new censored data is better than that of interval censored.     

Bayes estimation for a bivariate survival model based on exponential distributions

Bayesian analysis of a bivariate survival model based on exponential distributions is discussed using both vague and conjugate prior distributions. Parameter and reliability estimators are given for the maximum likelihood technique and the Bayesian approach using both types of priors. A Monte Carlo study indicates the vague prior Bayes estimator of reliability performs better than its maximum likelihood counterpart.     

Bhattacharyya and Kshirsagar Bounds in Generalized Gamma Distribution

In this article, we consider the exact computation of the famous halfspace depth (HD) and regression depth (RD) from the view of cutting a convex cone with hyperplanes. Two new algorithms are proposed for computing these two notions of depth. The first one is relatively straightforward but quite inefficient, whereas the second one is much faster. It is noteworthy that both of them can be implemented to spaces with dimension beyond three. Some numerical examples are also provided in what follows to illustrate the performances.