Partially Accelerated Life Tests for the Weibull Distribution Under Multiply Censored Data

This article aims to estimate the parameters of the Weibull distribution in step-stress partially accelerated life tests under multiply censored data. The step partially acceleration life test is that all test units are first run simultaneously under normal conditions for a pre-specified time, and the surviving units are then run under accelerated conditions until a predetermined censoring time. The maximum likelihood estimates are used to obtaining the parameters of the Weibull distribution and the acceleration factor under multiply censored data. Additionally, the confidence intervals for the estimators are obtained. Simulation results show that the maximum likelihood estimates perform well in most cases in terms of the mean bias, errors in the root mean square and the coverage rate. An example is used to illustrate the performance of the proposed approach.     

Storage Life Prediction for a High-Performance Capacitor Using Multi-Phase Wiener Degradation Model

Capacitance is a critical performance characteristic of high-voltage-pulse capacitor which is used to store and discharge electrical energy rapidly. The capacitors usually are stored for a long period of time before put into use. Experimental result and engineering experience indicate that the capacitance increases with storage time and will eventually exceed the failure threshold, which means that the capacitor may fail during storage. This is a typical mode of degradation failure for long storage products. Further, the capacitance degradation path can be extrapolated in several stages based on the shifting characteristics. That is, the capacitance increases slowly or fluctuates in the initial storage stage that lasts about three months. Then it increases sharply in the middle stage which lasts about four months. After the two stages, the capacitor enters into the third stage in which capacitance increases constantly. This degradation phenomenon motivates us to study the storage life prediction method based on multi-phase degradation path model. The storage performance degradation mechanism of high-voltage-pulse capacitor was investigated, which provides the physical basis for multi-phase Wiener degradation model. Identification procedure for the transition points in the degradation path was proposed using maximum likelihood principle (MLP). The result of Kruskal-Wallis test which is the method to test whether two populations are consistent or not in statistics showed that the transition points are statistically effective. Other parameters in the multi-phase degradation model are estimated with maximum likelihood estimation (MLE) after the transition points have been specified. The multi-phase Inverse Gaussian (IG) distribution for storage life was deduced for the capacitor, and the point and interval estimation procedure for reliable storage life are constructed with bootstrap method. The efficiency and effectiveness of the proposed multi-phase degradation model is compared with storage life prediction under single-phase condition.     

Exponentiated power Lindley power series class of distributions: Theory and applications

ABSTRACT

We introduce a new four-parameter generalization of the exponentiated power Lindley (EPL) distribution, called the exponentiated power Lindley power series (EPLPS) distribution. The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the minimum lifetime value among all risks. The distribution exhibits a variety of bathtub-shaped hazard rate functions. It contains as particular cases several lifetime distributions. Various properties of the distribution are investigated including closed-form expressions for the density function, cumulative distribution function, survival function, hazard rate function, the rth raw moment, and also the moments of order statistics. Expressions for the Rényi and Shannon entropies are also given. Moreover, we discuss maximum likelihood estimation and provide formulas for the elements of the Fisher information matrix. Finally, two data applications are given showing flexibility and potentiality of the EPLPS distribution.     

Performance of standard imputation methods for missing quality of life data as covariate in survival analysis based on simulations from the International Breast Cancer Study Group Trials VI and VII*

Abstract

Imputation methods for missing data on a time-dependent variable within time-dependent Cox models are investigated in a simulation study. Quality of life (QoL) assessments were removed from the complete simulated datasets, which have a positive relationship between QoL and disease-free survival (DFS) and delayed chemotherapy and DFS, by missing at random and missing not at random (MNAR) mechanisms. Standard imputation methods were applied before analysis. Method performance was influenced by missing data mechanism, with one exception for simple imputation. The greatest bias occurred under MNAR and large effect sizes. It is important to carefully investigate the missing data mechanism.     

Optimum M-step,step-stress design with K stress variables

Most of the available literature on accelerated life testing deals with tests that use only one accelerating variable and no other explanatory variables. Frequently, however, there is a need to use more than one accelerating or other experimental variables. Examples include a test of capacitors at higher than usual levels of temperature and voltage, and a test of circuit boards at higher than usual levels of temperature, humidity, and voltage. M-step, step-stress models are extended to include k stress variables. Optimum M-step, step-stress designs with k stress variables are found. The polynomial model is considered as a special case, and a lack of fit test is discussed. Also a goodness-of-fit test is proposed and the appropriateness of using its asymptotic chi-square distribution for small samples is shown.     

On Upshifted Reversed Mean Residual Life Order

Recently, the concept of reversed mean residual life order based on the mean of the random variable X _t  = (t ? X | X ≤ t), t > 0, called the reversed residual life, defined for the nonnegative random variable X, has been introduced in the literature. In this paper, a stochastic order based on the shifted version of the reversed mean residual life is proposed, based on the reversed mean residual life function for a random variable X with support (l _X , ∞), where l _X may be negative infinity, and its properties are studied. Closure under the Poisson shock model and properties for spare allocation are also discussed.     

流动人口二代研究:概念、挑战与进路

人口流动对中国社会的复杂性、持续性影响,要求我们不仅要关注流动人口本身,还要关注流 动人口的子代群体,即本文所说的“流动人口二代”。 尽管既有研究提出了一些与“流动人口二代”近似 的概念,并在代际传递视角下围绕代际关系、身心健康、教育状况、职业发展、社会融入等方面开展了经验 研究,但这些研究都没有直接针对这一群体全貌展开系统考察,没有给出流动人口二代的群体画像、总体 特质,也没有对影响流动人口二代发展的社会事件与生命历程展开讨论。 鉴于此,本研究提出要着眼于 流动人口二代生命历程,聚焦流动人口二代生命历程中的健康风险、聚焦数字化场域下的流动人口二代 职业新发展、聚焦人口结构性变迁背景下的流动人口二代家庭化问题、聚焦新时代新形势下的流动人口 二代社会融入问题、聚焦新型城镇化情境下的流动人口二代政策保障,思考流动人口二代研究的总体性 框架与发展进路。     

《共产党宣言》中美好生活观及其中国实践

马克思、恩格斯在《共产党宣言》中通过对资本主义社会中无产阶级生活异化状况的考察,从维持人类生存的自然属性、保障人类社会属性的健康发展、建立在生存且发展基础上的自由人联合体三重维度出发,建构起美好生活的内涵。区别于纯粹的理论建构,《共产党宣言》同时为实现美好生活提供了实践路径,即消灭私有制,挖掉剥削制度存在的经济根基;同传统的观念实行最彻底的决裂,实现人的主体意识的自觉;发挥无产阶级主体力量和无产阶级政党的先锋作用。立足新时代,中国共产党守正创新,通过解放和发展社会生产力与保护自然生产力并举、繁荣和发展中国特色社会主义文化、发挥人民群众的主体力量和中国共产党的领导力量,积极践行与发展《共产党宣言》中美好生活观。     

Book reviews

S.M.Kendall:Multivariate Analysis.Charles Griffin & Co. Ltd., London and High Wycombe 1975, 210 pp

C.T.Leondes (ed.):Control and Dynamic Systems, Advances in Theory and Applications. Vol. 11, Academic Press, New York and London 1974, 516 pp., $ 24.50.

CH. R.Nelson:Applied Time Series Analysis for Managerial Forecasting. Holden Day, Inc., San Francisco 1973, 231 pp., $ 14.95.

B.DE Finetti:Theory of Probability. Vol. 1, 2, John Wiley & Sons, New York, London, Sydney, Toronto. Vol. 1, 1974, 300 pp., £ 7.50 - Vol. 2 1975, 375 pp., £ 10.50.

P.Erdördos, J. Spencer:Probabilistic Methods in Combinatorics. Akadémic Press, New York and London; Akadémiai Kiadó, Budapest 1974, 106 pp., $ 11.75.

J.S.R.Ustagi:Variational Methods in Statistics.Academic Press, New York and London 1975.

J.S.Rustagi:Optimizing Methods in Statistics.Academic Press, New York and London 1971,488 pp., $ 17.00.

Karl V. Bury:Statistical Models in Applied Science. John Wiley & Sons, New York-London-Sydney-Toronto 1975,.625 pp., £ 15.60; $ 28.00.

Michael R. Anderberg:Cluster Analysis for Applications. Academic Press, New York-San Francisco-London 1973, 359 pp., $ 27,–.

J.L.Fleiss:Statistical Methods for Rates and Proportions. John Wiley & Sons, New York-London-Sydney-Toronto 1973. 223 pp., £ 6.50.

J.Tanur et al. (Ed.):Statistics:A Guide to the Unknown. Holden Day, Inc., San Francisco 1972, 430 pp.

H.VÁliaho, T. Pekkonen:A Procedure for Stepwise Regression Analysis.Akademie-Verlag, Berlin 1976, 90 pp., 18,– M.

M.Reinfeldt, U. TrÁnkle:Signifikanztabellen statistischer Testvertellungen. R. Oldenbourg Verlag, Mnchen, Wien 1976, 151 S., DM 44,–.

R.E.Barlow, D.J.Batholomew, J.M.Bremner, H.D.Brunk:Statistical Inference Under Order Restrictions.(The Theory and Applications of Isotonic Regression.) John Wiley & Sons, New York 1972, 388 pp., £ 7.50.

H.J.Larson:Introduction to Probability Theory and Statistical Inference. Wiley, New York 1974, 430 pp., £ 6.85.

R.A.Carlson:Statistics. Holden Day, Inc., San Francisco 1973, 393 pp.

E. Page:Queueing Theory in OR. Butterworths, London 1972, 187 pp., £ 3.60.

H.Krampe, J.Kubat, W.Runge:Bedienungsmodelle. Ein Leitfaden für die praktische Anwendung, Verlag Die Wirtachaft, Berlin 1973, 512 S., 79,– M.

G.S.Fishman:Concepts and Methods in Discrete Events Digital Simulation. John Wiley & Sons, New York 1973, 385 pp., £ 8,75.     

Some results on the mean residual waiting time of records

Often, in reliability theory, risk analysis, renewal processes and actuarial studies, mean residual life function or life expectancy plays an important role in studying the conditional tail measure of lifetime data. In this paper, we introduce the notion of the mean residual waiting time of records and present some monotonic and aging properties. Sharp bounds for the mean residual waiting time of records are also investigated.