The decreasing percentile residual life ageing notion

Earlier researchers have studied some aspects of the classes of distribution functions with decreasing α-percentile residual life (DPRL(α)), 0<α<1. The purpose of this paper is to note some further properties of these classes, and to initiate a theory of non-parametric statistical estimation of DPRL(α) functions. Specifically, the close relationship between the DPRL(α) and the increasing failure rate ageing notions is studied. Other close relationships, between the DPRL(α) ageing notions and the percentile residual life stochastic orders, are described, and further properties of the above classes of distributions are derived. Finally, we introduce an estimator of the percentile residual life function, under the condition that it decreases, and we prove its strongly uniform consistency.     

The percentile residual life up to time t0: Ordering and aging properties

Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied and also an application in reliability theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t₀ aging notion.     

Covariate effect on the life expectancy and percentile residual life functions under the proportional hazards and the accelerated life models

The present paper is concerned with statistical models for the dependence of survival time or time to occurrence of an event, such as time to tumor, on a vector X of covariates or prognostic variables such as age, sex, blood pressure, length of exposure to a toxic material, etc., measured on a group of individuals in biomedical investigations. It is assumed that the covariates influence the distribution of time to tumor only through a linear predictor μ =β^′X.

The object of our paper is to investigate the effect due to the covariates on the Life Expectancy and the Percentile Residual Life (PRL) function of a family of organisms under the proportional hazards and the accelerated life models. The key result is that the families of survival distributions under these models have the 'setting the clock back to zero' property if the family of baseline survival distributions does. This property is a generalization of the lack of memory property of the exponential distribution. Simple examples of the members of this family are the linear hazard exponential, Pareto and Gompertz life distributions.

As a simple application of the main results obtained in the present paper, we have considered a stochastic survival model recently proposed by Chiang and Conforti (1989) for the time-to-tumor distribution in the context of a large-scale serial sacrifice experiment by the National Center of Toxicological Research (NCTR). This involves some mice that were fed 2-AAF from infancy and those that developed bladder and/or liver neoplasms, see Farmer et al (1980). It is shown that their stochastic model for tumor incidence intensity at time t leads to a family of survival models that has the setting the clock back to zero property. The survival functions and the effect of the vector X of covariates on the PRL and the tumor-free life expectancies are evaluated for the proportional hazards and accelerated life models.     

Optimal bounds for the mean of the total time on test for distributions with decreasing generalized failure rate

During any life test experiment it is of interest to study potential costs (or profits) of performing the test to the very end. Assuming that these costs are proportional to lifetimes of analysed items the experimenter needs to know the remaining total time on test, having just observed successive failure in the test. We derive sharp upper bounds on the expectation of the remaining total time on test statistic when the underlying distributions have decreasing generalized failure rate with respect to generalized Pareto distributions. In particular we obtain the bounds valid for distributions with decreasing density or failure rate. The results are illustrated with numerical examples.     

A note on the mean residual life function of a coherent system with exchangeable or nonidentical components

This article investigates some properties of the mean residual life function of (n−k+1)-out-of-n systems, when the lifetimes of the system components are independent random variables but not necessarily identically distributed and when the joint distribution of the component lifetimes is exchangeable, extending the results of Asadi and Goliforushani (2008) [On the mean residual life function of coherent systems. IEEE Transactions on Reliability 57 (4) 574-580] for the case of independent and identically distributed components. The extension to a coherent system with exchangeable components is also given.     

Least Squares estimation for the multivariate weibull model of bougaard based on accelerated life test of system and component

Accelerated life testing of products quickly yields information on life. In this article, we present a simple method to incorporate the information collected from accelerated life tests of both components and (series) systems. The multivariate Weibull distribution of Hougaard is applied to model lifetimes of components. Least-squares (LS) estimators of the model parameters and their joint asymptotic distribution are derived. The effects of the dependence parameter and the proportion of the system-data to the asymptotic relative efficiencies of the LS estimators are investigated.     

基于改进D—S证据理论的TOPSIS模型在科技奖励评价中的应用

针对科技奖励评价的特点,根据改进D—S证据合成规则,将专家的评价指标值转化为指标的综合得分并形成决策矩阵;结合TOPSIS模型求解理想解和负理想解,计算距离和贴近度,对各评价项目进行综合排名。实证结果表明：该模型能够很好地解决科技奖励评价过程中的不确定性问题,为科技奖励综合评价提供了一种新的思路。