Nonparametrie recursive estimator for mean residual life and vitality function under dependence conditions

In this paper, we develop a nonparametrie recursive estimator for the vitality and mena residual life function, based on kernel density estimators under mixing dependence conditions. The consistency and asymptotic normality of the estimator are established, under suitable regularity conditions. It is also shown that the Integrated Mean Squared Error converges to zero. The paper is concluyed with some simulation results.     

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto II and beta distributions. Further, we generalize the identities for the Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in the context of lengthbiased models are also explored.     

Prediction of the residual failure processes based on the process history

In the reliability area, the concept of the residual lifetime of a non repairable system is very important and its property has been intensively studied. In this article, we define the “residual failure process” for a repairable system and study its stochastic properties thoroughly. The detailed discussions are given when the corresponding failure process is a renewal process. An illustrative example is also discussed.     

L-moments of residual life

The mean, variance and coefficient of variation of residual life which are based on the usual moments of the residual life distribution are extensively used in reliability analysis. It has been established in various theoretical and empirical studies that the L-moments have some advantages over the usual moments in many situations. Accordingly in the present paper we study the properties of L-moments of residual life in the context of modeling lifetime data, characterizing life distributions and other applications. The role of certain quantile functions and quantile-based concepts in reliability analysis are also investigated.     

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.     

On the mean residual life of records

Suppose that a technical system is subject to shocks, e.g. peaks of voltages from a sequence of identically independent voltages having a lower limit value v>0$v>0$. We propose a new definition for the mean residual life of the records of the sequence and study its various properties.     

Some characterizations of multivariate distributions using products of the hazard gradient and mean residual life components

We give a general procedure to characterize multivariate distributions by using products of the hazard gradient and mean residual life components. This procedure is applied to characterize multivariate distributions as Gumbel exponential, Lomax, Burr, Pareto and generalized Pareto multivariate distributions. Our results extend the results of several authors and can be used to study how to extend univariate models to the multivariate set-up.     

Characterizations through reliability measures from weighted distributions

In this paper we obtain general characterizations of probability distributions from relationships between failure rate and mean residual life from the origin distribution and associated weighted distribution. Our characterization properties extend particular results given by Gupta and Keating (1986), Jain et al. (1989) and Asadi (1998). Using the theoretical results we obtain characterizations of some usual distributions. Received: December 7, 1998; revised version: May 10, 2000     

Some results on residual life and inactivity time at random time

In this article, we enhance the study of residual life at random time (RLRT) and inactivity time at random time (ITRT). To this aim, first we provide some stochastic orderings results among ITRT in two-sample problems when they failed at two different random times. Then, we develop some sufficient conditions which lead to the stochastic comparisons of RLRT and ITRT based on variance residual life order. The results are expected to be useful in reliability theory, forensic science, queue theory, and actuarial science.     

Classical estimation of hazard rate and mean residual life functions of Pareto distribution

Abstract

In this paper we find the maximum likelihood estimates (MLEs) of hazard rate and mean residual life functions (MRLF) of Pareto distribution, their asymptotic non degenerate distribution, exact distribution and moments. We also discuss the uniformly minimum variance unbiased estimate (UMVUE) of hazard rate function and MRLF. Finally, two numerical examples with simulated data and real data set, are presented to illustrate the proposed estimates.