G. Asha

RELIABILITY PROPERTIES OF MEAN TIME TO FAILURE IN AGE REPLACEMENT MODELS

In this article some properties of the mean time to failure in an age replacement model is presented by examining the relationship it has with hazard (reversed hazard) rate and mean (reversed mean) residual life functions. An ordering based on mean time to failure is used to examine its implications with other stochastic orders.

Probability Models with Constant Total Failure Rate

Abstract In this article, we investigate models that exhibit constant total failure rate (Sun, K., Basu, A. P. (1995). A characterization of a bivariate geometric distribution. Statistics and Probability Letters 23:307–311) and study the property in relation to the bivariate lack of memory property (BLMP).

Further results on discrete mean past lifetime

Abstract The present paper aims at studying the mean past lifetime of a discrete random variable. The notion of discrete mean past lifetime is studied in relation to the concepts of reversed hazard rate, reversed lack of memory property, and cumulative past entropy. New classes of distributions characterized by particular forms of discrete mean past life are also investigated. Implications of an increasing mean past lifetime on other reliability notions are studied and finally some bivariate generalizations are discussed.

An Extension of the Freund's Bivariate Distribution to Model Load-Sharing Systems

SYNOPTIC ABSTRACT Several authors have considered the analysis of load-sharing parallel systems. The main characteoristics of such a two-component system is that after the failure of one component, the surviving component has to shoulder extra load, and hence, it is more likely to fail earlier than would be expected under the original model. In other cases, the failure of one component may release extra resources to the other component, thus delaying the system failure. Freund introduced a bivariate extension of the exponential distribution, which is applicable to two-component load-sharing systems. It is based on the assumption that the lifetime distributions of the components are exponential random variables before and after the change. In this article, we introduce a new class of bivariate distribution using the proportional hazard model. It is observed that the bivariate model proposed by Freund is a particular case of our model. We study different properties of the proposed model. Different statistical inferences have also been developed. We have considered four different special cases: when the base distributions are exponential, Weibull, linear failure rate, and Pareto III distributions. One data analysis has been performed for illustrative purposes. Finally, we propose some generalizations.

Characterization of a Bivariate Geometric Distribution

In this paper two characterizations in terms of the properties of the residuai life distribution of a bivariate seometric model is established.

Discrete Models Characterized by Bivariate Conditional Mean Residual Life

The concept of the univariate mean residual life (mrl) function is generalized to the bivariate case in the discrete set up and its properties are studied. This bivariate mrl is utilized to characterize bivariate distributions by its functional form .