Failure-Correlated Opportunity-based Age Replacement Models

In this paper, we extend the existing opportunity-based age replacement policies by taking account of dependency between the failure time and the arrival time of a replacement opportunity for one-unit system. Based on the bivariate probability distribution function of the failure time and the arrival time of the opportunity, we focus on two opportunity-based age replacement problems and characterize the cost-optimal age replacement policies which minimize the relevant expected costs, with the hazard gradient, which is a vector-valued bivariate hazard rate. Through numerical examples with the Farlie–Gumbel–Morgenstern bivariate copula and the Gaussian bivariate copula having the general marginal distributions, we investigate the dependence of correlation between the failure time and the opportunistic replacement time on the age replacement policies.

RELIABILITY STUDIES OF BIVARIATE BIRNBAUM–SAUNDERS DISTRIBUTION

In this paper, we study the bivariate Birnbaum–Saunders (BVBS) distribution from a reliability point of view. The monotonicity of the hazard rates of the univariate as well as the conditional distributions is discussed. Clayton's association measure is obtained in terms of the hazard gradient and its value in the case of the BVBS distribution is derived. The probability distributions, in the case of series and parallel systems, are derived and the monotonicity of the failure rate, in the case of series system, is discussed.

MODELS BASED ON PARTIAL INFORMATION ABOUT SURVIVAL AND HAZARD GRADIENT

This article develops information optimal models for the joint distribution based on partial information about the survival function or hazard gradient in terms of inequalities. In the class of all distributions that satisfy the partial information, the optimal model is characterized by well-known information criteria. General results relate these information criteria with the upper orthant and the hazard gradient orderings. Applications include information characterizations of the bivariate Farlie–Gumbel–Morgenstern, bivariate Gumbel, and bivariate generalized Gumbel, for which no other information characterization are available. The generalized bivariate Gumbel model is obtained from partial information about the survival function and hazard gradient in terms of marginal hazard rates. Other examples include dynamic information characterizations of the bivariate Lomax and generalized bivariate Gumbel models having marginals that are transformations of exponential such as Pareto, Weibull, and extreme value. Mixtures of bivariate Gumbel and generalized Gumbel are obtained from partial information given in terms of mixtures of the marginal hazard rates.