No abstract

Two-dimensional renewal functions, which are naturally extensions of one-dimensional renewal functions, have wide applicability in areas where two random variables are needed to characterize the underlying process. These functions satisfy the renewal equation, which is not amenable for analytical solutions. This paper proposes a simple approximation for the computation of the two-dimensional renewal function based only on the first two moments and the correlation coefficient of the variables. The approximation yields exact values of renewal function for bivariate exponential distribution function. Illustrations are presented to compare our approximation with that of Iskandar (1991) who provided a computational procedure which requires the use of the bivariate distribution function of the two variables. A two-dimensional warranty model is used to illustrate the approximation.

Failure rate curves of many deteriorating systems are typically bathtub shaped. Bathtub failure curves based on failure rate functions show three distinct phases namely, infant mortality period, useful period, and wear out period. Existing reliability models have been developed purely from the consumer or manufacturer's perspective thereby delinking the third phase from the first two phases. The objective of the present work is to discuss several optimality issues based on the total average cost of the system over its entire useful life that encompasses the cost incurred on the system by the consumer as well as the manufacturer.Reference to this paper should be made as follows: Hadji, E.M. and Rangan, A. (2012) 'Optimal burn-in, warranty, and maintenance decisions in system design', Int.