On an Interrupted Bivariate Renewal Process and Its Applications

Abstract

A special case of the bivariate renewal process is investigated. It is supposed, that this process is considered while the second component has a positive value. The algorithm for a calculation of the corresponding time's density is presented. In addition, a case of preventive renewal is considered. Such renewal takes place when the value of the second component is positive but is less than a fixed level. The following characteristics are investigated: distribution of the number of such renewals, the density of the time of the failure, etc. Numerical examples illustrate the given presentation.