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.

中文翻译：

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间断二元更新过程及其应用

摘要

研究了二元更新过程的特殊情况。假设当第二分量具有正值时考虑该过程。给出了计算相应时间密度的算法。此外，还考虑了预防性更新的情况。当第二分量的值为正但小于固定水平时，就会发生这种更新。研究了以下特征：此类更新的数量分布、故障时间的密度等。数值示例说明了给定的演示。