Nonparametric Methods for Imperfect Repair Models

Abstract

In the age-dependent minimal repair model of Block, Borges and Savits (BBS), a system failing at age $t$ undergoes one of two types of repair. With probability $p(t)$, a perfect repair is performed and the system is returned to the "good-as-new" state, while with probability $1 - p(t)$, a minimal repair is performed and the system is repaired, but is only as good as a working system of age $t$. Whitaker and Samaniego propose an estimator for the system life distribution $F$ when data are collected under this model. In the present article, an appropriate probability model for the BBS process is developed and a counting process approach is used to extend the large sample theorems of Whitaker and Samaniego to the whole line. Applications of these results to confidence bands and an extension of the Wilcoxon two-sample test are examined.