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June, 1992 Nonparametric Methods for Imperfect Repair Models
Myles Hollander, Brett Presnell, Jayaram Sethuraman
Ann. Statist. 20(2): 879-896 (June, 1992). DOI: 10.1214/aos/1176348661

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.

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Myles Hollander. Brett Presnell. Jayaram Sethuraman. "Nonparametric Methods for Imperfect Repair Models." Ann. Statist. 20 (2) 879 - 896, June, 1992. https://doi.org/10.1214/aos/1176348661

Information

Published: June, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0756.62035
MathSciNet: MR1165597
Digital Object Identifier: 10.1214/aos/1176348661

Subjects:
Primary: 62N05
Secondary: 62E20 , 62G05 , 62G10 , 62G15 , 90B25

Keywords: Imperfect repair , life distribution , product integral

Rights: Copyright © 1992 Institute of Mathematical Statistics

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Vol.20 • No. 2 • June, 1992
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