The Annals of Statistics

Nonparametric Methods for Imperfect Repair Models

Myles Hollander, Brett Presnell, and Jayaram Sethuraman

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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.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 879-896.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348661

Digital Object Identifier
doi:10.1214/aos/1176348661

Mathematical Reviews number (MathSciNet)
MR1165597

Zentralblatt MATH identifier
0756.62035

JSTOR
links.jstor.org

Subjects
Primary: 62N05: Reliability and life testing [See also 90B25]
Secondary: 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05] 62E20: Asymptotic distribution theory 62G05: Estimation 62G10: Hypothesis testing 62G15: Tolerance and confidence regions

Keywords
Imperfect repair life distribution product integral

Citation

Hollander, Myles; Presnell, Brett; Sethuraman, Jayaram. Nonparametric Methods for Imperfect Repair Models. Ann. Statist. 20 (1992), no. 2, 879--896. doi:10.1214/aos/1176348661. https://projecteuclid.org/euclid.aos/1176348661


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