The Annals of Mathematical Statistics

Testing Whether New is Better than Used

Myles Hollander and Frank Proschan

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Abstract

A $U$-statistic $J_n$ is proposed for testing the hypothesis $H_0$ that a new item has stochastically the same life length as a used item of any age (i.e., the life distribution $F$ is exponential), against the alternative hypothesis $H_1$ that a new item has stochastically greater life length $(\bar{F}(x)\bar{F}(y) \geqq \bar{F}(x + y)$, for all $x \geqq 0, y \geqq 0$, where $\bar{F} = 1 - F). J_n$ is unbiased; in fact, under a partial ordering of $H_1$ distributions, $J_n$ is ordered stochastically in the same way. Consistency against $H_1$ alternatives is shown, and asymptotic relative efficiencies are computed. Small sample null tail probabilities are derived, and critical values are tabulated to permit application of the test.

Article information

Source
Ann. Math. Statist., Volume 43, Number 4 (1972), 1136-1146.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692466

Digital Object Identifier
doi:10.1214/aoms/1177692466

Mathematical Reviews number (MathSciNet)
MR348909

Zentralblatt MATH identifier
0241.62055

JSTOR
links.jstor.org

Citation

Hollander, Myles; Proschan, Frank. Testing Whether New is Better than Used. Ann. Math. Statist. 43 (1972), no. 4, 1136--1146. doi:10.1214/aoms/1177692466. https://projecteuclid.org/euclid.aoms/1177692466


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