Open Access
August, 1972 Testing Whether New is Better than Used
Myles Hollander, Frank Proschan
Ann. Math. Statist. 43(4): 1136-1146 (August, 1972). DOI: 10.1214/aoms/1177692466


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.


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Myles Hollander. Frank Proschan. "Testing Whether New is Better than Used." Ann. Math. Statist. 43 (4) 1136 - 1146, August, 1972.


Published: August, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0241.62055
MathSciNet: MR348909
Digital Object Identifier: 10.1214/aoms/1177692466

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 4 • August, 1972
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