Testing the Minimal Repair Assumption in an Imperfect Repair Model
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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We propose two nonparametric tests of the assumption that imperfectly repaired systems are minimally repaired in the models of Brown and Proschan 1983 and Block, Borges, and Savits BBS 1985. The large sample theory for these tests is derived from the asymptotic joint distribution of the survival function estimator of Whitaker and Samaniego 1989 and the ordinary empirical survival function based on the initial failure times of new, or perfectly repaired systems. Simulation results are also provided for the null hypothesis case, and under the alternatives proposed by Kijima 1989. Models assuming minimal repair specify that upon repair, a failed system is returned to the working state, while the effective age of the system is held constant that is, the distribution of the time until the next failure of the repaired system is the same as for a system of the same age which has not yet failed. These models are common in the literature of operations research and reliability, and probabilistic results and the recently proposed inferential procedures of Whitaker and Samaniego 1989 and Hollander, Presnell, and Sethuraman 1989 depend on the minimal repair assumption. Though tests have been proposed for goodness of fit of the model when a particular form of the distribution is assumed, we know of no previous proposal of a nonparametric method to test this assumption.
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