Testing the Minimal Repair Assumption in an Imperfect Repair Model
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1991
- Accession Number
- ADA244786
Entities
People
- Brett Presnell
- Jayaram Sethuraman
- Myles Hollander
Organizations
- Florida State University